id	sid	tid	token	lemma	pos
ejpam-5560	1	1	european	european	PROPN
ejpam-5560	1	2	journal	journal	PROPN
ejpam-5560	1	3	of	of	ADP
ejpam-5560	1	4	pure	pure	ADJ
ejpam-5560	1	5	and	and	CCONJ
ejpam-5560	1	6	applied	applied	ADJ
ejpam-5560	1	7	mathematics	mathematic	NOUN
ejpam-5560	1	8	2025	2025	NUM
ejpam-5560	1	9	,	,	PUNCT
ejpam-5560	1	10	vol	vol	NOUN
ejpam-5560	1	11	.	.	PROPN
ejpam-5560	1	12	18	18	NUM
ejpam-5560	1	13	,	,	PUNCT
ejpam-5560	1	14	issue	issue	NOUN
ejpam-5560	1	15	1	1	NUM
ejpam-5560	1	16	,	,	PUNCT
ejpam-5560	1	17	article	article	NOUN
ejpam-5560	1	18	number	number	NOUN
ejpam-5560	1	19	5560	5560	NUM
ejpam-5560	1	20	issn	issn	PROPN
ejpam-5560	1	21	1307	1307	NUM
ejpam-5560	1	22	-	-	SYM
ejpam-5560	1	23	5543	5543	NUM
ejpam-5560	1	24	–	–	PUNCT
ejpam-5560	1	25	ejpam.com	ejpam.com	X
ejpam-5560	1	26	published	publish	VERB
ejpam-5560	1	27	by	by	ADP
ejpam-5560	1	28	new	new	PROPN
ejpam-5560	1	29	york	york	PROPN
ejpam-5560	1	30	business	business	PROPN
ejpam-5560	1	31	global	global	ADJ
ejpam-5560	1	32	approximation	approximation	NOUN
ejpam-5560	1	33	theorems	theorem	NOUN
ejpam-5560	1	34	for	for	ADP
ejpam-5560	1	35	exponentially	exponentially	ADV
ejpam-5560	1	36	bounded	bound	VERB
ejpam-5560	1	37	k	k	ADJ
ejpam-5560	1	38	-	-	ADJ
ejpam-5560	1	39	convoluted	convoluted	ADJ
ejpam-5560	1	40	c	c	NOUN
ejpam-5560	1	41	-	-	PUNCT
ejpam-5560	1	42	cosine	cosine	NOUN
ejpam-5560	1	43	functions	function	NOUN
ejpam-5560	1	44	youssef	youssef	PROPN
ejpam-5560	1	45	bajjou1,∗	bajjou1,∗	PROPN
ejpam-5560	1	46	,	,	PUNCT
ejpam-5560	1	47	abdelkhalek	abdelkhalek	PROPN
ejpam-5560	1	48	el	el	PROPN
ejpam-5560	1	49	amrani1	amrani1	PROPN
ejpam-5560	1	50	,	,	PUNCT
ejpam-5560	1	51	aziz	aziz	PROPN
ejpam-5560	1	52	blali3	blali3	PROPN
ejpam-5560	1	53	1	1	NUM
ejpam-5560	1	54	department	department	NOUN
ejpam-5560	1	55	of	of	ADP
ejpam-5560	1	56	mathematics	mathematic	NOUN
ejpam-5560	1	57	,	,	PUNCT
ejpam-5560	1	58	dhar	dhar	PROPN
ejpam-5560	1	59	el	el	PROPN
ejpam-5560	1	60	mahraz	mahraz	PROPN
ejpam-5560	1	61	faculty	faculty	NOUN
ejpam-5560	1	62	of	of	ADP
ejpam-5560	1	63	sciences	science	NOUN
ejpam-5560	1	64	,	,	PUNCT
ejpam-5560	1	65	sidi	sidi	PROPN
ejpam-5560	1	66	mohamed	mohamed	PROPN
ejpam-5560	1	67	ben	ben	PROPN
ejpam-5560	1	68	abdellah	abdellah	PROPN
ejpam-5560	1	69	university	university	PROPN
ejpam-5560	1	70	,	,	PUNCT
ejpam-5560	1	71	atlas	atlas	PROPN
ejpam-5560	1	72	fez	fez	PROPN
ejpam-5560	1	73	,	,	PUNCT
ejpam-5560	1	74	morocco	morocco	PROPN
ejpam-5560	1	75	2	2	NUM
ejpam-5560	1	76	department	department	NOUN
ejpam-5560	1	77	of	of	ADP
ejpam-5560	1	78	mathematics	mathematic	NOUN
ejpam-5560	1	79	,	,	PUNCT
ejpam-5560	1	80	higher	high	ADJ
ejpam-5560	1	81	normal	normal	ADJ
ejpam-5560	1	82	school	school	NOUN
ejpam-5560	2	1	,	,	PUNCT
ejpam-5560	2	2	sidi	sidi	PROPN
ejpam-5560	2	3	mohamed	mohamed	PROPN
ejpam-5560	2	4	ben	ben	PROPN
ejpam-5560	2	5	abdellah	abdellah	PROPN
ejpam-5560	2	6	university	university	PROPN
ejpam-5560	2	7	,	,	PUNCT
ejpam-5560	2	8	b.p	b.p	PROPN
ejpam-5560	2	9	.	.	PROPN
ejpam-5560	2	10	5206	5206	NUM
ejpam-5560	2	11	bensouda	bensouda	NOUN
ejpam-5560	2	12	-	-	PUNCT
ejpam-5560	2	13	fez	fez	NOUN
ejpam-5560	2	14	,	,	PUNCT
ejpam-5560	2	15	morocco	morocco	PROPN
ejpam-5560	2	16	abstract	abstract	NOUN
ejpam-5560	2	17	.	.	PUNCT
ejpam-5560	3	1	let	let	VERB
ejpam-5560	3	2	c	c	NOUN
ejpam-5560	3	3	:	:	PUNCT
ejpam-5560	3	4	e	e	X
ejpam-5560	3	5	→	→	PUNCT
ejpam-5560	3	6	e	e	AUX
ejpam-5560	3	7	be	be	AUX
ejpam-5560	3	8	a	a	DET
ejpam-5560	3	9	bounded	bounded	ADJ
ejpam-5560	3	10	linear	linear	ADJ
ejpam-5560	3	11	operator	operator	NOUN
ejpam-5560	3	12	on	on	ADP
ejpam-5560	3	13	a	a	DET
ejpam-5560	3	14	complex	complex	ADJ
ejpam-5560	3	15	banach	banach	NOUN
ejpam-5560	3	16	space	space	NOUN
ejpam-5560	3	17	e	e	NOUN
ejpam-5560	3	18	and	and	CCONJ
ejpam-5560	3	19	k	k	NOUN
ejpam-5560	3	20	:	:	PUNCT
ejpam-5560	4	1	[	[	X
ejpam-5560	4	2	0,+∞[→	0,+∞[→	NOUN
ejpam-5560	4	3	c	c	VERB
ejpam-5560	4	4	a	a	DET
ejpam-5560	4	5	locally	locally	ADV
ejpam-5560	4	6	integrable	integrable	ADJ
ejpam-5560	4	7	function	function	NOUN
ejpam-5560	4	8	.	.	PUNCT
ejpam-5560	5	1	the	the	DET
ejpam-5560	5	2	aim	aim	NOUN
ejpam-5560	5	3	of	of	ADP
ejpam-5560	5	4	this	this	DET
ejpam-5560	5	5	paper	paper	NOUN
ejpam-5560	5	6	,	,	PUNCT
ejpam-5560	5	7	based	base	VERB
ejpam-5560	5	8	on	on	ADP
ejpam-5560	5	9	the	the	DET
ejpam-5560	5	10	theory	theory	NOUN
ejpam-5560	5	11	of	of	ADP
ejpam-5560	5	12	kconvoluted	kconvoluted	ADJ
ejpam-5560	5	13	c	c	NOUN
ejpam-5560	5	14	-	-	PUNCT
ejpam-5560	5	15	cosine	cosine	NOUN
ejpam-5560	5	16	functions	function	NOUN
ejpam-5560	5	17	,	,	PUNCT
ejpam-5560	5	18	is	be	AUX
ejpam-5560	5	19	to	to	PART
ejpam-5560	5	20	study	study	VERB
ejpam-5560	5	21	the	the	DET
ejpam-5560	5	22	approximation	approximation	NOUN
ejpam-5560	5	23	theorem	theorem	NOUN
ejpam-5560	5	24	for	for	ADP
ejpam-5560	5	25	k	k	ADV
ejpam-5560	5	26	-	-	ADJ
ejpam-5560	5	27	convoluted	convoluted	ADJ
ejpam-5560	5	28	c	c	NOUN
ejpam-5560	5	29	-	-	PUNCT
ejpam-5560	5	30	cosine	cosine	NOUN
ejpam-5560	5	31	functions	function	NOUN
ejpam-5560	5	32	by	by	ADP
ejpam-5560	5	33	showing	show	VERB
ejpam-5560	5	34	the	the	DET
ejpam-5560	5	35	relation	relation	NOUN
ejpam-5560	5	36	between	between	ADP
ejpam-5560	5	37	the	the	DET
ejpam-5560	5	38	convergence	convergence	NOUN
ejpam-5560	5	39	of	of	ADP
ejpam-5560	5	40	the	the	DET
ejpam-5560	5	41	sequence	sequence	NOUN
ejpam-5560	5	42	of	of	ADP
ejpam-5560	5	43	c	c	NOUN
ejpam-5560	5	44	-	-	NOUN
ejpam-5560	5	45	resolvent	resolvent	NOUN
ejpam-5560	5	46	and	and	CCONJ
ejpam-5560	5	47	the	the	DET
ejpam-5560	5	48	exponentially	exponentially	ADV
ejpam-5560	5	49	bounded	bounded	ADJ
ejpam-5560	5	50	sequence	sequence	NOUN
ejpam-5560	5	51	of	of	ADP
ejpam-5560	5	52	k	k	NOUN
ejpam-5560	5	53	-	-	ADJ
ejpam-5560	5	54	convoluted	convoluted	ADJ
ejpam-5560	5	55	c	c	NOUN
ejpam-5560	5	56	-	-	PUNCT
ejpam-5560	5	57	cosine	cosine	NOUN
ejpam-5560	5	58	functions	function	NOUN
ejpam-5560	5	59	.	.	PUNCT
ejpam-5560	6	1	2020	2020	NUM
ejpam-5560	6	2	mathematics	mathematic	NOUN
ejpam-5560	6	3	subject	subject	NOUN
ejpam-5560	6	4	classifications	classification	NOUN
ejpam-5560	6	5	:	:	PUNCT
ejpam-5560	6	6	46a32	46a32	NUM
ejpam-5560	6	7	,	,	PUNCT
ejpam-5560	6	8	47d09	47d09	NUM
ejpam-5560	6	9	,	,	PUNCT
ejpam-5560	6	10	47a58	47a58	NUM
ejpam-5560	6	11	,	,	PUNCT
ejpam-5560	6	12	60j35	60j35	NUM
ejpam-5560	6	13	key	key	ADJ
ejpam-5560	6	14	words	word	NOUN
ejpam-5560	6	15	and	and	CCONJ
ejpam-5560	6	16	phrases	phrase	NOUN
ejpam-5560	6	17	:	:	PUNCT
ejpam-5560	6	18	k	k	ADJ
ejpam-5560	6	19	-	-	ADJ
ejpam-5560	6	20	convoluted	convoluted	ADJ
ejpam-5560	6	21	c	c	NOUN
ejpam-5560	6	22	-	-	PUNCT
ejpam-5560	6	23	cosine	cosine	NOUN
ejpam-5560	6	24	functions	function	NOUN
ejpam-5560	6	25	,	,	PUNCT
ejpam-5560	6	26	c	c	NOUN
ejpam-5560	6	27	-	-	PUNCT
ejpam-5560	6	28	resolvent	resolvent	ADJ
ejpam-5560	6	29	,	,	PUNCT
ejpam-5560	6	30	approximation	approximation	NOUN
ejpam-5560	6	31	1	1	NUM
ejpam-5560	6	32	.	.	PUNCT
ejpam-5560	6	33	introduction	introduction	NOUN
ejpam-5560	6	34	throughout	throughout	ADP
ejpam-5560	6	35	this	this	DET
ejpam-5560	6	36	paper	paper	NOUN
ejpam-5560	6	37	e	e	NOUN
ejpam-5560	6	38	denote	denote	VERB
ejpam-5560	6	39	a	a	DET
ejpam-5560	6	40	non	non	ADJ
ejpam-5560	6	41	-	-	ADJ
ejpam-5560	6	42	trivial	trivial	ADJ
ejpam-5560	6	43	complex	complex	ADJ
ejpam-5560	6	44	banach	banach	NOUN
ejpam-5560	6	45	space	space	NOUN
ejpam-5560	6	46	,	,	PUNCT
ejpam-5560	6	47	l(e	l(e	NOUN
ejpam-5560	6	48	)	)	PUNCT
ejpam-5560	6	49	denotes	denote	VERB
ejpam-5560	6	50	the	the	DET
ejpam-5560	6	51	banach	banach	NOUN
ejpam-5560	6	52	algebra	algebra	NOUN
ejpam-5560	6	53	of	of	ADP
ejpam-5560	6	54	bounded	bounded	ADJ
ejpam-5560	6	55	linear	linear	PROPN
ejpam-5560	6	56	operators	operator	NOUN
ejpam-5560	6	57	from	from	ADP
ejpam-5560	6	58	e	e	PROPN
ejpam-5560	6	59	into	into	ADP
ejpam-5560	6	60	e	e	NOUN
ejpam-5560	6	61	,	,	PUNCT
ejpam-5560	6	62	c	c	PROPN
ejpam-5560	6	63	is	be	AUX
ejpam-5560	6	64	an	an	DET
ejpam-5560	6	65	injective	injective	ADJ
ejpam-5560	6	66	element	element	NOUN
ejpam-5560	6	67	of	of	ADP
ejpam-5560	6	68	l(e	l(e	NOUN
ejpam-5560	6	69	)	)	PUNCT
ejpam-5560	6	70	.	.	PUNCT
ejpam-5560	7	1	for	for	ADP
ejpam-5560	7	2	a	a	DET
ejpam-5560	7	3	linear	linear	ADJ
ejpam-5560	7	4	operator	operator	NOUN
ejpam-5560	7	5	a	a	DET
ejpam-5560	7	6	acting	acting	NOUN
ejpam-5560	7	7	on	on	ADP
ejpam-5560	7	8	e	e	NOUN
ejpam-5560	7	9	,	,	PUNCT
ejpam-5560	7	10	d(a	d(a	PROPN
ejpam-5560	7	11	)	)	PUNCT
ejpam-5560	7	12	,	,	PUNCT
ejpam-5560	7	13	n(a	n(a	PROPN
ejpam-5560	7	14	)	)	PUNCT
ejpam-5560	7	15	,	,	PUNCT
ejpam-5560	7	16	r(a	r(a	PROPN
ejpam-5560	7	17	)	)	PUNCT
ejpam-5560	7	18	and	and	CCONJ
ejpam-5560	7	19	ρc(a	ρc(a	NOUN
ejpam-5560	7	20	)	)	PUNCT
ejpam-5560	7	21	,	,	PUNCT
ejpam-5560	7	22	denotes	denote	VERB
ejpam-5560	7	23	its	its	PRON
ejpam-5560	7	24	domain	domain	NOUN
ejpam-5560	7	25	(	(	PUNCT
ejpam-5560	7	26	equipped	equip	VERB
ejpam-5560	7	27	with	with	ADP
ejpam-5560	7	28	the	the	DET
ejpam-5560	7	29	graph	graph	NOUN
ejpam-5560	7	30	norm	norm	NOUN
ejpam-5560	7	31	)	)	PUNCT
ejpam-5560	7	32	,	,	PUNCT
ejpam-5560	7	33	kernel	kernel	NOUN
ejpam-5560	7	34	,	,	PUNCT
ejpam-5560	7	35	range	range	NOUN
ejpam-5560	7	36	and	and	CCONJ
ejpam-5560	7	37	the	the	DET
ejpam-5560	7	38	c	c	NOUN
ejpam-5560	7	39	-	-	PUNCT
ejpam-5560	7	40	resolvent	resolvent	ADJ
ejpam-5560	7	41	set	set	NOUN
ejpam-5560	7	42	ofa	ofa	PROPN
ejpam-5560	7	43	,	,	PUNCT
ejpam-5560	7	44	defined	define	VERB
ejpam-5560	7	45	by	by	ADP
ejpam-5560	7	46	ρc(a	ρc(a	NOUN
ejpam-5560	7	47	)	)	PUNCT
ejpam-5560	7	48	:	:	PUNCT
ejpam-5560	8	1	=	=	SYM
ejpam-5560	8	2	{	{	PUNCT
ejpam-5560	8	3	λ	λ	X
ejpam-5560	8	4	∈	∈	PROPN
ejpam-5560	8	5	c	c	NOUN
ejpam-5560	8	6	|	|	ADV
ejpam-5560	8	7	r(c	r(c	ADJ
ejpam-5560	8	8	)	)	PUNCT
ejpam-5560	8	9	⊆	⊆	NUM
ejpam-5560	8	10	r(λi−a	r(λi−a	NOUN
ejpam-5560	8	11	)	)	PUNCT
ejpam-5560	8	12	and	and	CCONJ
ejpam-5560	8	13	λi−a	λi−a	PROPN
ejpam-5560	8	14	is	be	AUX
ejpam-5560	8	15	injective	injective	ADJ
ejpam-5560	8	16	in	in	ADP
ejpam-5560	8	17	b(e	b(e	PROPN
ejpam-5560	8	18	)	)	PUNCT
ejpam-5560	8	19	}	}	PUNCT
ejpam-5560	8	20	and	and	CCONJ
ejpam-5560	8	21	if	if	SCONJ
ejpam-5560	8	22	λ	λ	X
ejpam-5560	8	23	∈	∈	PROPN
ejpam-5560	8	24	ρc(a	ρc(a	NOUN
ejpam-5560	8	25	)	)	PUNCT
ejpam-5560	8	26	then	then	ADV
ejpam-5560	8	27	we	we	PRON
ejpam-5560	8	28	denoted	denote	VERB
ejpam-5560	8	29	by	by	ADP
ejpam-5560	8	30	rc(λ	rc(λ	PROPN
ejpam-5560	8	31	,	,	PUNCT
ejpam-5560	8	32	a	a	X
ejpam-5560	8	33	)	)	PUNCT
ejpam-5560	8	34	the	the	DET
ejpam-5560	8	35	c	c	NOUN
ejpam-5560	8	36	-	-	PUNCT
ejpam-5560	8	37	resolvent	resolvent	NOUN
ejpam-5560	8	38	defined	define	VERB
ejpam-5560	8	39	by	by	ADP
ejpam-5560	8	40	rc(λ	rc(λ	PROPN
ejpam-5560	8	41	,	,	PUNCT
ejpam-5560	8	42	a	a	X
ejpam-5560	8	43	)	)	PUNCT
ejpam-5560	8	44	=	=	SYM
ejpam-5560	8	45	(	(	PUNCT
ejpam-5560	8	46	λi	λi	ADP
ejpam-5560	8	47	−	−	PROPN
ejpam-5560	8	48	a)−1c	a)−1c	NOUN
ejpam-5560	8	49	.	.	PUNCT
ejpam-5560	9	1	if	if	SCONJ
ejpam-5560	9	2	t	t	PROPN
ejpam-5560	9	3	∈	∈	PROPN
ejpam-5560	9	4	r	r	NOUN
ejpam-5560	9	5	,	,	PUNCT
ejpam-5560	9	6	⌊t⌋	⌊t⌋	PUNCT
ejpam-5560	9	7	=	=	PUNCT
ejpam-5560	9	8	sup{n	sup{n	PROPN
ejpam-5560	9	9	∈	∈	PROPN
ejpam-5560	9	10	z	z	PROPN
ejpam-5560	9	11	,	,	PUNCT
ejpam-5560	9	12	n	n	PROPN
ejpam-5560	9	13	≤	≤	PROPN
ejpam-5560	9	14	t	t	PROPN
ejpam-5560	9	15	}	}	PUNCT
ejpam-5560	9	16	denotes	denote	VERB
ejpam-5560	9	17	the	the	DET
ejpam-5560	9	18	integer	integer	NOUN
ejpam-5560	9	19	part	part	NOUN
ejpam-5560	9	20	of	of	ADP
ejpam-5560	9	21	t.	t.	PROPN
ejpam-5560	9	22	k	k	PROPN
ejpam-5560	9	23	is	be	AUX
ejpam-5560	9	24	a	a	DET
ejpam-5560	9	25	complex	complex	ADV
ejpam-5560	9	26	-	-	PUNCT
ejpam-5560	9	27	valued	value	VERB
ejpam-5560	9	28	locally	locally	ADV
ejpam-5560	9	29	integrable	integrable	ADJ
ejpam-5560	9	30	function	function	NOUN
ejpam-5560	9	31	in	in	ADP
ejpam-5560	9	32	[	[	X
ejpam-5560	9	33	0,+∞	0,+∞	NUM
ejpam-5560	9	34	[	[	PUNCT
ejpam-5560	9	35	(	(	PUNCT
ejpam-5560	9	36	ie	ie	X
ejpam-5560	9	37	k	k	PROPN
ejpam-5560	9	38	∈	∈	PROPN
ejpam-5560	9	39	l1	l1	PROPN
ejpam-5560	9	40	loc([0,+∞	loc([0,+∞	PROPN
ejpam-5560	9	41	[	[	X
ejpam-5560	9	42	)	)	PUNCT
ejpam-5560	9	43	)	)	PUNCT
ejpam-5560	9	44	,	,	PUNCT
ejpam-5560	9	45	not	not	PART
ejpam-5560	9	46	identical	identical	ADJ
ejpam-5560	9	47	to	to	ADP
ejpam-5560	9	48	zero	zero	NUM
ejpam-5560	9	49	such	such	ADJ
ejpam-5560	9	50	that	that	PRON
ejpam-5560	9	51	:	:	PUNCT
ejpam-5560	9	52	•	•	X
ejpam-5560	9	53	(	(	PUNCT
ejpam-5560	9	54	p	p	X
ejpam-5560	9	55	):	):	PUNCT
ejpam-5560	9	56	k	k	PROPN
ejpam-5560	9	57	is	be	AUX
ejpam-5560	9	58	laplace	laplace	NOUN
ejpam-5560	9	59	transformable	transformable	NOUN
ejpam-5560	9	60	,	,	PUNCT
ejpam-5560	9	61	that	that	PRON
ejpam-5560	9	62	is	be	AUX
ejpam-5560	9	63	to	to	PART
ejpam-5560	9	64	say	say	VERB
ejpam-5560	9	65	there	there	PRON
ejpam-5560	9	66	exists	exist	VERB
ejpam-5560	9	67	β	β	X
ejpam-5560	9	68	∈	∈	NOUN
ejpam-5560	9	69	r	r	NOUN
ejpam-5560	10	1	so	so	SCONJ
ejpam-5560	10	2	that	that	SCONJ
ejpam-5560	10	3	l(k)(λ	l(k)(λ	X
ejpam-5560	10	4	)	)	PUNCT
ejpam-5560	11	1	=	=	NOUN
ejpam-5560	12	1	∫	∫	X
ejpam-5560	13	1	+	+	ADJ
ejpam-5560	13	2	∞	∞	NOUN
ejpam-5560	13	3	0	0	X
ejpam-5560	13	4	e−λtk(t)dt	e−λtk(t)dt	PROPN
ejpam-5560	14	1	<	<	X
ejpam-5560	14	2	+	+	PROPN
ejpam-5560	14	3	∞	∞	PROPN
ejpam-5560	14	4	for	for	ADP
ejpam-5560	14	5	all	all	DET
ejpam-5560	14	6	λ	λ	PROPN
ejpam-5560	14	7	∈	∈	PROPN
ejpam-5560	14	8	c	c	NOUN
ejpam-5560	14	9	with	with	ADP
ejpam-5560	14	10	re(λ	re(λ	NOUN
ejpam-5560	14	11	)	)	PUNCT
ejpam-5560	14	12	>	>	X
ejpam-5560	14	13	β	β	X
ejpam-5560	14	14	.	.	PUNCT
ejpam-5560	14	15	put	put	VERB
ejpam-5560	14	16	abs(k	abs(k	PROPN
ejpam-5560	14	17	)	)	PUNCT
ejpam-5560	14	18	:	:	PUNCT
ejpam-5560	15	1	=	=	PUNCT
ejpam-5560	15	2	inf{re(λ	inf{re(λ	NOUN
ejpam-5560	15	3	)	)	PUNCT
ejpam-5560	15	4	:	:	PUNCT
ejpam-5560	15	5	l(k)(λ	l(k)(λ	X
ejpam-5560	15	6	)	)	PUNCT
ejpam-5560	15	7	<	<	X
ejpam-5560	15	8	+	+	PUNCT
ejpam-5560	15	9	∞	∞	NOUN
ejpam-5560	15	10	}	}	PUNCT
ejpam-5560	15	11	.	.	PUNCT
ejpam-5560	16	1	•	•	NOUN
ejpam-5560	16	2	(	(	PUNCT
ejpam-5560	16	3	q	q	NOUN
ejpam-5560	16	4	):	):	PUNCT
ejpam-5560	16	5	for	for	ADP
ejpam-5560	16	6	all	all	DET
ejpam-5560	16	7	λ	λ	PROPN
ejpam-5560	16	8	>	>	X
ejpam-5560	16	9	abs(k	abs(k	PROPN
ejpam-5560	16	10	)	)	PUNCT
ejpam-5560	16	11	,	,	PUNCT
ejpam-5560	16	12	l(k)(λ	l(k)(λ	NUM
ejpam-5560	16	13	)	)	PUNCT
ejpam-5560	16	14	̸=	̸=	PROPN
ejpam-5560	16	15	0	0	NUM
ejpam-5560	16	16	.	.	PUNCT
ejpam-5560	17	1	∗corresponding	∗corresponde	VERB
ejpam-5560	17	2	author	author	NOUN
ejpam-5560	17	3	.	.	PUNCT
ejpam-5560	18	1	doi	doi	NOUN
ejpam-5560	18	2	:	:	PUNCT
ejpam-5560	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5560	https://doi.org/10.29020/nybg.ejpam.v18i1.5560	PROPN
ejpam-5560	18	4	email	email	NOUN
ejpam-5560	18	5	addresses	address	NOUN
ejpam-5560	18	6	:	:	PUNCT
ejpam-5560	18	7	youssefbajjou2017@gmail.com	youssefbajjou2017@gmail.com	X
ejpam-5560	19	1	(	(	PUNCT
ejpam-5560	19	2	y.	y.	NOUN
ejpam-5560	19	3	bajjou	bajjou	PROPN
ejpam-5560	19	4	)	)	PUNCT
ejpam-5560	19	5	,	,	PUNCT
ejpam-5560	19	6	abdelkhalek.elamrani@usmba.ac.ma	abdelkhalek.elamrani@usmba.ac.ma	PUNCT
ejpam-5560	19	7	(	(	PUNCT
ejpam-5560	19	8	a.	a.	NOUN
ejpam-5560	19	9	el	el	PROPN
ejpam-5560	19	10	amrani	amrani	PROPN
ejpam-5560	19	11	)	)	PUNCT
ejpam-5560	19	12	,	,	PUNCT
ejpam-5560	19	13	aziz.blali@usmba.ac.ma	aziz.blali@usmba.ac.ma	PUNCT
ejpam-5560	19	14	(	(	PUNCT
ejpam-5560	19	15	a.	a.	NOUN
ejpam-5560	19	16	blali	blali	PROPN
ejpam-5560	19	17	)	)	PUNCT
ejpam-5560	19	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5560	19	19	1	1	NUM
ejpam-5560	20	1	copyright	copyright	NOUN
ejpam-5560	20	2	:	:	PUNCT
ejpam-5560	20	3	©	©	PROPN
ejpam-5560	20	4	2025	2025	NUM
ejpam-5560	20	5	the	the	DET
ejpam-5560	20	6	author(s	author(s	NOUN
ejpam-5560	20	7	)	)	PUNCT
ejpam-5560	20	8	.	.	PUNCT
ejpam-5560	21	1	(	(	PUNCT
ejpam-5560	21	2	cc	cc	NOUN
ejpam-5560	21	3	by	by	ADP
ejpam-5560	21	4	-	-	PUNCT
ejpam-5560	21	5	nc	nc	PROPN
ejpam-5560	21	6	4.0	4.0	NUM
ejpam-5560	21	7	)	)	PUNCT
ejpam-5560	21	8	y.	y.	NOUN
ejpam-5560	21	9	bajjou	bajjou	PROPN
ejpam-5560	21	10	,	,	PUNCT
ejpam-5560	21	11	a.	a.	PROPN
ejpam-5560	21	12	el	el	PROPN
ejpam-5560	21	13	amrani	amrani	PROPN
ejpam-5560	21	14	,	,	PUNCT
ejpam-5560	21	15	a.	a.	PROPN
ejpam-5560	21	16	blali	blali	PROPN
ejpam-5560	21	17	/	/	SYM
ejpam-5560	21	18	eur	eur	PROPN
ejpam-5560	21	19	.	.	PUNCT
ejpam-5560	22	1	j.	j.	PROPN
ejpam-5560	22	2	pure	pure	PROPN
ejpam-5560	22	3	appl	appl	PROPN
ejpam-5560	22	4	.	.	PROPN
ejpam-5560	22	5	math	math	PROPN
ejpam-5560	22	6	,	,	PUNCT
ejpam-5560	22	7	18	18	NUM
ejpam-5560	22	8	(	(	PUNCT
ejpam-5560	22	9	1	1	NUM
ejpam-5560	22	10	)	)	PUNCT
ejpam-5560	22	11	(	(	PUNCT
ejpam-5560	22	12	2025	2025	NUM
ejpam-5560	22	13	)	)	PUNCT
ejpam-5560	22	14	,	,	PUNCT
ejpam-5560	22	15	5560	5560	NUM
ejpam-5560	22	16	2	2	NUM
ejpam-5560	22	17	of	of	ADP
ejpam-5560	22	18	15	15	NUM
ejpam-5560	22	19	•	•	NOUN
ejpam-5560	22	20	(	(	PUNCT
ejpam-5560	22	21	r	r	NOUN
ejpam-5560	22	22	):	):	PUNCT
ejpam-5560	22	23	0	0	NUM
ejpam-5560	22	24	∈	∈	PROPN
ejpam-5560	22	25	supp(k	supp(k	PROPN
ejpam-5560	22	26	)	)	PUNCT
ejpam-5560	22	27	(	(	PUNCT
ejpam-5560	22	28	according	accord	VERB
ejpam-5560	22	29	to	to	ADP
ejpam-5560	22	30	titchmarsh	titchmarsh	ADJ
ejpam-5560	22	31	’s	’s	PART
ejpam-5560	22	32	theorem	theorem	NOUN
ejpam-5560	22	33	[	[	X
ejpam-5560	22	34	[	[	X
ejpam-5560	22	35	2	2	NUM
ejpam-5560	22	36	]	]	X
ejpam-5560	22	37	]	]	PUNCT
ejpam-5560	22	38	,	,	PUNCT
ejpam-5560	22	39	for	for	ADP
ejpam-5560	22	40	every	every	DET
ejpam-5560	22	41	φ	φ	PROPN
ejpam-5560	22	42	∈	∈	PROPN
ejpam-5560	22	43	c([0,+∞	c([0,+∞	PROPN
ejpam-5560	23	1	[	[	X
ejpam-5560	23	2	,	,	PUNCT
ejpam-5560	23	3	the	the	DET
ejpam-5560	23	4	assumption	assumption	NOUN
ejpam-5560	23	5	for	for	ADP
ejpam-5560	23	6	all	all	DET
ejpam-5560	23	7	t	t	NOUN
ejpam-5560	23	8	∈	∈	PROPN
ejpam-5560	24	1	[	[	X
ejpam-5560	24	2	0,+∞	0,+∞	NUM
ejpam-5560	25	1	[	[	X
ejpam-5560	25	2	,	,	PUNCT
ejpam-5560	25	3	∫	∫	PROPN
ejpam-5560	25	4	t	t	PROPN
ejpam-5560	25	5	0	0	NUM
ejpam-5560	25	6	k(t−	k(t−	PROPN
ejpam-5560	25	7	s)φ(s)ds	s)φ(s)ds	NOUN
ejpam-5560	25	8	=	=	SYM
ejpam-5560	25	9	0	0	NUM
ejpam-5560	25	10	implies	imply	VERB
ejpam-5560	25	11	φ	φ	PROPN
ejpam-5560	25	12	≡	≡	PROPN
ejpam-5560	25	13	0	0	NUM
ejpam-5560	25	14	)	)	PUNCT
ejpam-5560	25	15	.	.	PUNCT
ejpam-5560	26	1	for	for	ADP
ejpam-5560	26	2	example	example	NOUN
ejpam-5560	26	3	the	the	DET
ejpam-5560	26	4	following	follow	VERB
ejpam-5560	26	5	function	function	NOUN
ejpam-5560	26	6	is	be	AUX
ejpam-5560	26	7	a	a	DET
ejpam-5560	26	8	kernel	kernel	NOUN
ejpam-5560	26	9	:	:	PUNCT
ejpam-5560	26	10	k(t	k(t	X
ejpam-5560	26	11	)	)	PUNCT
ejpam-5560	26	12	:	:	PUNCT
ejpam-5560	27	1	=	=	SYM
ejpam-5560	27	2	1	1	NUM
ejpam-5560	27	3	2	2	NUM
ejpam-5560	27	4	√	√	NUM
ejpam-5560	27	5	2πt3	2πt3	NUM
ejpam-5560	27	6	e	e	NOUN
ejpam-5560	27	7	−1	−1	NOUN
ejpam-5560	27	8	4	4	NUM
ejpam-5560	27	9	t	t	NOUN
ejpam-5560	27	10	if	if	SCONJ
ejpam-5560	27	11	t	t	PROPN
ejpam-5560	27	12	>	>	X
ejpam-5560	27	13	0	0	PROPN
ejpam-5560	27	14	and	and	CCONJ
ejpam-5560	27	15	k(0	k(0	PROPN
ejpam-5560	27	16	)	)	PUNCT
ejpam-5560	27	17	=	=	SYM
ejpam-5560	27	18	0	0	NUM
ejpam-5560	27	19	see	see	VERB
ejpam-5560	27	20	[	[	X
ejpam-5560	27	21	1	1	NUM
ejpam-5560	27	22	]	]	PUNCT
ejpam-5560	27	23	.	.	PUNCT
ejpam-5560	28	1	we	we	PRON
ejpam-5560	28	2	can	can	AUX
ejpam-5560	28	3	define	define	VERB
ejpam-5560	28	4	on	on	ADP
ejpam-5560	28	5	[	[	X
ejpam-5560	28	6	0,+∞	0,+∞	PROPN
ejpam-5560	28	7	[	[	X
ejpam-5560	28	8	,	,	PUNCT
ejpam-5560	28	9	the	the	DET
ejpam-5560	28	10	absolutely	absolutely	ADV
ejpam-5560	28	11	continuous	continuous	ADJ
ejpam-5560	28	12	function	function	NOUN
ejpam-5560	28	13	by	by	ADP
ejpam-5560	28	14	for	for	ADP
ejpam-5560	28	15	all	all	DET
ejpam-5560	28	16	t	t	PROPN
ejpam-5560	28	17	≥	≥	NOUN
ejpam-5560	28	18	0	0	NUM
ejpam-5560	28	19	,	,	PUNCT
ejpam-5560	28	20	θ(t	θ(t	PROPN
ejpam-5560	28	21	)	)	PUNCT
ejpam-5560	28	22	:	:	PUNCT
ejpam-5560	29	1	=	=	SYM
ejpam-5560	29	2	∫	∫	PROPN
ejpam-5560	29	3	t	t	PROPN
ejpam-5560	29	4	0	0	NUM
ejpam-5560	29	5	k(s)ds	k(s)ds	PROPN
ejpam-5560	29	6	,	,	PUNCT
ejpam-5560	29	7	then	then	ADV
ejpam-5560	29	8	for	for	ADP
ejpam-5560	29	9	all	all	DET
ejpam-5560	29	10	t	t	PROPN
ejpam-5560	29	11	≥	≥	NOUN
ejpam-5560	29	12	0	0	NUM
ejpam-5560	29	13	,	,	PUNCT
ejpam-5560	29	14	θ′(t	θ′(t	NOUN
ejpam-5560	29	15	)	)	PUNCT
ejpam-5560	29	16	=	=	PUNCT
ejpam-5560	29	17	k(t	k(t	X
ejpam-5560	29	18	)	)	PUNCT
ejpam-5560	30	1	a.e	a.e	PROPN
ejpam-5560	30	2	t	t	NOUN
ejpam-5560	30	3	∈	∈	PROPN
ejpam-5560	31	1	[	[	X
ejpam-5560	31	2	0,+∞	0,+∞	NUM
ejpam-5560	32	1	[	[	X
ejpam-5560	32	2	.	.	PUNCT
ejpam-5560	33	1	we	we	PRON
ejpam-5560	33	2	let	let	VERB
ejpam-5560	33	3	l∞(e	l∞(e	NOUN
ejpam-5560	33	4	)	)	PUNCT
ejpam-5560	34	1	=	=	PRON
ejpam-5560	34	2	{	{	PUNCT
ejpam-5560	34	3	(	(	PUNCT
ejpam-5560	34	4	xk)k∈n	xk)k∈n	PROPN
ejpam-5560	34	5	:	:	PUNCT
ejpam-5560	34	6	xk	xk	PROPN
ejpam-5560	34	7	∈	∈	PROPN
ejpam-5560	34	8	e	e	PROPN
ejpam-5560	34	9	and	and	CCONJ
ejpam-5560	34	10	sup	sup	NOUN
ejpam-5560	34	11	k∈n	k∈n	PROPN
ejpam-5560	34	12	|	|	ADV
ejpam-5560	34	13	xk	xk	PROPN
ejpam-5560	35	1	|	|	ADV
ejpam-5560	35	2	<	<	X
ejpam-5560	35	3	+	+	NOUN
ejpam-5560	35	4	∞	∞	NOUN
ejpam-5560	35	5	}	}	PUNCT
ejpam-5560	35	6	the	the	DET
ejpam-5560	35	7	banach	banach	NOUN
ejpam-5560	35	8	space	space	NOUN
ejpam-5560	35	9	equipped	equip	VERB
ejpam-5560	35	10	with	with	ADP
ejpam-5560	35	11	the	the	DET
ejpam-5560	35	12	norm	norm	NOUN
ejpam-5560	35	13	∥	∥	X
ejpam-5560	35	14	(	(	PUNCT
ejpam-5560	35	15	xk)k∈n	xk)k∈n	PROPN
ejpam-5560	35	16	∥=	∥=	NOUN
ejpam-5560	35	17	sup	sup	NOUN
ejpam-5560	35	18	k∈n	k∈n	PROPN
ejpam-5560	36	1	|	|	ADV
ejpam-5560	36	2	xk	xk	PROPN
ejpam-5560	37	1	|	|	ADV
ejpam-5560	37	2	for	for	ADP
ejpam-5560	37	3	all	all	DET
ejpam-5560	37	4	sequence	sequence	NOUN
ejpam-5560	37	5	x	x	PUNCT
ejpam-5560	37	6	=	=	SYM
ejpam-5560	37	7	(	(	PUNCT
ejpam-5560	37	8	xk)k∈n	xk)k∈n	PROPN
ejpam-5560	37	9	∈	∈	PROPN
ejpam-5560	37	10	l∞(e	l∞(e	NOUN
ejpam-5560	37	11	)	)	PUNCT
ejpam-5560	37	12	and	and	CCONJ
ejpam-5560	37	13	c(e	c(e	NOUN
ejpam-5560	37	14	)	)	PUNCT
ejpam-5560	37	15	,	,	PUNCT
ejpam-5560	37	16	the	the	DET
ejpam-5560	37	17	closed	closed	ADJ
ejpam-5560	37	18	subspace	subspace	NOUN
ejpam-5560	37	19	of	of	ADP
ejpam-5560	37	20	l∞(e	l∞(e	NOUN
ejpam-5560	37	21	)	)	PUNCT
ejpam-5560	37	22	,	,	PUNCT
ejpam-5560	37	23	defined	define	VERB
ejpam-5560	37	24	by	by	ADP
ejpam-5560	37	25	c(e	c(e	NOUN
ejpam-5560	37	26	)	)	PUNCT
ejpam-5560	37	27	=	=	PRON
ejpam-5560	37	28	{	{	PUNCT
ejpam-5560	37	29	(	(	PUNCT
ejpam-5560	37	30	xk)k∈n	xk)k∈n	PROPN
ejpam-5560	37	31	:	:	PUNCT
ejpam-5560	37	32	xk	xk	PROPN
ejpam-5560	37	33	∈	∈	PROPN
ejpam-5560	37	34	e	e	PROPN
ejpam-5560	37	35	and	and	CCONJ
ejpam-5560	37	36	lim	lim	PROPN
ejpam-5560	37	37	k→∞	k→∞	PROPN
ejpam-5560	37	38	xk	xk	PROPN
ejpam-5560	37	39	exists	exist	VERB
ejpam-5560	37	40	}	}	PUNCT
ejpam-5560	37	41	.	.	PUNCT
ejpam-5560	38	1	see	see	VERB
ejpam-5560	39	1	[	[	X
ejpam-5560	39	2	1	1	X
ejpam-5560	39	3	]	]	PUNCT
ejpam-5560	39	4	for	for	ADP
ejpam-5560	39	5	more	more	ADJ
ejpam-5560	39	6	details	detail	NOUN
ejpam-5560	39	7	.	.	PUNCT
ejpam-5560	40	1	in	in	ADP
ejpam-5560	40	2	this	this	DET
ejpam-5560	40	3	work	work	NOUN
ejpam-5560	40	4	we	we	PRON
ejpam-5560	40	5	will	will	AUX
ejpam-5560	40	6	use	use	VERB
ejpam-5560	40	7	the	the	DET
ejpam-5560	40	8	theory	theory	NOUN
ejpam-5560	40	9	of	of	ADP
ejpam-5560	40	10	integration	integration	NOUN
ejpam-5560	40	11	in	in	ADP
ejpam-5560	40	12	the	the	DET
ejpam-5560	40	13	sense	sense	NOUN
ejpam-5560	40	14	of	of	ADP
ejpam-5560	40	15	bochner	bochner	NOUN
ejpam-5560	40	16	.	.	PUNCT
ejpam-5560	41	1	2	2	X
ejpam-5560	41	2	.	.	X
ejpam-5560	41	3	k	k	X
ejpam-5560	41	4	-	-	ADJ
ejpam-5560	41	5	convoluted	convoluted	ADJ
ejpam-5560	41	6	c	c	NOUN
ejpam-5560	41	7	-	-	ADJ
ejpam-5560	41	8	cosine	cosine	NOUN
ejpam-5560	41	9	function	function	NOUN
ejpam-5560	41	10	a	a	DET
ejpam-5560	41	11	strongly	strongly	ADV
ejpam-5560	41	12	continous	continous	ADJ
ejpam-5560	41	13	operator	operator	NOUN
ejpam-5560	41	14	family	family	NOUN
ejpam-5560	41	15	(	(	PUNCT
ejpam-5560	41	16	c(t))t≥0	c(t))t≥0	X
ejpam-5560	41	17	such	such	ADJ
ejpam-5560	41	18	that	that	PRON
ejpam-5560	41	19	:	:	PUNCT
ejpam-5560	41	20	•	•	NOUN
ejpam-5560	41	21	for	for	ADP
ejpam-5560	41	22	all	all	DET
ejpam-5560	41	23	t	t	PROPN
ejpam-5560	41	24	≥	≥	NOUN
ejpam-5560	41	25	0	0	NUM
ejpam-5560	41	26	c(t)a	c(t)a	NOUN
ejpam-5560	41	27	⊆	⊆	NUM
ejpam-5560	41	28	ac(t	ac(t	NUM
ejpam-5560	41	29	)	)	PUNCT
ejpam-5560	41	30	,	,	PUNCT
ejpam-5560	41	31	•	•	NOUN
ejpam-5560	41	32	for	for	ADP
ejpam-5560	41	33	all	all	DET
ejpam-5560	41	34	t	t	PROPN
ejpam-5560	41	35	≥	≥	NOUN
ejpam-5560	41	36	0	0	NUM
ejpam-5560	42	1	c(t)c	c(t)c	PROPN
ejpam-5560	42	2	⊆	⊆	NUM
ejpam-5560	42	3	cc(t	cc(t	NUM
ejpam-5560	42	4	)	)	PUNCT
ejpam-5560	42	5	,	,	PUNCT
ejpam-5560	42	6	•	•	NOUN
ejpam-5560	42	7	for	for	ADP
ejpam-5560	42	8	all	all	DET
ejpam-5560	42	9	x	x	SYM
ejpam-5560	42	10	∈	∈	PROPN
ejpam-5560	42	11	e	e	NOUN
ejpam-5560	42	12	and	and	CCONJ
ejpam-5560	42	13	t	t	PROPN
ejpam-5560	42	14	≥	≥	NOUN
ejpam-5560	42	15	0∫	0∫	NUM
ejpam-5560	42	16	t	t	NOUN
ejpam-5560	42	17	0	0	NUM
ejpam-5560	43	1	(	(	PUNCT
ejpam-5560	43	2	t−	t−	PROPN
ejpam-5560	43	3	s)c(s)xds	s)c(s)xds	PROPN
ejpam-5560	43	4	∈	∈	PROPN
ejpam-5560	43	5	d(a	d(a	PROPN
ejpam-5560	43	6	)	)	PUNCT
ejpam-5560	43	7	and	and	CCONJ
ejpam-5560	43	8	a	a	DET
ejpam-5560	43	9	∫	∫	PROPN
ejpam-5560	43	10	t	t	PROPN
ejpam-5560	43	11	0	0	NUM
ejpam-5560	43	12	c(s)xds	c(s)xds	NOUN
ejpam-5560	43	13	=	=	SYM
ejpam-5560	43	14	c(t)x−θ(t)cx	c(t)x−θ(t)cx	NOUN
ejpam-5560	43	15	,	,	PUNCT
ejpam-5560	43	16	•	•	ADP
ejpam-5560	43	17	there	there	PRON
ejpam-5560	43	18	exist	exist	VERB
ejpam-5560	43	19	m	m	PROPN
ejpam-5560	43	20	≥	≥	NOUN
ejpam-5560	43	21	1	1	NUM
ejpam-5560	43	22	,	,	PUNCT
ejpam-5560	43	23	there	there	PRON
ejpam-5560	43	24	exist	exist	VERB
ejpam-5560	43	25	ω	ω	NUM
ejpam-5560	43	26	≥	≥	NOUN
ejpam-5560	43	27	0	0	NUM
ejpam-5560	43	28	:	:	PUNCT
ejpam-5560	43	29	for	for	ADP
ejpam-5560	43	30	all	all	DET
ejpam-5560	43	31	t	t	PROPN
ejpam-5560	43	32	≥	≥	NOUN
ejpam-5560	43	33	0	0	NUM
ejpam-5560	43	34	,	,	PUNCT
ejpam-5560	43	35	∥	∥	X
ejpam-5560	43	36	c(t	c(t	PROPN
ejpam-5560	43	37	)	)	PUNCT
ejpam-5560	43	38	∥≤	∥≤	PROPN
ejpam-5560	43	39	meωt	meωt	NOUN
ejpam-5560	43	40	,	,	PUNCT
ejpam-5560	43	41	y.	y.	PROPN
ejpam-5560	43	42	bajjou	bajjou	PROPN
ejpam-5560	43	43	,	,	PUNCT
ejpam-5560	43	44	a.	a.	PROPN
ejpam-5560	43	45	el	el	PROPN
ejpam-5560	43	46	amrani	amrani	PROPN
ejpam-5560	43	47	,	,	PUNCT
ejpam-5560	43	48	a.	a.	PROPN
ejpam-5560	43	49	blali	blali	PROPN
ejpam-5560	43	50	/	/	SYM
ejpam-5560	43	51	eur	eur	PROPN
ejpam-5560	43	52	.	.	PUNCT
ejpam-5560	44	1	j.	j.	PROPN
ejpam-5560	44	2	pure	pure	PROPN
ejpam-5560	44	3	appl	appl	PROPN
ejpam-5560	44	4	.	.	PROPN
ejpam-5560	44	5	math	math	PROPN
ejpam-5560	44	6	,	,	PUNCT
ejpam-5560	44	7	18	18	NUM
ejpam-5560	44	8	(	(	PUNCT
ejpam-5560	44	9	1	1	NUM
ejpam-5560	44	10	)	)	PUNCT
ejpam-5560	44	11	(	(	PUNCT
ejpam-5560	44	12	2025	2025	NUM
ejpam-5560	44	13	)	)	PUNCT
ejpam-5560	44	14	,	,	PUNCT
ejpam-5560	44	15	5560	5560	NUM
ejpam-5560	44	16	3	3	NUM
ejpam-5560	44	17	of	of	ADP
ejpam-5560	44	18	15	15	NUM
ejpam-5560	44	19	is	be	AUX
ejpam-5560	44	20	called	call	VERB
ejpam-5560	44	21	an	an	DET
ejpam-5560	44	22	exponentially	exponentially	ADV
ejpam-5560	44	23	bounded	bound	VERB
ejpam-5560	44	24	k−convoluted	k−convoluted	PROPN
ejpam-5560	44	25	c−cosine	c−cosine	PROPN
ejpam-5560	44	26	function	function	VERB
ejpam-5560	44	27	with	with	ADP
ejpam-5560	44	28	subgenerator	subgenerator	NOUN
ejpam-5560	44	29	a.	a.	NOUN
ejpam-5560	44	30	we	we	PRON
ejpam-5560	44	31	can	can	AUX
ejpam-5560	44	32	prove	prove	VERB
ejpam-5560	44	33	that	that	SCONJ
ejpam-5560	44	34	ca	can	AUX
ejpam-5560	44	35	⊂	⊂	PROPN
ejpam-5560	44	36	ac	ac	PROPN
ejpam-5560	44	37	see	see	VERB
ejpam-5560	44	38	[	[	X
ejpam-5560	44	39	9	9	NUM
ejpam-5560	44	40	]	]	PUNCT
ejpam-5560	44	41	.	.	PUNCT
ejpam-5560	45	1	for	for	ADP
ejpam-5560	45	2	example	example	NOUN
ejpam-5560	45	3	,	,	PUNCT
ejpam-5560	45	4	if	if	SCONJ
ejpam-5560	45	5	k(t	k(t	VERB
ejpam-5560	45	6	)	)	PUNCT
ejpam-5560	45	7	=	=	SYM
ejpam-5560	45	8	tα−1	tα−1	NOUN
ejpam-5560	45	9	γ(α	γ(α	NOUN
ejpam-5560	45	10	)	)	PUNCT
ejpam-5560	45	11	for	for	ADP
ejpam-5560	45	12	some	some	DET
ejpam-5560	45	13	α	α	PRON
ejpam-5560	45	14	≥	≥	NOUN
ejpam-5560	45	15	0	0	NUM
ejpam-5560	45	16	a	a	DET
ejpam-5560	45	17	k−convoluted	k−convoluted	PROPN
ejpam-5560	45	18	c−cosine	c−cosine	PROPN
ejpam-5560	45	19	function	function	NOUN
ejpam-5560	45	20	on	on	ADP
ejpam-5560	45	21	e	e	PROPN
ejpam-5560	45	22	is	be	AUX
ejpam-5560	45	23	called	call	VERB
ejpam-5560	45	24	an	an	DET
ejpam-5560	45	25	α−times	α−time	NOUN
ejpam-5560	45	26	integrated	integrate	VERB
ejpam-5560	45	27	c−cosine	c−cosine	NOUN
ejpam-5560	45	28	function	function	VERB
ejpam-5560	45	29	on	on	ADP
ejpam-5560	45	30	e	e	PRON
ejpam-5560	45	31	see	see	VERB
ejpam-5560	45	32	[	[	X
ejpam-5560	45	33	10	10	NUM
ejpam-5560	45	34	]	]	PUNCT
ejpam-5560	45	35	and	and	CCONJ
ejpam-5560	45	36	[	[	X
ejpam-5560	45	37	13	13	NUM
ejpam-5560	45	38	]	]	PUNCT
ejpam-5560	45	39	for	for	ADP
ejpam-5560	45	40	more	more	ADJ
ejpam-5560	45	41	details	detail	NOUN
ejpam-5560	45	42	.	.	PUNCT
ejpam-5560	46	1	we	we	PRON
ejpam-5560	46	2	say	say	VERB
ejpam-5560	46	3	that	that	SCONJ
ejpam-5560	46	4	(	(	PUNCT
ejpam-5560	46	5	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	46	6	is	be	AUX
ejpam-5560	46	7	non	non	ADJ
ejpam-5560	46	8	-	-	ADJ
ejpam-5560	46	9	degenerate	degenerate	ADJ
ejpam-5560	46	10	if	if	SCONJ
ejpam-5560	46	11	additionnally	additionnally	ADV
ejpam-5560	46	12	c(t)x	c(t)x	VERB
ejpam-5560	46	13	=	=	SYM
ejpam-5560	46	14	0	0	NUM
ejpam-5560	46	15	for	for	ADP
ejpam-5560	46	16	all	all	DET
ejpam-5560	46	17	t	t	PROPN
ejpam-5560	46	18	≥	≥	NOUN
ejpam-5560	46	19	0	0	NUM
ejpam-5560	46	20	implies	imply	VERB
ejpam-5560	46	21	that	that	SCONJ
ejpam-5560	46	22	x	x	X
ejpam-5560	46	23	=	=	SYM
ejpam-5560	46	24	0	0	NUM
ejpam-5560	46	25	,	,	PUNCT
ejpam-5560	46	26	since	since	SCONJ
ejpam-5560	46	27	c	c	PROPN
ejpam-5560	46	28	is	be	AUX
ejpam-5560	46	29	injective	injective	ADJ
ejpam-5560	46	30	then	then	ADV
ejpam-5560	46	31	each	each	PRON
ejpam-5560	46	32	k−convoluted	k−convolute	VERB
ejpam-5560	46	33	c	c	X
ejpam-5560	46	34	-	-	PUNCT
ejpam-5560	46	35	cosine	cosine	ADJ
ejpam-5560	46	36	function	function	NOUN
ejpam-5560	46	37	is	be	AUX
ejpam-5560	46	38	no	no	DET
ejpam-5560	46	39	degenerate	degenerate	ADJ
ejpam-5560	46	40	(	(	PUNCT
ejpam-5560	46	41	see	see	VERB
ejpam-5560	46	42	[	[	X
ejpam-5560	46	43	11	11	NUM
ejpam-5560	46	44	]	]	PUNCT
ejpam-5560	46	45	,	,	PUNCT
ejpam-5560	47	1	[	[	X
ejpam-5560	47	2	3	3	NUM
ejpam-5560	47	3	]	]	PUNCT
ejpam-5560	47	4	,	,	PUNCT
ejpam-5560	47	5	[	[	X
ejpam-5560	47	6	6	6	NUM
ejpam-5560	47	7	]	]	PUNCT
ejpam-5560	47	8	,	,	PUNCT
ejpam-5560	47	9	[	[	X
ejpam-5560	47	10	12	12	NUM
ejpam-5560	47	11	]	]	PUNCT
ejpam-5560	47	12	,	,	PUNCT
ejpam-5560	47	13	[	[	X
ejpam-5560	47	14	8	8	NUM
ejpam-5560	47	15	]	]	PUNCT
ejpam-5560	47	16	,	,	PUNCT
ejpam-5560	48	1	[	[	X
ejpam-5560	48	2	7	7	X
ejpam-5560	48	3	]	]	PUNCT
ejpam-5560	48	4	and	and	CCONJ
ejpam-5560	48	5	[	[	X
ejpam-5560	48	6	4	4	NUM
ejpam-5560	48	7	]	]	PUNCT
ejpam-5560	48	8	)	)	PUNCT
ejpam-5560	48	9	.	.	PUNCT
ejpam-5560	49	1	if	if	SCONJ
ejpam-5560	49	2	(	(	PUNCT
ejpam-5560	49	3	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	49	4	is	be	AUX
ejpam-5560	49	5	k−convoluted	k−convolute	VERB
ejpam-5560	49	6	c	c	X
ejpam-5560	49	7	-	-	PUNCT
ejpam-5560	49	8	cosine	cosine	ADJ
ejpam-5560	49	9	function	function	NOUN
ejpam-5560	49	10	then	then	ADV
ejpam-5560	49	11	the	the	DET
ejpam-5560	49	12	following	follow	VERB
ejpam-5560	49	13	formulae	formulae	NOUN
ejpam-5560	49	14	holds	hold	VERB
ejpam-5560	49	15	:	:	PUNCT
ejpam-5560	49	16	2c(t)c(s)x	2c(t)c(s)x	NUM
ejpam-5560	49	17	=	=	SYM
ejpam-5560	49	18	{	{	PUNCT
ejpam-5560	49	19	∫	∫	PROPN
ejpam-5560	49	20	t+s	t+s	NUM
ejpam-5560	49	21	0	0	NUM
ejpam-5560	50	1	−	−	NUM
ejpam-5560	50	2	∫	∫	PROPN
ejpam-5560	50	3	t	t	PROPN
ejpam-5560	50	4	0	0	NUM
ejpam-5560	51	1	−	−	PROPN
ejpam-5560	51	2	∫	∫	PROPN
ejpam-5560	51	3	s	s	PART
ejpam-5560	51	4	0	0	NUM
ejpam-5560	51	5	}	}	PUNCT
ejpam-5560	51	6	k(t+	k(t+	NOUN
ejpam-5560	51	7	s−	s−	PROPN
ejpam-5560	51	8	r)c(r)xdr	r)c(r)xdr	PROPN
ejpam-5560	51	9	+	+	CCONJ
ejpam-5560	51	10	∫	∫	PROPN
ejpam-5560	51	11	t	t	PROPN
ejpam-5560	51	12	|t−s|	|t−s|	PUNCT
ejpam-5560	51	13	k(s−	k(s−	PROPN
ejpam-5560	51	14	t+	t+	PUNCT
ejpam-5560	51	15	r)c(r)cx	r)c(r)cx	PROPN
ejpam-5560	51	16	(	(	PUNCT
ejpam-5560	51	17	1	1	NUM
ejpam-5560	51	18	)	)	PUNCT
ejpam-5560	51	19	+	+	CCONJ
ejpam-5560	51	20	∫	∫	PROPN
ejpam-5560	51	21	s	s	PART
ejpam-5560	51	22	|t−s|	|t−s|	INTJ
ejpam-5560	51	23	k(t−	k(t−	NOUN
ejpam-5560	51	24	s+	s+	X
ejpam-5560	51	25	r)c(r)cxdr	r)c(r)cxdr	X
ejpam-5560	51	26	+	+	CCONJ
ejpam-5560	51	27	∫	∫	PROPN
ejpam-5560	51	28	|t−s|	|t−s|	SYM
ejpam-5560	51	29	0	0	NUM
ejpam-5560	52	1	k(|	k(|	PROPN
ejpam-5560	52	2	t−	t−	PROPN
ejpam-5560	52	3	s	s	PART
ejpam-5560	52	4	|	|	ADV
ejpam-5560	52	5	+	+	NOUN
ejpam-5560	52	6	r)c(r)cxdr	r)c(r)cxdr	NOUN
ejpam-5560	52	7	for	for	ADP
ejpam-5560	52	8	all	all	DET
ejpam-5560	52	9	t	t	PROPN
ejpam-5560	52	10	,	,	PUNCT
ejpam-5560	52	11	s	s	PART
ejpam-5560	52	12	≥	≥	NOUN
ejpam-5560	52	13	0	0	NUM
ejpam-5560	52	14	and	and	CCONJ
ejpam-5560	52	15	x	x	SYM
ejpam-5560	52	16	∈	∈	PROPN
ejpam-5560	52	17	e	e	NOUN
ejpam-5560	52	18	,	,	PUNCT
ejpam-5560	52	19	see	see	VERB
ejpam-5560	52	20	chapter	chapter	NOUN
ejpam-5560	52	21	2	2	NUM
ejpam-5560	52	22	theorem	theorem	NOUN
ejpam-5560	52	23	2.1.13	2.1.13	NUM
ejpam-5560	52	24	of	of	ADP
ejpam-5560	52	25	[	[	X
ejpam-5560	52	26	5	5	NUM
ejpam-5560	52	27	]	]	PUNCT
ejpam-5560	52	28	.	.	PUNCT
ejpam-5560	53	1	for	for	ADP
ejpam-5560	53	2	a	a	DET
ejpam-5560	53	3	k−convoluted	k−convoluted	PROPN
ejpam-5560	53	4	c−cosine	c−cosine	PROPN
ejpam-5560	53	5	function	function	NOUN
ejpam-5560	53	6	(	(	PUNCT
ejpam-5560	53	7	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	53	8	,	,	PUNCT
ejpam-5560	53	9	we	we	PRON
ejpam-5560	53	10	define	define	VERB
ejpam-5560	53	11	its	its	PRON
ejpam-5560	53	12	integral	integral	ADJ
ejpam-5560	53	13	generator	generator	NOUN
ejpam-5560	53	14	â	â	PROPN
ejpam-5560	53	15	:	:	PUNCT
ejpam-5560	53	16	d(â	d(â	NOUN
ejpam-5560	53	17	)	)	PUNCT
ejpam-5560	53	18	⊂	⊂	PROPN
ejpam-5560	53	19	e	e	X
ejpam-5560	53	20	→	→	SYM
ejpam-5560	53	21	e	e	X
ejpam-5560	53	22	by	by	ADP
ejpam-5560	53	23	d(â	d(â	NOUN
ejpam-5560	53	24	)	)	PUNCT
ejpam-5560	53	25	=	=	PRON
ejpam-5560	54	1	{	{	PUNCT
ejpam-5560	54	2	x	x	PUNCT
ejpam-5560	54	3	∈	∈	PROPN
ejpam-5560	54	4	e	e	NOUN
ejpam-5560	54	5	:	:	PUNCT
ejpam-5560	54	6	(	(	PUNCT
ejpam-5560	54	7	∃yx	∃yx	ADV
ejpam-5560	54	8	∈	∈	PROPN
ejpam-5560	54	9	e	e	NOUN
ejpam-5560	54	10	)	)	PUNCT
ejpam-5560	54	11	:	:	PUNCT
ejpam-5560	54	12	c(t)x−θ(t)cx	c(t)x−θ(t)cx	X
ejpam-5560	54	13	=	=	SYM
ejpam-5560	54	14	∫	∫	PROPN
ejpam-5560	54	15	t	t	PROPN
ejpam-5560	54	16	0	0	NUM
ejpam-5560	54	17	(	(	PUNCT
ejpam-5560	54	18	t−	t−	DET
ejpam-5560	54	19	s)c(s)yxds	s)c(s)yxds	NOUN
ejpam-5560	54	20	for	for	ADP
ejpam-5560	54	21	all	all	DET
ejpam-5560	54	22	t	t	PROPN
ejpam-5560	54	23	≥	≥	NOUN
ejpam-5560	54	24	0	0	NUM
ejpam-5560	54	25	}	}	PUNCT
ejpam-5560	54	26	and	and	CCONJ
ejpam-5560	54	27	âx	âx	PROPN
ejpam-5560	54	28	=	=	SYM
ejpam-5560	54	29	yx	yx	NOUN
ejpam-5560	54	30	for	for	ADP
ejpam-5560	54	31	all	all	DET
ejpam-5560	54	32	x	x	SYM
ejpam-5560	54	33	∈	∈	PROPN
ejpam-5560	54	34	d(â	d(â	NOUN
ejpam-5560	54	35	)	)	PUNCT
ejpam-5560	54	36	.	.	PUNCT
ejpam-5560	55	1	â	â	X
ejpam-5560	55	2	is	be	AUX
ejpam-5560	55	3	a	a	DET
ejpam-5560	55	4	closed	closed	ADJ
ejpam-5560	55	5	operator	operator	NOUN
ejpam-5560	55	6	which	which	PRON
ejpam-5560	55	7	is	be	AUX
ejpam-5560	55	8	an	an	DET
ejpam-5560	55	9	extension	extension	NOUN
ejpam-5560	55	10	of	of	ADP
ejpam-5560	55	11	any	any	DET
ejpam-5560	55	12	subgenerator	subgenerator	NOUN
ejpam-5560	55	13	of	of	ADP
ejpam-5560	55	14	(	(	PUNCT
ejpam-5560	55	15	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	55	16	,	,	PUNCT
ejpam-5560	55	17	c	c	PROPN
ejpam-5560	55	18	−1ac	−1ac	PROPN
ejpam-5560	55	19	=	=	SYM
ejpam-5560	55	20	â	â	PROPN
ejpam-5560	55	21	and	and	CCONJ
ejpam-5560	55	22	(	(	PUNCT
ejpam-5560	55	23	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	55	24	is	be	AUX
ejpam-5560	55	25	uniquely	uniquely	ADV
ejpam-5560	55	26	determined	determine	VERB
ejpam-5560	55	27	by	by	ADP
ejpam-5560	55	28	one	one	NUM
ejpam-5560	55	29	of	of	ADP
ejpam-5560	55	30	its	its	PRON
ejpam-5560	55	31	subgenerators	subgenerator	NOUN
ejpam-5560	55	32	see	see	VERB
ejpam-5560	55	33	[	[	X
ejpam-5560	55	34	9	9	NUM
ejpam-5560	55	35	]	]	PUNCT
ejpam-5560	55	36	.	.	PUNCT
ejpam-5560	56	1	in	in	ADP
ejpam-5560	56	2	the	the	DET
ejpam-5560	56	3	rest	rest	NOUN
ejpam-5560	56	4	of	of	ADP
ejpam-5560	56	5	this	this	DET
ejpam-5560	56	6	part	part	NOUN
ejpam-5560	56	7	,	,	PUNCT
ejpam-5560	56	8	let	let	VERB
ejpam-5560	56	9	m	m	PRON
ejpam-5560	56	10	>	>	X
ejpam-5560	56	11	0	0	PROPN
ejpam-5560	56	12	,	,	PUNCT
ejpam-5560	56	13	ω	ω	NUM
ejpam-5560	56	14	≥	≥	NOUN
ejpam-5560	56	15	max(0	max(0	NOUN
ejpam-5560	56	16	,	,	PUNCT
ejpam-5560	56	17	abs(k	abs(k	PROPN
ejpam-5560	56	18	)	)	PUNCT
ejpam-5560	56	19	)	)	PUNCT
ejpam-5560	56	20	and	and	CCONJ
ejpam-5560	56	21	let	let	VERB
ejpam-5560	56	22	’s	’s	NOUN
ejpam-5560	56	23	put	put	VERB
ejpam-5560	56	24	ω1	ω1	PROPN
ejpam-5560	56	25	=	=	PUNCT
ejpam-5560	56	26	max(ω	max(ω	PROPN
ejpam-5560	56	27	,	,	PUNCT
ejpam-5560	56	28	abs(k	abs(k	PROPN
ejpam-5560	56	29	)	)	PUNCT
ejpam-5560	56	30	)	)	PUNCT
ejpam-5560	56	31	.	.	PUNCT
ejpam-5560	57	1	suppose	suppose	VERB
ejpam-5560	57	2	that	that	SCONJ
ejpam-5560	57	3	(	(	PUNCT
ejpam-5560	57	4	a	a	PRON
ejpam-5560	57	5	,	,	PUNCT
ejpam-5560	57	6	d(a	d(a	PROPN
ejpam-5560	57	7	)	)	PUNCT
ejpam-5560	57	8	)	)	PUNCT
ejpam-5560	57	9	is	be	AUX
ejpam-5560	57	10	closed	close	VERB
ejpam-5560	57	11	linear	linear	ADJ
ejpam-5560	57	12	operator	operator	NOUN
ejpam-5560	57	13	and	and	CCONJ
ejpam-5560	57	14	(	(	PUNCT
ejpam-5560	57	15	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	57	16	is	be	AUX
ejpam-5560	57	17	strongly	strongly	ADV
ejpam-5560	57	18	continuous	continuous	ADJ
ejpam-5560	57	19	operator	operator	NOUN
ejpam-5560	57	20	family	family	NOUN
ejpam-5560	57	21	and	and	CCONJ
ejpam-5560	57	22	for	for	ADP
ejpam-5560	57	23	all	all	DET
ejpam-5560	57	24	t	t	PROPN
ejpam-5560	57	25	≥	≥	NOUN
ejpam-5560	57	26	0	0	NUM
ejpam-5560	57	27	∥	∥	SYM
ejpam-5560	57	28	c(t	c(t	PROPN
ejpam-5560	57	29	)	)	PUNCT
ejpam-5560	57	30	∥≤	∥≤	PROPN
ejpam-5560	57	31	meωt	meωt	NOUN
ejpam-5560	57	32	then	then	ADV
ejpam-5560	57	33	we	we	PRON
ejpam-5560	57	34	have	have	VERB
ejpam-5560	57	35	the	the	DET
ejpam-5560	57	36	following	follow	VERB
ejpam-5560	57	37	useful	useful	ADJ
ejpam-5560	57	38	properties	property	NOUN
ejpam-5560	57	39	:	:	PUNCT
ejpam-5560	57	40	(	(	PUNCT
ejpam-5560	57	41	i	i	NOUN
ejpam-5560	57	42	)	)	PUNCT
ejpam-5560	57	43	•	•	INTJ
ejpam-5560	57	44	(	(	PUNCT
ejpam-5560	57	45	i	i	NOUN
ejpam-5560	57	46	)	)	PUNCT
ejpam-5560	57	47	assume	assume	VERB
ejpam-5560	57	48	thata	thata	PROPN
ejpam-5560	57	49	is	be	AUX
ejpam-5560	57	50	a	a	DET
ejpam-5560	57	51	subgenerator	subgenerator	NOUN
ejpam-5560	57	52	of	of	ADP
ejpam-5560	57	53	an	an	DET
ejpam-5560	57	54	exponentially	exponentially	ADV
ejpam-5560	57	55	bounded	bound	VERB
ejpam-5560	57	56	,	,	PUNCT
ejpam-5560	57	57	k−convoluted	k−convoluted	PROPN
ejpam-5560	57	58	c−cosine	c−cosine	PROPN
ejpam-5560	57	59	function	function	NOUN
ejpam-5560	57	60	(	(	PUNCT
ejpam-5560	57	61	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	57	62	then	then	ADV
ejpam-5560	57	63	{	{	PUNCT
ejpam-5560	57	64	λ2	λ2	NOUN
ejpam-5560	57	65	:	:	PUNCT
ejpam-5560	57	66	ℜ(λ	ℜ(λ	X
ejpam-5560	57	67	)	)	PUNCT
ejpam-5560	57	68	>	>	X
ejpam-5560	58	1	ω1	ω1	PROPN
ejpam-5560	58	2	l(k)(λ	l(k)(λ	NOUN
ejpam-5560	58	3	)	)	PUNCT
ejpam-5560	58	4	̸=	̸=	PROPN
ejpam-5560	58	5	0	0	NUM
ejpam-5560	58	6	}	}	PUNCT
ejpam-5560	58	7	⊂	⊂	PRON
ejpam-5560	58	8	ρc(a	ρc(a	NOUN
ejpam-5560	58	9	)	)	PUNCT
ejpam-5560	58	10	,	,	PUNCT
ejpam-5560	58	11	(	(	PUNCT
ejpam-5560	58	12	2	2	X
ejpam-5560	58	13	)	)	PUNCT
ejpam-5560	58	14	and	and	CCONJ
ejpam-5560	58	15	λ(λ2	λ(λ2	NOUN
ejpam-5560	58	16	−a)cx	−a)cx	NOUN
ejpam-5560	58	17	=	=	SYM
ejpam-5560	58	18	1	1	NUM
ejpam-5560	58	19	l(k)(λ	l(k)(λ	NOUN
ejpam-5560	58	20	)	)	PUNCT
ejpam-5560	58	21	∫	∫	PROPN
ejpam-5560	59	1	+	+	PROPN
ejpam-5560	59	2	∞	∞	PROPN
ejpam-5560	59	3	0	0	NUM
ejpam-5560	59	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	59	5	,	,	PUNCT
ejpam-5560	59	6	x	x	PROPN
ejpam-5560	59	7	∈	∈	PROPN
ejpam-5560	59	8	e,ℜ(λ	e,ℜ(λ	PROPN
ejpam-5560	59	9	)	)	PUNCT
ejpam-5560	59	10	>	>	X
ejpam-5560	59	11	ω1	ω1	PROPN
ejpam-5560	59	12	,	,	PUNCT
ejpam-5560	59	13	l(k)(λ	l(k)(λ	NUM
ejpam-5560	59	14	)	)	PUNCT
ejpam-5560	59	15	̸=	̸=	PROPN
ejpam-5560	59	16	0	0	NUM
ejpam-5560	59	17	.	.	PUNCT
ejpam-5560	60	1	(	(	PUNCT
ejpam-5560	60	2	3	3	X
ejpam-5560	60	3	)	)	PUNCT
ejpam-5560	60	4	for	for	ADP
ejpam-5560	60	5	more	more	ADJ
ejpam-5560	60	6	details	detail	NOUN
ejpam-5560	60	7	see	see	VERB
ejpam-5560	60	8	[	[	X
ejpam-5560	60	9	9	9	NUM
ejpam-5560	60	10	]	]	PUNCT
ejpam-5560	60	11	and	and	CCONJ
ejpam-5560	60	12	[	[	X
ejpam-5560	60	13	5	5	NUM
ejpam-5560	60	14	]	]	PUNCT
ejpam-5560	60	15	.	.	PUNCT
ejpam-5560	61	1	•	•	NUM
ejpam-5560	61	2	(	(	PUNCT
ejpam-5560	61	3	ii	ii	NOUN
ejpam-5560	61	4	)	)	PUNCT
ejpam-5560	61	5	suppose	suppose	VERB
ejpam-5560	61	6	that	that	SCONJ
ejpam-5560	61	7	the	the	DET
ejpam-5560	61	8	family	family	NOUN
ejpam-5560	61	9	(	(	PUNCT
ejpam-5560	61	10	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	61	11	satisfies	satisfy	VERB
ejpam-5560	61	12	the	the	DET
ejpam-5560	61	13	two	two	NUM
ejpam-5560	61	14	conditions	condition	NOUN
ejpam-5560	61	15	(	(	PUNCT
ejpam-5560	61	16	2)-(3	2)-(3	NUM
ejpam-5560	61	17	)	)	PUNCT
ejpam-5560	61	18	,	,	PUNCT
ejpam-5560	61	19	then	then	ADV
ejpam-5560	61	20	(	(	PUNCT
ejpam-5560	61	21	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	61	22	is	be	AUX
ejpam-5560	61	23	an	an	DET
ejpam-5560	61	24	exponentially	exponentially	ADV
ejpam-5560	61	25	bounded	bound	VERB
ejpam-5560	61	26	,	,	PUNCT
ejpam-5560	61	27	k−convoluted	k−convoluted	PROPN
ejpam-5560	61	28	c−cosine	c−cosine	PROPN
ejpam-5560	61	29	function	function	VERB
ejpam-5560	61	30	with	with	ADP
ejpam-5560	61	31	subgenerator	subgenerator	NOUN
ejpam-5560	61	32	a.	a.	NOUN
ejpam-5560	61	33	for	for	ADP
ejpam-5560	61	34	more	more	ADJ
ejpam-5560	61	35	details	detail	NOUN
ejpam-5560	61	36	see	see	VERB
ejpam-5560	61	37	[	[	X
ejpam-5560	61	38	9	9	NUM
ejpam-5560	61	39	]	]	PUNCT
ejpam-5560	61	40	and	and	CCONJ
ejpam-5560	61	41	[	[	X
ejpam-5560	61	42	5	5	NUM
ejpam-5560	61	43	]	]	PUNCT
ejpam-5560	61	44	.	.	PUNCT
ejpam-5560	62	1	•	•	NUM
ejpam-5560	62	2	(	(	PUNCT
ejpam-5560	62	3	iii	iii	NOUN
ejpam-5560	62	4	)	)	PUNCT
ejpam-5560	62	5	assume	assume	VERB
ejpam-5560	62	6	that	that	SCONJ
ejpam-5560	62	7	(	(	PUNCT
ejpam-5560	62	8	2)-(3	2)-(3	NOUN
ejpam-5560	62	9	)	)	PUNCT
ejpam-5560	62	10	hold	hold	VERB
ejpam-5560	62	11	only	only	ADV
ejpam-5560	62	12	for	for	ADP
ejpam-5560	62	13	real	real	ADJ
ejpam-5560	62	14	values	value	NOUN
ejpam-5560	62	15	of	of	ADP
ejpam-5560	62	16	λ	λ	NOUN
ejpam-5560	62	17	’s	’s	PART
ejpam-5560	62	18	,	,	PUNCT
ejpam-5560	62	19	then	then	ADV
ejpam-5560	62	20	(	(	PUNCT
ejpam-5560	62	21	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	62	22	is	be	AUX
ejpam-5560	62	23	still	still	ADV
ejpam-5560	62	24	an	an	DET
ejpam-5560	62	25	exponentially	exponentially	ADV
ejpam-5560	62	26	bounded	bound	VERB
ejpam-5560	62	27	,	,	PUNCT
ejpam-5560	62	28	k−convoluted	k−convoluted	PROPN
ejpam-5560	62	29	c−cosine	c−cosine	PROPN
ejpam-5560	62	30	function	function	VERB
ejpam-5560	62	31	with	with	ADP
ejpam-5560	62	32	subgenerator	subgenerator	NOUN
ejpam-5560	62	33	a.	a.	NOUN
ejpam-5560	62	34	for	for	ADP
ejpam-5560	62	35	more	more	ADJ
ejpam-5560	62	36	details	detail	NOUN
ejpam-5560	62	37	see	see	VERB
ejpam-5560	63	1	[	[	X
ejpam-5560	63	2	[	[	X
ejpam-5560	63	3	9	9	NUM
ejpam-5560	63	4	]	]	SYM
ejpam-5560	63	5	]	]	PUNCT
ejpam-5560	63	6	.	.	PUNCT
ejpam-5560	64	1	y.	y.	PROPN
ejpam-5560	64	2	bajjou	bajjou	PROPN
ejpam-5560	64	3	,	,	PUNCT
ejpam-5560	64	4	a.	a.	PROPN
ejpam-5560	64	5	el	el	PROPN
ejpam-5560	64	6	amrani	amrani	PROPN
ejpam-5560	64	7	,	,	PUNCT
ejpam-5560	64	8	a.	a.	PROPN
ejpam-5560	64	9	blali	blali	PROPN
ejpam-5560	64	10	/	/	SYM
ejpam-5560	64	11	eur	eur	PROPN
ejpam-5560	64	12	.	.	PUNCT
ejpam-5560	65	1	j.	j.	PROPN
ejpam-5560	65	2	pure	pure	PROPN
ejpam-5560	65	3	appl	appl	PROPN
ejpam-5560	65	4	.	.	PROPN
ejpam-5560	65	5	math	math	PROPN
ejpam-5560	65	6	,	,	PUNCT
ejpam-5560	65	7	18	18	NUM
ejpam-5560	65	8	(	(	PUNCT
ejpam-5560	65	9	1	1	NUM
ejpam-5560	65	10	)	)	PUNCT
ejpam-5560	65	11	(	(	PUNCT
ejpam-5560	65	12	2025	2025	NUM
ejpam-5560	65	13	)	)	PUNCT
ejpam-5560	65	14	,	,	PUNCT
ejpam-5560	65	15	5560	5560	NUM
ejpam-5560	65	16	4	4	NUM
ejpam-5560	65	17	of	of	ADP
ejpam-5560	65	18	15	15	NUM
ejpam-5560	65	19	(	(	PUNCT
ejpam-5560	65	20	ii	ii	NOUN
ejpam-5560	65	21	)	)	PUNCT
ejpam-5560	65	22	put	put	VERB
ejpam-5560	65	23	for	for	ADP
ejpam-5560	65	24	all	all	DET
ejpam-5560	65	25	x	x	SYM
ejpam-5560	65	26	∈	∈	PROPN
ejpam-5560	65	27	e	e	NOUN
ejpam-5560	65	28	and	and	CCONJ
ejpam-5560	65	29	λ	λ	PROPN
ejpam-5560	65	30	>	>	X
ejpam-5560	65	31	ω	ω	PROPN
ejpam-5560	65	32	,	,	PUNCT
ejpam-5560	65	33	rλ2x	rλ2x	PROPN
ejpam-5560	65	34	:	:	PUNCT
ejpam-5560	65	35	=	=	SYM
ejpam-5560	65	36	1	1	NUM
ejpam-5560	65	37	λl(k)(λ	λl(k)(λ	NOUN
ejpam-5560	65	38	)	)	PUNCT
ejpam-5560	65	39	∫	∫	PROPN
ejpam-5560	66	1	+	+	PROPN
ejpam-5560	66	2	∞	∞	PROPN
ejpam-5560	66	3	0	0	NUM
ejpam-5560	66	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	66	5	.	.	PUNCT
ejpam-5560	67	1	then	then	ADV
ejpam-5560	67	2	for	for	ADP
ejpam-5560	67	3	all	all	DET
ejpam-5560	67	4	λ	λ	PROPN
ejpam-5560	67	5	,	,	PUNCT
ejpam-5560	67	6	µ	µ	X
ejpam-5560	67	7	>	>	X
ejpam-5560	67	8	ω	ω	PROPN
ejpam-5560	67	9	and	and	CCONJ
ejpam-5560	67	10	all	all	DET
ejpam-5560	67	11	x	x	SYM
ejpam-5560	67	12	∈	∈	PROPN
ejpam-5560	67	13	e	e	NOUN
ejpam-5560	67	14	,	,	PUNCT
ejpam-5560	67	15	(	(	PUNCT
ejpam-5560	67	16	λ2	λ2	NOUN
ejpam-5560	67	17	−	−	PROPN
ejpam-5560	67	18	µ2)rλ2rµ2x	µ2)rλ2rµ2x	NOUN
ejpam-5560	67	19	=	=	PUNCT
ejpam-5560	68	1	rµ2cx	rµ2cx	ADJ
ejpam-5560	68	2	−	−	PROPN
ejpam-5560	68	3	rλ2cx	rλ2cx	NOUN
ejpam-5560	68	4	if	if	SCONJ
ejpam-5560	68	5	the	the	DET
ejpam-5560	68	6	formula	formula	NOUN
ejpam-5560	68	7	(	(	PUNCT
ejpam-5560	68	8	1	1	X
ejpam-5560	68	9	)	)	PUNCT
ejpam-5560	68	10	holds	hold	VERB
ejpam-5560	68	11	for	for	ADP
ejpam-5560	68	12	all	all	DET
ejpam-5560	68	13	x	x	SYM
ejpam-5560	68	14	∈	∈	PROPN
ejpam-5560	68	15	e	e	NOUN
ejpam-5560	68	16	and	and	CCONJ
ejpam-5560	68	17	s	s	X
ejpam-5560	68	18	≥	≥	NOUN
ejpam-5560	68	19	0	0	NUM
ejpam-5560	68	20	.	.	PUNCT
ejpam-5560	69	1	for	for	ADP
ejpam-5560	69	2	more	more	ADJ
ejpam-5560	69	3	details	detail	NOUN
ejpam-5560	69	4	see	see	VERB
ejpam-5560	69	5	[	[	X
ejpam-5560	69	6	13	13	NUM
ejpam-5560	69	7	]	]	PUNCT
ejpam-5560	69	8	.	.	PUNCT
ejpam-5560	70	1	remark	remark	PROPN
ejpam-5560	70	2	1	1	NUM
ejpam-5560	70	3	.	.	PUNCT
ejpam-5560	71	1	(	(	PUNCT
ejpam-5560	71	2	i	i	NOUN
ejpam-5560	71	3	)	)	PUNCT
ejpam-5560	71	4	if	if	SCONJ
ejpam-5560	71	5	for	for	ADP
ejpam-5560	71	6	all	all	DET
ejpam-5560	71	7	t	t	PROPN
ejpam-5560	71	8	≥	≥	NOUN
ejpam-5560	71	9	0	0	NUM
ejpam-5560	71	10	,	,	PUNCT
ejpam-5560	71	11	cc(t	cc(t	NOUN
ejpam-5560	71	12	)	)	PUNCT
ejpam-5560	72	1	=	=	VERB
ejpam-5560	73	1	c(t)c	c(t)c	X
ejpam-5560	73	2	then	then	ADV
ejpam-5560	73	3	for	for	ADP
ejpam-5560	73	4	all	all	DET
ejpam-5560	73	5	λ	λ	PROPN
ejpam-5560	73	6	>	>	X
ejpam-5560	73	7	ω	ω	PROPN
ejpam-5560	73	8	,	,	PUNCT
ejpam-5560	73	9	crλ2	crλ2	PROPN
ejpam-5560	73	10	=	=	SYM
ejpam-5560	73	11	rλ2c	rλ2c	PROPN
ejpam-5560	73	12	.	.	PUNCT
ejpam-5560	74	1	indeed	indeed	ADV
ejpam-5560	74	2	for	for	ADP
ejpam-5560	74	3	all	all	DET
ejpam-5560	74	4	x	x	SYM
ejpam-5560	74	5	∈	∈	PROPN
ejpam-5560	74	6	e	e	NOUN
ejpam-5560	74	7	and	and	CCONJ
ejpam-5560	74	8	all	all	DET
ejpam-5560	74	9	λ	λ	PROPN
ejpam-5560	74	10	>	>	X
ejpam-5560	74	11	ω	ω	NUM
ejpam-5560	74	12	we	we	PRON
ejpam-5560	74	13	have	have	VERB
ejpam-5560	74	14	:	:	PUNCT
ejpam-5560	74	15	rλ2cx	rλ2cx	NOUN
ejpam-5560	74	16	=	=	SYM
ejpam-5560	74	17	1	1	NUM
ejpam-5560	74	18	λl(k)(λ	λl(k)(λ	NOUN
ejpam-5560	74	19	)	)	PUNCT
ejpam-5560	74	20	∫	∫	PROPN
ejpam-5560	75	1	+	+	PROPN
ejpam-5560	75	2	∞	∞	PROPN
ejpam-5560	75	3	0	0	NUM
ejpam-5560	75	4	e−λtc(t)cxdt	e−λtc(t)cxdt	NOUN
ejpam-5560	75	5	=	=	NOUN
ejpam-5560	75	6	1	1	NUM
ejpam-5560	75	7	λl(k)(λ	λl(k)(λ	NOUN
ejpam-5560	75	8	)	)	PUNCT
ejpam-5560	75	9	∫	∫	PROPN
ejpam-5560	76	1	+	+	PROPN
ejpam-5560	76	2	∞	∞	PROPN
ejpam-5560	76	3	0	0	NUM
ejpam-5560	76	4	ce−λtc(t)xdt	ce−λtc(t)xdt	NOUN
ejpam-5560	76	5	=	=	SYM
ejpam-5560	76	6	c	c	PROPN
ejpam-5560	76	7	1	1	NUM
ejpam-5560	76	8	λl(k)(λ	λl(k)(λ	NOUN
ejpam-5560	76	9	)	)	PUNCT
ejpam-5560	76	10	∫	∫	PROPN
ejpam-5560	77	1	+	+	PROPN
ejpam-5560	77	2	∞	∞	PROPN
ejpam-5560	77	3	0	0	NUM
ejpam-5560	77	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	77	5	=	=	PUNCT
ejpam-5560	77	6	crλ2x	crλ2x	PROPN
ejpam-5560	77	7	.	.	PUNCT
ejpam-5560	77	8	(	(	PUNCT
ejpam-5560	77	9	ii	ii	NOUN
ejpam-5560	77	10	)	)	PUNCT
ejpam-5560	77	11	we	we	PRON
ejpam-5560	77	12	assumed	assume	VERB
ejpam-5560	77	13	that	that	SCONJ
ejpam-5560	77	14	for	for	ADP
ejpam-5560	77	15	all	all	DET
ejpam-5560	77	16	λ	λ	PROPN
ejpam-5560	77	17	,	,	PUNCT
ejpam-5560	77	18	µ	µ	X
ejpam-5560	77	19	>	>	X
ejpam-5560	77	20	ω	ω	PROPN
ejpam-5560	77	21	and	and	CCONJ
ejpam-5560	77	22	all	all	DET
ejpam-5560	77	23	x	x	SYM
ejpam-5560	77	24	∈	∈	PROPN
ejpam-5560	77	25	e	e	NOUN
ejpam-5560	77	26	,	,	PUNCT
ejpam-5560	77	27	(	(	PUNCT
ejpam-5560	77	28	λ2	λ2	NOUN
ejpam-5560	77	29	−	−	PROPN
ejpam-5560	77	30	µ2)rλ2rµ2	µ2)rλ2rµ2	PROPN
ejpam-5560	77	31	=	=	SYM
ejpam-5560	77	32	rµ2cx−rλ2cx	rµ2cx−rλ2cx	PROPN
ejpam-5560	77	33	,	,	PUNCT
ejpam-5560	77	34	then	then	ADV
ejpam-5560	77	35	for	for	ADP
ejpam-5560	77	36	all	all	DET
ejpam-5560	77	37	λ	λ	PROPN
ejpam-5560	77	38	,	,	PUNCT
ejpam-5560	77	39	µ	µ	X
ejpam-5560	77	40	>	>	X
ejpam-5560	77	41	ω	ω	NUM
ejpam-5560	77	42	rλ2rµ2	rλ2rµ2	NOUN
ejpam-5560	77	43	=	=	X
ejpam-5560	77	44	rµ2rλ2	rµ2rλ2	NOUN
ejpam-5560	77	45	.	.	PUNCT
ejpam-5560	78	1	indeed	indeed	ADV
ejpam-5560	78	2	for	for	ADP
ejpam-5560	78	3	all	all	DET
ejpam-5560	78	4	x	x	SYM
ejpam-5560	78	5	∈	∈	PROPN
ejpam-5560	78	6	e	e	NOUN
ejpam-5560	78	7	and	and	CCONJ
ejpam-5560	78	8	all	all	DET
ejpam-5560	78	9	λ	λ	PROPN
ejpam-5560	78	10	,	,	PUNCT
ejpam-5560	78	11	µ	µ	X
ejpam-5560	78	12	>	>	X
ejpam-5560	78	13	ω	ω	NUM
ejpam-5560	78	14	we	we	PRON
ejpam-5560	78	15	have	have	VERB
ejpam-5560	78	16	0	0	NUM
ejpam-5560	78	17	=	=	SYM
ejpam-5560	78	18	(	(	PUNCT
ejpam-5560	78	19	r2	r2	PROPN
ejpam-5560	78	20	λcx−r2	λcx−r2	X
ejpam-5560	78	21	µcx	µcx	NOUN
ejpam-5560	78	22	)	)	PUNCT
ejpam-5560	78	23	+	+	CCONJ
ejpam-5560	78	24	(	(	PUNCT
ejpam-5560	78	25	r2	r2	PROPN
ejpam-5560	78	26	µcx−r2	µcx−r2	SYM
ejpam-5560	78	27	λcx	λcx	PROPN
ejpam-5560	78	28	)	)	PUNCT
ejpam-5560	78	29	=	=	PUNCT
ejpam-5560	79	1	(	(	PUNCT
ejpam-5560	79	2	µ2	µ2	NOUN
ejpam-5560	79	3	−	−	PROPN
ejpam-5560	79	4	λ2)rλ2rµ2x+	λ2)rλ2rµ2x+	PROPN
ejpam-5560	79	5	(	(	PUNCT
ejpam-5560	79	6	λ2	λ2	NOUN
ejpam-5560	79	7	−	−	NOUN
ejpam-5560	79	8	µ2)rµ2rλ2	µ2)rµ2rλ2	PROPN
ejpam-5560	79	9	=	=	SYM
ejpam-5560	79	10	(	(	PUNCT
ejpam-5560	79	11	λ2	λ2	NOUN
ejpam-5560	79	12	−	−	NOUN
ejpam-5560	79	13	µ2)(rµ2rλ2x−rλ2rµ2x	µ2)(rµ2rλ2x−rλ2rµ2x	PROPN
ejpam-5560	79	14	)	)	PUNCT
ejpam-5560	79	15	(	(	PUNCT
ejpam-5560	79	16	iii	iii	X
ejpam-5560	79	17	)	)	PUNCT
ejpam-5560	79	18	we	we	PRON
ejpam-5560	79	19	assumed	assume	VERB
ejpam-5560	79	20	that	that	SCONJ
ejpam-5560	79	21	cc	cc	PROPN
ejpam-5560	79	22	(	(	PUNCT
ejpam-5560	79	23	.	.	PUNCT
ejpam-5560	79	24	)	)	PUNCT
ejpam-5560	80	1	=	=	NOUN
ejpam-5560	80	2	c(.)c	c(.)c	NOUN
ejpam-5560	80	3	and	and	CCONJ
ejpam-5560	80	4	for	for	ADP
ejpam-5560	80	5	all	all	DET
ejpam-5560	80	6	λ	λ	PROPN
ejpam-5560	80	7	,	,	PUNCT
ejpam-5560	80	8	µ	µ	X
ejpam-5560	80	9	>	>	X
ejpam-5560	80	10	ω	ω	PROPN
ejpam-5560	80	11	and	and	CCONJ
ejpam-5560	80	12	all	all	DET
ejpam-5560	80	13	x	x	SYM
ejpam-5560	80	14	∈	∈	PROPN
ejpam-5560	80	15	e	e	NOUN
ejpam-5560	80	16	,	,	PUNCT
ejpam-5560	80	17	(	(	PUNCT
ejpam-5560	80	18	λ2	λ2	NOUN
ejpam-5560	80	19	−	−	PROPN
ejpam-5560	80	20	µ2)rλ2rµ2	µ2)rλ2rµ2	PROPN
ejpam-5560	80	21	=	=	SYM
ejpam-5560	80	22	rµ2cx−rλ2cx	rµ2cx−rλ2cx	PROPN
ejpam-5560	80	23	,	,	PUNCT
ejpam-5560	80	24	then	then	ADV
ejpam-5560	80	25	•	•	NUM
ejpam-5560	80	26	n(rλ2	n(rλ2	NOUN
ejpam-5560	80	27	)	)	PUNCT
ejpam-5560	80	28	is	be	AUX
ejpam-5560	80	29	independent	independent	ADJ
ejpam-5560	80	30	of	of	ADP
ejpam-5560	80	31	λ	λ	PROPN
ejpam-5560	80	32	>	>	X
ejpam-5560	80	33	ω	ω	PROPN
ejpam-5560	80	34	.	.	PUNCT
ejpam-5560	81	1	indeed	indeed	ADV
ejpam-5560	81	2	for	for	ADP
ejpam-5560	81	3	all	all	DET
ejpam-5560	81	4	λ	λ	PROPN
ejpam-5560	81	5	>	>	X
ejpam-5560	81	6	ω	ω	PROPN
ejpam-5560	81	7	,	,	PUNCT
ejpam-5560	81	8	all	all	PRON
ejpam-5560	81	9	x	x	SYM
ejpam-5560	81	10	∈	∈	NOUN
ejpam-5560	81	11	e	e	NOUN
ejpam-5560	81	12	such	such	ADJ
ejpam-5560	81	13	that	that	SCONJ
ejpam-5560	81	14	rλ2x	rλ2x	PROPN
ejpam-5560	81	15	=	=	SYM
ejpam-5560	81	16	0	0	NUM
ejpam-5560	81	17	and	and	CCONJ
ejpam-5560	81	18	for	for	ADP
ejpam-5560	81	19	all	all	DET
ejpam-5560	81	20	µ	µ	PROPN
ejpam-5560	81	21	>	>	X
ejpam-5560	81	22	ω	ω	NUM
ejpam-5560	81	23	we	we	PRON
ejpam-5560	81	24	have	have	VERB
ejpam-5560	81	25	0	0	NUM
ejpam-5560	82	1	=	=	SYM
ejpam-5560	82	2	crλ2x	crλ2x	NOUN
ejpam-5560	83	1	=	=	PUNCT
ejpam-5560	83	2	rλ2cx	rλ2cx	NOUN
ejpam-5560	83	3	=	=	SYM
ejpam-5560	83	4	(	(	PUNCT
ejpam-5560	83	5	rλ2cx−rµ2cx	rλ2cx−rµ2cx	ADJ
ejpam-5560	83	6	)	)	PUNCT
ejpam-5560	84	1	+	+	ADJ
ejpam-5560	84	2	rµ2cx	rµ2cx	NOUN
ejpam-5560	84	3	=	=	PUNCT
ejpam-5560	84	4	(	(	PUNCT
ejpam-5560	84	5	µ2	µ2	PROPN
ejpam-5560	84	6	−	−	PROPN
ejpam-5560	84	7	λ2)rλ2rµ2x+rµ2cx	λ2)rλ2rµ2x+rµ2cx	PROPN
ejpam-5560	84	8	=	=	PUNCT
ejpam-5560	84	9	(	(	PUNCT
ejpam-5560	84	10	µ2	µ2	NOUN
ejpam-5560	84	11	−	−	PROPN
ejpam-5560	84	12	λ2)rµ2rλ2x+rµ2cx	λ2)rµ2rλ2x+rµ2cx	NOUN
ejpam-5560	84	13	=	=	PUNCT
ejpam-5560	84	14	0	0	PUNCT
ejpam-5560	85	1	+	+	ADJ
ejpam-5560	85	2	rµ2cx	rµ2cx	ADJ
ejpam-5560	85	3	=	=	NOUN
ejpam-5560	85	4	rµ2cx	rµ2cx	NOUN
ejpam-5560	85	5	=	=	SYM
ejpam-5560	85	6	crµ2x	crµ2x	PROPN
ejpam-5560	85	7	,	,	PUNCT
ejpam-5560	85	8	hence	hence	ADV
ejpam-5560	85	9	rµ2x	rµ2x	PROPN
ejpam-5560	85	10	=	=	PUNCT
ejpam-5560	85	11	0	0	PUNCT
ejpam-5560	85	12	since	since	SCONJ
ejpam-5560	85	13	c	c	PROPN
ejpam-5560	85	14	is	be	AUX
ejpam-5560	85	15	injective	injective	ADJ
ejpam-5560	85	16	.	.	PUNCT
ejpam-5560	86	1	y.	y.	PROPN
ejpam-5560	86	2	bajjou	bajjou	PROPN
ejpam-5560	86	3	,	,	PUNCT
ejpam-5560	86	4	a.	a.	PROPN
ejpam-5560	86	5	el	el	PROPN
ejpam-5560	86	6	amrani	amrani	PROPN
ejpam-5560	86	7	,	,	PUNCT
ejpam-5560	86	8	a.	a.	PROPN
ejpam-5560	86	9	blali	blali	PROPN
ejpam-5560	86	10	/	/	SYM
ejpam-5560	86	11	eur	eur	PROPN
ejpam-5560	86	12	.	.	PUNCT
ejpam-5560	87	1	j.	j.	PROPN
ejpam-5560	87	2	pure	pure	PROPN
ejpam-5560	87	3	appl	appl	PROPN
ejpam-5560	87	4	.	.	PROPN
ejpam-5560	87	5	math	math	PROPN
ejpam-5560	87	6	,	,	PUNCT
ejpam-5560	87	7	18	18	NUM
ejpam-5560	87	8	(	(	PUNCT
ejpam-5560	87	9	1	1	NUM
ejpam-5560	87	10	)	)	PUNCT
ejpam-5560	87	11	(	(	PUNCT
ejpam-5560	87	12	2025	2025	NUM
ejpam-5560	87	13	)	)	PUNCT
ejpam-5560	87	14	,	,	PUNCT
ejpam-5560	87	15	5560	5560	NUM
ejpam-5560	87	16	5	5	NUM
ejpam-5560	87	17	of	of	ADP
ejpam-5560	87	18	15	15	NUM
ejpam-5560	87	19	•	•	NOUN
ejpam-5560	87	20	if	if	SCONJ
ejpam-5560	87	21	r(rλ2	r(rλ2	NOUN
ejpam-5560	87	22	)	)	PUNCT
ejpam-5560	87	23	⊂	⊂	NOUN
ejpam-5560	87	24	r(c	r(c	ADV
ejpam-5560	87	25	)	)	PUNCT
ejpam-5560	87	26	then	then	ADV
ejpam-5560	87	27	r(rλ2	r(rλ2	NOUN
ejpam-5560	87	28	)	)	PUNCT
ejpam-5560	87	29	is	be	AUX
ejpam-5560	87	30	independent	independent	ADJ
ejpam-5560	87	31	of	of	ADP
ejpam-5560	87	32	λ	λ	PROPN
ejpam-5560	87	33	>	>	X
ejpam-5560	87	34	ω	ω	PROPN
ejpam-5560	87	35	.	.	PUNCT
ejpam-5560	88	1	indeed	indeed	ADV
ejpam-5560	88	2	for	for	ADP
ejpam-5560	88	3	all	all	DET
ejpam-5560	88	4	λ	λ	PROPN
ejpam-5560	88	5	>	>	X
ejpam-5560	88	6	ω	ω	PROPN
ejpam-5560	88	7	,	,	PUNCT
ejpam-5560	88	8	all	all	DET
ejpam-5560	88	9	y	y	PROPN
ejpam-5560	88	10	∈	∈	PROPN
ejpam-5560	88	11	r(rλ2	r(rλ2	ADV
ejpam-5560	88	12	)	)	PUNCT
ejpam-5560	88	13	such	such	ADJ
ejpam-5560	88	14	that	that	SCONJ
ejpam-5560	88	15	y	y	PROPN
ejpam-5560	88	16	=	=	SYM
ejpam-5560	88	17	rλ2x	rλ2x	PROPN
ejpam-5560	88	18	and	and	CCONJ
ejpam-5560	88	19	for	for	ADP
ejpam-5560	88	20	all	all	DET
ejpam-5560	88	21	µ	µ	PROPN
ejpam-5560	88	22	>	>	X
ejpam-5560	88	23	ω	ω	NUM
ejpam-5560	88	24	we	we	PRON
ejpam-5560	88	25	have	have	VERB
ejpam-5560	88	26	crµ2(x+	crµ2(x+	PROPN
ejpam-5560	88	27	(	(	PUNCT
ejpam-5560	88	28	µ2	µ2	PROPN
ejpam-5560	88	29	−	−	NUM
ejpam-5560	88	30	λ2)c−1y	λ2)c−1y	NOUN
ejpam-5560	88	31	)	)	PUNCT
ejpam-5560	89	1	=	=	SYM
ejpam-5560	89	2	crµ2x+	crµ2x+	NOUN
ejpam-5560	89	3	(	(	PUNCT
ejpam-5560	89	4	µ2	µ2	PROPN
ejpam-5560	89	5	−	−	PROPN
ejpam-5560	89	6	λ2)crµ2c−1y	λ2)crµ2c−1y	NOUN
ejpam-5560	89	7	=	=	PROPN
ejpam-5560	89	8	r2	r2	PROPN
ejpam-5560	89	9	µcx+	µcx+	NOUN
ejpam-5560	89	10	(	(	PUNCT
ejpam-5560	89	11	µ2	µ2	PROPN
ejpam-5560	89	12	−	−	PROPN
ejpam-5560	89	13	λ2)r2	λ2)r2	NOUN
ejpam-5560	89	14	µcc−1y	µcc−1y	ADJ
ejpam-5560	89	15	=	=	SYM
ejpam-5560	89	16	rµ2cx+	rµ2cx+	NOUN
ejpam-5560	89	17	(	(	PUNCT
ejpam-5560	89	18	µ2	µ2	NOUN
ejpam-5560	89	19	−	−	NUM
ejpam-5560	89	20	λ2)rµ2y	λ2)rµ2y	NOUN
ejpam-5560	89	21	=	=	SYM
ejpam-5560	89	22	rµ2cx+	rµ2cx+	NOUN
ejpam-5560	89	23	(	(	PUNCT
ejpam-5560	89	24	µ2	µ2	NOUN
ejpam-5560	89	25	−	−	PROPN
ejpam-5560	89	26	λ2)rµ2rλ2x	λ2)rµ2rλ2x	PROPN
ejpam-5560	89	27	=	=	PUNCT
ejpam-5560	89	28	rµ2cx+	rµ2cx+	NUM
ejpam-5560	89	29	(	(	PUNCT
ejpam-5560	89	30	rλ2cx−rµ2cx	rλ2cx−rµ2cx	ADJ
ejpam-5560	89	31	)	)	PUNCT
ejpam-5560	89	32	=	=	SYM
ejpam-5560	90	1	rλ2cx	rλ2cx	NOUN
ejpam-5560	90	2	=	=	SYM
ejpam-5560	90	3	crλ2x	crλ2x	PROPN
ejpam-5560	91	1	=	=	SYM
ejpam-5560	91	2	cy	cy	PROPN
ejpam-5560	91	3	,	,	PUNCT
ejpam-5560	91	4	hence	hence	ADV
ejpam-5560	91	5	y	y	NOUN
ejpam-5560	91	6	=	=	PUNCT
ejpam-5560	91	7	rµ2(x+	rµ2(x+	PROPN
ejpam-5560	91	8	(	(	PUNCT
ejpam-5560	91	9	µ2	µ2	PROPN
ejpam-5560	91	10	−	−	PROPN
ejpam-5560	91	11	λ2)c−1y	λ2)c−1y	NOUN
ejpam-5560	91	12	)	)	PUNCT
ejpam-5560	91	13	∈	∈	PROPN
ejpam-5560	91	14	r(rµ2	r(rµ2	PROPN
ejpam-5560	91	15	)	)	PUNCT
ejpam-5560	91	16	since	since	SCONJ
ejpam-5560	91	17	c	c	PROPN
ejpam-5560	91	18	is	be	AUX
ejpam-5560	91	19	injective	injective	ADJ
ejpam-5560	91	20	.	.	PUNCT
ejpam-5560	92	1	•	•	NOUN
ejpam-5560	92	2	if	if	SCONJ
ejpam-5560	92	3	r(rλ2	r(rλ2	NOUN
ejpam-5560	92	4	)	)	PUNCT
ejpam-5560	92	5	⊂	⊂	NOUN
ejpam-5560	92	6	r(c	r(c	ADJ
ejpam-5560	92	7	)	)	PUNCT
ejpam-5560	92	8	and	and	CCONJ
ejpam-5560	92	9	there	there	PRON
ejpam-5560	92	10	exists	exist	VERB
ejpam-5560	92	11	µ	µ	PROPN
ejpam-5560	92	12	>	>	X
ejpam-5560	92	13	ω	ω	NUM
ejpam-5560	92	14	such	such	ADJ
ejpam-5560	92	15	that	that	DET
ejpam-5560	92	16	n(rµ2	n(rµ2	NOUN
ejpam-5560	92	17	)	)	PUNCT
ejpam-5560	92	18	=	=	PRON
ejpam-5560	92	19	{	{	PUNCT
ejpam-5560	92	20	0	0	NUM
ejpam-5560	92	21	}	}	PUNCT
ejpam-5560	92	22	then	then	ADV
ejpam-5560	92	23	there	there	PRON
ejpam-5560	92	24	is	be	VERB
ejpam-5560	92	25	a	a	DET
ejpam-5560	92	26	linear	linear	ADJ
ejpam-5560	92	27	operator	operator	NOUN
ejpam-5560	92	28	(	(	PUNCT
ejpam-5560	92	29	a	a	PRON
ejpam-5560	92	30	,	,	PUNCT
ejpam-5560	92	31	d(a	d(a	PROPN
ejpam-5560	92	32	)	)	PUNCT
ejpam-5560	92	33	)	)	PUNCT
ejpam-5560	93	1	such	such	ADJ
ejpam-5560	93	2	that	that	PRON
ejpam-5560	93	3	rc(λ	rc(λ	PROPN
ejpam-5560	93	4	,	,	PUNCT
ejpam-5560	93	5	a	a	X
ejpam-5560	93	6	)	)	PUNCT
ejpam-5560	93	7	=	=	SYM
ejpam-5560	93	8	rλ2	rλ2	ADJ
ejpam-5560	93	9	.	.	PUNCT
ejpam-5560	94	1	indeed	indeed	ADV
ejpam-5560	94	2	for	for	ADP
ejpam-5560	94	3	all	all	DET
ejpam-5560	94	4	λ	λ	PROPN
ejpam-5560	94	5	,	,	PUNCT
ejpam-5560	94	6	µ	µ	X
ejpam-5560	94	7	>	>	X
ejpam-5560	94	8	ω	ω	PROPN
ejpam-5560	94	9	,	,	PUNCT
ejpam-5560	94	10	for	for	ADP
ejpam-5560	94	11	all	all	DET
ejpam-5560	94	12	y	y	PROPN
ejpam-5560	94	13	∈	∈	PROPN
ejpam-5560	94	14	r(rλ2	r(rλ2	NOUN
ejpam-5560	94	15	)	)	PUNCT
ejpam-5560	94	16	,	,	PUNCT
ejpam-5560	94	17	there	there	PRON
ejpam-5560	94	18	is	be	VERB
ejpam-5560	94	19	a	a	DET
ejpam-5560	94	20	unique	unique	ADJ
ejpam-5560	94	21	xλ2	xλ2	NOUN
ejpam-5560	94	22	,	,	PUNCT
ejpam-5560	94	23	xµ2	xµ2	PROPN
ejpam-5560	94	24	)	)	PUNCT
ejpam-5560	94	25	∈	∈	PROPN
ejpam-5560	94	26	e2	e2	PROPN
ejpam-5560	94	27	:	:	PUNCT
ejpam-5560	94	28	y	y	X
ejpam-5560	94	29	=	=	PUNCT
ejpam-5560	94	30	rλ2xλ2	rλ2xλ2	VERB
ejpam-5560	94	31	=	=	SYM
ejpam-5560	94	32	rµ2xµ2	rµ2xµ2	ADJ
ejpam-5560	94	33	.	.	PUNCT
ejpam-5560	95	1	on	on	ADP
ejpam-5560	95	2	the	the	DET
ejpam-5560	95	3	other	other	ADJ
ejpam-5560	95	4	hand	hand	NOUN
ejpam-5560	95	5	,	,	PUNCT
ejpam-5560	95	6	if	if	SCONJ
ejpam-5560	95	7	we	we	PRON
ejpam-5560	95	8	put	put	VERB
ejpam-5560	95	9	w	w	NOUN
ejpam-5560	95	10	=	=	NOUN
ejpam-5560	95	11	rλ2rµ2((µ2y	rλ2rµ2((µ2y	NUM
ejpam-5560	95	12	−	−	PROPN
ejpam-5560	95	13	cxµ2)−	cxµ2)−	PROPN
ejpam-5560	95	14	(	(	PUNCT
ejpam-5560	95	15	λ2y	λ2y	PUNCT
ejpam-5560	95	16	−	−	PROPN
ejpam-5560	95	17	cxλ2	cxλ2	NOUN
ejpam-5560	95	18	)	)	PUNCT
ejpam-5560	95	19	)	)	PUNCT
ejpam-5560	95	20	,	,	PUNCT
ejpam-5560	95	21	then	then	ADV
ejpam-5560	95	22	we	we	PRON
ejpam-5560	95	23	have	have	VERB
ejpam-5560	95	24	:	:	PUNCT
ejpam-5560	95	25	w	w	NOUN
ejpam-5560	95	26	=	=	SYM
ejpam-5560	95	27	rλ2rµ2((µ2	rλ2rµ2((µ2	ADJ
ejpam-5560	95	28	−	−	PROPN
ejpam-5560	95	29	λ2)y	λ2)y	NOUN
ejpam-5560	95	30	−	−	PROPN
ejpam-5560	96	1	c(xµ2	c(xµ2	PROPN
ejpam-5560	96	2	−	−	PROPN
ejpam-5560	96	3	xλ2	xλ2	PROPN
ejpam-5560	96	4	)	)	PUNCT
ejpam-5560	96	5	)	)	PUNCT
ejpam-5560	97	1	=	=	PUNCT
ejpam-5560	97	2	(	(	PUNCT
ejpam-5560	97	3	µ2	µ2	NOUN
ejpam-5560	97	4	−	−	PROPN
ejpam-5560	97	5	λ2)rλ2rµ2y	λ2)rλ2rµ2y	PRON
ejpam-5560	97	6	−	−	PUNCT
ejpam-5560	97	7	crλ2rµ2(xµ2	crλ2rµ2(xµ2	NUM
ejpam-5560	97	8	−	−	PROPN
ejpam-5560	97	9	xλ2	xλ2	PROPN
ejpam-5560	97	10	)	)	PUNCT
ejpam-5560	97	11	=	=	PUNCT
ejpam-5560	97	12	(	(	PUNCT
ejpam-5560	97	13	rλ2cy	rλ2cy	ADJ
ejpam-5560	97	14	−rµ2cy)−	−rµ2cy)−	PROPN
ejpam-5560	97	15	(	(	PUNCT
ejpam-5560	97	16	crλ2y	crλ2y	PROPN
ejpam-5560	97	17	−	−	PROPN
ejpam-5560	97	18	crµ2y	crµ2y	NOUN
ejpam-5560	97	19	)	)	PUNCT
ejpam-5560	97	20	=	=	SYM
ejpam-5560	97	21	(	(	PUNCT
ejpam-5560	97	22	rλ2cy	rλ2cy	ADJ
ejpam-5560	97	23	−rµ2cy)−	−rµ2cy)−	PROPN
ejpam-5560	97	24	(	(	PUNCT
ejpam-5560	97	25	rλ2cy	rλ2cy	ADJ
ejpam-5560	97	26	−rµ2cy	−rµ2cy	NOUN
ejpam-5560	97	27	)	)	PUNCT
ejpam-5560	97	28	=	=	SYM
ejpam-5560	97	29	0	0	NUM
ejpam-5560	98	1	it	it	PRON
ejpam-5560	98	2	is	be	AUX
ejpam-5560	98	3	(	(	PUNCT
ejpam-5560	98	4	µ2y−cxµ2	µ2y−cxµ2	X
ejpam-5560	98	5	)	)	PUNCT
ejpam-5560	98	6	=	=	SYM
ejpam-5560	98	7	(	(	PUNCT
ejpam-5560	98	8	λ2y−cxλ2	λ2y−cxλ2	CCONJ
ejpam-5560	98	9	)	)	PUNCT
ejpam-5560	98	10	since	since	SCONJ
ejpam-5560	98	11	rλ2rµ2	rλ2rµ2	NOUN
ejpam-5560	98	12	is	be	AUX
ejpam-5560	98	13	injective	injective	ADJ
ejpam-5560	98	14	,	,	PUNCT
ejpam-5560	98	15	so	so	SCONJ
ejpam-5560	98	16	we	we	PRON
ejpam-5560	98	17	cane	cane	VERB
ejpam-5560	98	18	defined	define	VERB
ejpam-5560	98	19	the	the	DET
ejpam-5560	98	20	operator	operator	NOUN
ejpam-5560	98	21	(	(	PUNCT
ejpam-5560	98	22	a	a	PRON
ejpam-5560	98	23	,	,	PUNCT
ejpam-5560	98	24	d(a	d(a	PROPN
ejpam-5560	98	25	)	)	PUNCT
ejpam-5560	98	26	)	)	PUNCT
ejpam-5560	98	27	by	by	ADP
ejpam-5560	98	28	d(a	d(a	PROPN
ejpam-5560	98	29	)	)	PUNCT
ejpam-5560	98	30	=	=	SYM
ejpam-5560	98	31	r(rµ2	r(rµ2	PROPN
ejpam-5560	98	32	)	)	PUNCT
ejpam-5560	98	33	and	and	CCONJ
ejpam-5560	98	34	for	for	ADP
ejpam-5560	98	35	all	all	DET
ejpam-5560	98	36	y	y	PROPN
ejpam-5560	98	37	∈	∈	PROPN
ejpam-5560	98	38	r(rλ2	r(rλ2	NOUN
ejpam-5560	98	39	)	)	PUNCT
ejpam-5560	98	40	,	,	PUNCT
ejpam-5560	98	41	ay	ay	PROPN
ejpam-5560	98	42	=	=	PUNCT
ejpam-5560	99	1	λ2y	λ2y	PUNCT
ejpam-5560	99	2	−	−	NUM
ejpam-5560	99	3	cr−1	cr−1	PROPN
ejpam-5560	99	4	λ2	λ2	PROPN
ejpam-5560	99	5	y	y	PROPN
ejpam-5560	99	6	,	,	PUNCT
ejpam-5560	99	7	since	since	SCONJ
ejpam-5560	99	8	rλ2	rλ2	PROPN
ejpam-5560	99	9	∈	∈	PROPN
ejpam-5560	99	10	b(e	b(e	PROPN
ejpam-5560	99	11	)	)	PUNCT
ejpam-5560	99	12	,	,	PUNCT
ejpam-5560	99	13	moreover	moreover	ADV
ejpam-5560	99	14	for	for	SCONJ
ejpam-5560	99	15	all	all	DET
ejpam-5560	99	16	y	y	PROPN
ejpam-5560	99	17	∈	∈	PROPN
ejpam-5560	99	18	r(rλ2	r(rλ2	ADV
ejpam-5560	99	19	)	)	PUNCT
ejpam-5560	99	20	we	we	PRON
ejpam-5560	99	21	have	have	VERB
ejpam-5560	99	22	cr−1	cr−1	PROPN
ejpam-5560	99	23	λ2	λ2	PROPN
ejpam-5560	99	24	(	(	PUNCT
ejpam-5560	99	25	y	y	NOUN
ejpam-5560	99	26	)	)	PUNCT
ejpam-5560	99	27	=	=	PRON
ejpam-5560	99	28	λ2y	λ2y	VERB
ejpam-5560	99	29	−ay	−ay	NOUN
ejpam-5560	99	30	=	=	SYM
ejpam-5560	99	31	(	(	PUNCT
ejpam-5560	100	1	λ2i	λ2i	X
ejpam-5560	100	2	−a)y	−a)y	NOUN
ejpam-5560	100	3	as	as	ADP
ejpam-5560	100	4	result	result	NOUN
ejpam-5560	100	5	rλ2	rλ2	ADV
ejpam-5560	100	6	=	=	SYM
ejpam-5560	100	7	(	(	PUNCT
ejpam-5560	100	8	λ2i	λ2i	X
ejpam-5560	100	9	−a)−1c	−a)−1c	X
ejpam-5560	100	10	=	=	SYM
ejpam-5560	100	11	rc(λ	rc(λ	ADJ
ejpam-5560	100	12	2	2	NUM
ejpam-5560	100	13	,	,	PUNCT
ejpam-5560	100	14	a	a	PRON
ejpam-5560	100	15	)	)	PUNCT
ejpam-5560	100	16	.	.	PUNCT
ejpam-5560	101	1	(	(	PUNCT
ejpam-5560	101	2	iv	iv	X
ejpam-5560	101	3	)	)	PUNCT
ejpam-5560	101	4	if	if	SCONJ
ejpam-5560	101	5	(	(	PUNCT
ejpam-5560	101	6	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	101	7	is	be	AUX
ejpam-5560	101	8	k	k	ADV
ejpam-5560	101	9	-	-	ADJ
ejpam-5560	101	10	convoluted	convoluted	ADJ
ejpam-5560	101	11	c−cosine	c−cosine	NOUN
ejpam-5560	101	12	function	function	VERB
ejpam-5560	101	13	with	with	ADP
ejpam-5560	101	14	subgenerator	subgenerator	NOUN
ejpam-5560	101	15	(	(	PUNCT
ejpam-5560	101	16	a	a	PRON
ejpam-5560	101	17	,	,	PUNCT
ejpam-5560	101	18	d(a	d(a	PROPN
ejpam-5560	101	19	)	)	PUNCT
ejpam-5560	101	20	)	)	PUNCT
ejpam-5560	101	21	such	such	ADJ
ejpam-5560	101	22	that	that	PRON
ejpam-5560	101	23	for	for	ADP
ejpam-5560	101	24	all	all	DET
ejpam-5560	101	25	t	t	PROPN
ejpam-5560	101	26	≥	≥	NOUN
ejpam-5560	101	27	0	0	NUM
ejpam-5560	101	28	,	,	PUNCT
ejpam-5560	101	29	∥	∥	X
ejpam-5560	101	30	c(t	c(t	PROPN
ejpam-5560	101	31	)	)	PUNCT
ejpam-5560	101	32	∥≤	∥≤	PROPN
ejpam-5560	101	33	meωt	meωt	NOUN
ejpam-5560	101	34	,	,	PUNCT
ejpam-5560	101	35	then	then	ADV
ejpam-5560	101	36	for	for	SCONJ
ejpam-5560	101	37	all	all	DET
ejpam-5560	101	38	λ	λ	PROPN
ejpam-5560	101	39	>	>	X
ejpam-5560	101	40	ω	ω	PROPN
ejpam-5560	101	41	,	,	PUNCT
ejpam-5560	101	42	rλ2	rλ2	PROPN
ejpam-5560	101	43	=	=	SYM
ejpam-5560	101	44	rc(λ	rc(λ	PUNCT
ejpam-5560	101	45	2	2	NUM
ejpam-5560	101	46	,	,	PUNCT
ejpam-5560	101	47	a	a	PRON
ejpam-5560	101	48	)	)	PUNCT
ejpam-5560	101	49	.	.	PUNCT
ejpam-5560	102	1	y.	y.	PROPN
ejpam-5560	102	2	bajjou	bajjou	PROPN
ejpam-5560	102	3	,	,	PUNCT
ejpam-5560	102	4	a.	a.	PROPN
ejpam-5560	102	5	el	el	PROPN
ejpam-5560	102	6	amrani	amrani	PROPN
ejpam-5560	102	7	,	,	PUNCT
ejpam-5560	102	8	a.	a.	PROPN
ejpam-5560	102	9	blali	blali	PROPN
ejpam-5560	102	10	/	/	SYM
ejpam-5560	102	11	eur	eur	PROPN
ejpam-5560	102	12	.	.	PUNCT
ejpam-5560	103	1	j.	j.	PROPN
ejpam-5560	103	2	pure	pure	PROPN
ejpam-5560	103	3	appl	appl	PROPN
ejpam-5560	103	4	.	.	PROPN
ejpam-5560	103	5	math	math	PROPN
ejpam-5560	103	6	,	,	PUNCT
ejpam-5560	103	7	18	18	NUM
ejpam-5560	103	8	(	(	PUNCT
ejpam-5560	103	9	1	1	NUM
ejpam-5560	103	10	)	)	PUNCT
ejpam-5560	103	11	(	(	PUNCT
ejpam-5560	103	12	2025	2025	NUM
ejpam-5560	103	13	)	)	PUNCT
ejpam-5560	103	14	,	,	PUNCT
ejpam-5560	103	15	5560	5560	NUM
ejpam-5560	103	16	6	6	NUM
ejpam-5560	103	17	of	of	ADP
ejpam-5560	103	18	15	15	NUM
ejpam-5560	103	19	3	3	NUM
ejpam-5560	103	20	.	.	PUNCT
ejpam-5560	103	21	main	main	ADJ
ejpam-5560	103	22	results	result	NOUN
ejpam-5560	103	23	theorem	theorem	VERB
ejpam-5560	103	24	1	1	NUM
ejpam-5560	103	25	.	.	PUNCT
ejpam-5560	104	1	let	let	VERB
ejpam-5560	104	2	(	(	PUNCT
ejpam-5560	104	3	c(t))t≥0	c(t))t≥0	NOUN
ejpam-5560	104	4	be	be	AUX
ejpam-5560	104	5	a	a	DET
ejpam-5560	104	6	k−convoluted	k−convoluted	PROPN
ejpam-5560	104	7	c−cosine	c−cosine	PROPN
ejpam-5560	104	8	functions	function	NOUN
ejpam-5560	104	9	with	with	ADP
ejpam-5560	104	10	subgenerator	subgenerator	NOUN
ejpam-5560	104	11	a.	a.	NOUN
ejpam-5560	104	12	for	for	ADP
ejpam-5560	104	13	each	each	DET
ejpam-5560	104	14	n	n	PRON
ejpam-5560	104	15	∈	∈	PROPN
ejpam-5560	104	16	n	n	CCONJ
ejpam-5560	104	17	,	,	PUNCT
ejpam-5560	104	18	let	let	VERB
ejpam-5560	104	19	(	(	PUNCT
ejpam-5560	104	20	cn(t))t≥0	cn(t))t≥0	PROPN
ejpam-5560	104	21	a	a	DET
ejpam-5560	104	22	k−convoluted	k−convoluted	PROPN
ejpam-5560	104	23	c−cosine	c−cosine	PROPN
ejpam-5560	104	24	function	function	NOUN
ejpam-5560	104	25	with	with	ADP
ejpam-5560	104	26	subgenerator	subgenerator	NOUN
ejpam-5560	104	27	(	(	PUNCT
ejpam-5560	104	28	an	an	PRON
ejpam-5560	104	29	,	,	PUNCT
ejpam-5560	104	30	d(an	d(an	NOUN
ejpam-5560	104	31	)	)	PUNCT
ejpam-5560	104	32	)	)	PUNCT
ejpam-5560	104	33	and	and	CCONJ
ejpam-5560	104	34	suppose	suppose	VERB
ejpam-5560	104	35	that	that	SCONJ
ejpam-5560	104	36	there	there	PRON
ejpam-5560	104	37	exist	exist	VERB
ejpam-5560	104	38	ω	ω	NUM
ejpam-5560	104	39	≥	≥	NOUN
ejpam-5560	104	40	0	0	NUM
ejpam-5560	104	41	and	and	CCONJ
ejpam-5560	104	42	m	m	VERB
ejpam-5560	104	43	>	>	X
ejpam-5560	104	44	0	0	NUM
ejpam-5560	104	45	such	such	ADJ
ejpam-5560	104	46	that	that	PRON
ejpam-5560	104	47	for	for	ADP
ejpam-5560	104	48	all	all	DET
ejpam-5560	104	49	t	t	PROPN
ejpam-5560	104	50	≥	≥	NOUN
ejpam-5560	104	51	0	0	NUM
ejpam-5560	104	52	and	and	CCONJ
ejpam-5560	104	53	all	all	DET
ejpam-5560	104	54	x	x	SYM
ejpam-5560	104	55	∈	∈	PROPN
ejpam-5560	104	56	e	e	NOUN
ejpam-5560	104	57	,	,	PUNCT
ejpam-5560	104	58	∥	∥	PUNCT
ejpam-5560	105	1	c(t)x	c(t)x	PROPN
ejpam-5560	105	2	∥≤	∥≤	VERB
ejpam-5560	105	3	meωt	meωt	NOUN
ejpam-5560	105	4	and	and	CCONJ
ejpam-5560	105	5	for	for	ADP
ejpam-5560	105	6	all	all	PRON
ejpam-5560	105	7	n	n	PRON
ejpam-5560	105	8	∈	∈	PROPN
ejpam-5560	105	9	n	n	CCONJ
ejpam-5560	105	10	∥	∥	PROPN
ejpam-5560	105	11	cn(t)x	cn(t)x	PROPN
ejpam-5560	105	12	∥≤	∥≤	PROPN
ejpam-5560	105	13	meωt	meωt	NOUN
ejpam-5560	105	14	.	.	PUNCT
ejpam-5560	106	1	if	if	SCONJ
ejpam-5560	106	2	we	we	PRON
ejpam-5560	106	3	put	put	VERB
ejpam-5560	106	4	ω1	ω1	PROPN
ejpam-5560	106	5	=	=	PUNCT
ejpam-5560	106	6	max(ω	max(ω	NOUN
ejpam-5560	106	7	+	+	CCONJ
ejpam-5560	106	8	1	1	NUM
ejpam-5560	106	9	,	,	PUNCT
ejpam-5560	106	10	abs(k	abs(k	PROPN
ejpam-5560	106	11	)	)	PUNCT
ejpam-5560	106	12	)	)	PUNCT
ejpam-5560	106	13	,	,	PUNCT
ejpam-5560	106	14	then	then	ADV
ejpam-5560	106	15	the	the	DET
ejpam-5560	106	16	following	following	ADJ
ejpam-5560	106	17	statements	statement	NOUN
ejpam-5560	106	18	are	be	AUX
ejpam-5560	106	19	equivalent	equivalent	ADJ
ejpam-5560	106	20	:	:	PUNCT
ejpam-5560	106	21	(	(	PUNCT
ejpam-5560	106	22	i	i	NOUN
ejpam-5560	106	23	)	)	PUNCT
ejpam-5560	106	24	there	there	PRON
ejpam-5560	106	25	exist	exist	VERB
ejpam-5560	106	26	λ0	λ0	NOUN
ejpam-5560	106	27	>	>	X
ejpam-5560	106	28	ω1	ω1	PROPN
ejpam-5560	106	29	)	)	PUNCT
ejpam-5560	106	30	:	:	PUNCT
ejpam-5560	106	31	for	for	ADP
ejpam-5560	106	32	all	all	PRON
ejpam-5560	106	33	x	x	SYM
ejpam-5560	106	34	∈	∈	PROPN
ejpam-5560	106	35	e	e	NOUN
ejpam-5560	106	36	lim	lim	PROPN
ejpam-5560	106	37	n→+∞	n→+∞	PROPN
ejpam-5560	106	38	rc(λ	rc(λ	PUNCT
ejpam-5560	106	39	2	2	NUM
ejpam-5560	106	40	0	0	NUM
ejpam-5560	106	41	,	,	PUNCT
ejpam-5560	106	42	an)x	an)x	PROPN
ejpam-5560	106	43	=	=	PUNCT
ejpam-5560	106	44	rc(λ	rc(λ	PUNCT
ejpam-5560	106	45	2	2	NUM
ejpam-5560	106	46	0	0	NUM
ejpam-5560	106	47	,	,	PUNCT
ejpam-5560	106	48	a)x	a)x	PUNCT
ejpam-5560	106	49	and	and	CCONJ
ejpam-5560	106	50	(	(	PUNCT
ejpam-5560	106	51	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	106	52	is	be	AUX
ejpam-5560	106	53	equicontinuous	equicontinuous	ADJ
ejpam-5560	106	54	.	.	PUNCT
ejpam-5560	107	1	(	(	PUNCT
ejpam-5560	107	2	ii	ii	NOUN
ejpam-5560	107	3	)	)	PUNCT
ejpam-5560	107	4	there	there	PRON
ejpam-5560	107	5	exist	exist	VERB
ejpam-5560	107	6	λ0	λ0	NOUN
ejpam-5560	107	7	>	>	X
ejpam-5560	107	8	ω1	ω1	PROPN
ejpam-5560	107	9	:	:	PUNCT
ejpam-5560	107	10	for	for	ADP
ejpam-5560	107	11	all	all	DET
ejpam-5560	107	12	y	y	PROPN
ejpam-5560	107	13	∈	∈	PROPN
ejpam-5560	107	14	r(c	r(c	PROPN
ejpam-5560	107	15	)	)	PUNCT
ejpam-5560	107	16	)	)	PUNCT
ejpam-5560	108	1	lim	lim	PROPN
ejpam-5560	108	2	n→+∞	n→+∞	PROPN
ejpam-5560	108	3	(	(	PUNCT
ejpam-5560	108	4	λ2i	λ2i	PROPN
ejpam-5560	108	5	−	−	X
ejpam-5560	108	6	an	an	NOUN
ejpam-5560	108	7	)	)	PUNCT
ejpam-5560	108	8	−1y	−1y	NOUN
ejpam-5560	108	9	=	=	SYM
ejpam-5560	108	10	(	(	PUNCT
ejpam-5560	108	11	λ2i	λ2i	PROPN
ejpam-5560	108	12	−	−	PROPN
ejpam-5560	108	13	a)−1y	a)−1y	NOUN
ejpam-5560	108	14	and	and	CCONJ
ejpam-5560	108	15	for	for	ADP
ejpam-5560	108	16	all	all	DET
ejpam-5560	108	17	x	x	SYM
ejpam-5560	108	18	∈	∈	PROPN
ejpam-5560	108	19	e	e	NOUN
ejpam-5560	108	20	,	,	PUNCT
ejpam-5560	108	21	(	(	PUNCT
ejpam-5560	108	22	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	108	23	is	be	AUX
ejpam-5560	108	24	equicontinuous	equicontinuous	ADJ
ejpam-5560	108	25	.	.	PUNCT
ejpam-5560	109	1	(	(	PUNCT
ejpam-5560	109	2	iii	iii	NOUN
ejpam-5560	109	3	)	)	PUNCT
ejpam-5560	109	4	for	for	ADP
ejpam-5560	109	5	all	all	DET
ejpam-5560	109	6	λ	λ	PROPN
ejpam-5560	109	7	>	>	X
ejpam-5560	109	8	ω1	ω1	PROPN
ejpam-5560	109	9	,	,	PUNCT
ejpam-5560	109	10	for	for	ADP
ejpam-5560	109	11	all	all	DET
ejpam-5560	109	12	y	y	PROPN
ejpam-5560	109	13	∈	∈	PROPN
ejpam-5560	109	14	r(c	r(c	PROPN
ejpam-5560	109	15	)	)	PUNCT
ejpam-5560	109	16	)	)	PUNCT
ejpam-5560	109	17	,	,	PUNCT
ejpam-5560	109	18	lim	lim	PROPN
ejpam-5560	109	19	n→+∞	n→+∞	PROPN
ejpam-5560	109	20	(	(	PUNCT
ejpam-5560	109	21	λ2i	λ2i	X
ejpam-5560	109	22	−an	−an	PROPN
ejpam-5560	109	23	)	)	PUNCT
ejpam-5560	109	24	−1y	−1y	NOUN
ejpam-5560	109	25	=	=	SYM
ejpam-5560	109	26	(	(	PUNCT
ejpam-5560	109	27	λ2i	λ2i	X
ejpam-5560	109	28	−a)−1y	−a)−1y	PROPN
ejpam-5560	109	29	and	and	CCONJ
ejpam-5560	109	30	for	for	ADP
ejpam-5560	109	31	all	all	DET
ejpam-5560	109	32	x	x	SYM
ejpam-5560	109	33	∈	∈	PROPN
ejpam-5560	109	34	e	e	NOUN
ejpam-5560	109	35	,	,	PUNCT
ejpam-5560	109	36	(	(	PUNCT
ejpam-5560	109	37	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	109	38	is	be	AUX
ejpam-5560	109	39	equicontinuous	equicontinuous	ADJ
ejpam-5560	109	40	.	.	PUNCT
ejpam-5560	110	1	(	(	PUNCT
ejpam-5560	110	2	iv	iv	X
ejpam-5560	110	3	)	)	PUNCT
ejpam-5560	110	4	for	for	ADP
ejpam-5560	110	5	all	all	DET
ejpam-5560	110	6	λ	λ	PROPN
ejpam-5560	110	7	>	>	X
ejpam-5560	110	8	ω1	ω1	PROPN
ejpam-5560	110	9	,	,	PUNCT
ejpam-5560	110	10	for	for	ADP
ejpam-5560	110	11	all	all	PRON
ejpam-5560	110	12	,	,	PUNCT
ejpam-5560	110	13	x	x	X
ejpam-5560	110	14	∈	∈	PROPN
ejpam-5560	110	15	e	e	NOUN
ejpam-5560	110	16	,	,	PUNCT
ejpam-5560	110	17	lim	lim	PROPN
ejpam-5560	110	18	n→+∞	n→+∞	PROPN
ejpam-5560	110	19	rc(λ	rc(λ	PUNCT
ejpam-5560	110	20	2	2	NUM
ejpam-5560	110	21	,	,	PUNCT
ejpam-5560	110	22	an)x	an)x	PROPN
ejpam-5560	110	23	=	=	PUNCT
ejpam-5560	110	24	rc(λ	rc(λ	PUNCT
ejpam-5560	110	25	2	2	NUM
ejpam-5560	110	26	,	,	PUNCT
ejpam-5560	110	27	a)x	a)x	PUNCT
ejpam-5560	110	28	and	and	CCONJ
ejpam-5560	110	29	(	(	PUNCT
ejpam-5560	110	30	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	110	31	is	be	AUX
ejpam-5560	110	32	equicontinuous	equicontinuous	ADJ
ejpam-5560	110	33	.	.	PUNCT
ejpam-5560	111	1	(	(	PUNCT
ejpam-5560	111	2	v	v	NOUN
ejpam-5560	111	3	)	)	PUNCT
ejpam-5560	111	4	for	for	ADP
ejpam-5560	111	5	all	all	DET
ejpam-5560	111	6	t	t	PROPN
ejpam-5560	111	7	≥	≥	NOUN
ejpam-5560	111	8	0	0	NUM
ejpam-5560	111	9	,	,	PUNCT
ejpam-5560	111	10	for	for	ADP
ejpam-5560	111	11	allx	allx	PROPN
ejpam-5560	111	12	∈	∈	PROPN
ejpam-5560	111	13	e	e	PROPN
ejpam-5560	111	14	,	,	PUNCT
ejpam-5560	111	15	lim	lim	PROPN
ejpam-5560	111	16	n→+∞	n→+∞	PROPN
ejpam-5560	111	17	cn(t)x	cn(t)x	PROPN
ejpam-5560	111	18	=	=	SYM
ejpam-5560	111	19	c(t)x	c(t)x	PROPN
ejpam-5560	111	20	,	,	PUNCT
ejpam-5560	111	21	the	the	DET
ejpam-5560	111	22	convergence	convergence	NOUN
ejpam-5560	111	23	is	be	AUX
ejpam-5560	111	24	uniform	uniform	ADJ
ejpam-5560	111	25	on	on	ADP
ejpam-5560	111	26	any	any	DET
ejpam-5560	111	27	compact	compact	NOUN
ejpam-5560	111	28	of	of	ADP
ejpam-5560	111	29	[	[	X
ejpam-5560	111	30	0,+∞	0,+∞	PROPN
ejpam-5560	111	31	[	[	X
ejpam-5560	111	32	.	.	PUNCT
ejpam-5560	111	33	proof	proof	NOUN
ejpam-5560	111	34	.	.	PUNCT
ejpam-5560	112	1	1	1	NUM
ejpam-5560	112	2	⇒	⇒	NOUN
ejpam-5560	112	3	2	2	NUM
ejpam-5560	112	4	|	|	ADV
ejpam-5560	112	5	like	like	INTJ
ejpam-5560	112	6	rc(λ	rc(λ	PUNCT
ejpam-5560	112	7	2	2	NUM
ejpam-5560	112	8	0	0	NUM
ejpam-5560	112	9	,	,	PUNCT
ejpam-5560	112	10	an	an	PRON
ejpam-5560	112	11	)	)	PUNCT
ejpam-5560	112	12	=	=	SYM
ejpam-5560	112	13	(	(	PUNCT
ejpam-5560	112	14	λ2	λ2	NOUN
ejpam-5560	112	15	0i	0i	NOUN
ejpam-5560	112	16	−	−	PROPN
ejpam-5560	112	17	an	an	PRON
ejpam-5560	112	18	)	)	PUNCT
ejpam-5560	112	19	−1c	−1c	PROPN
ejpam-5560	112	20	and	and	CCONJ
ejpam-5560	112	21	rc(λ	rc(λ	X
ejpam-5560	112	22	2	2	NUM
ejpam-5560	112	23	0	0	NUM
ejpam-5560	112	24	,	,	PUNCT
ejpam-5560	112	25	a	a	PRON
ejpam-5560	112	26	)	)	PUNCT
ejpam-5560	112	27	=	=	SYM
ejpam-5560	112	28	(	(	PUNCT
ejpam-5560	112	29	λ2i	λ2i	X
ejpam-5560	112	30	−	−	PROPN
ejpam-5560	112	31	a)−1c	a)−1c	NOUN
ejpam-5560	112	32	,	,	PUNCT
ejpam-5560	112	33	then	then	ADV
ejpam-5560	112	34	the	the	DET
ejpam-5560	112	35	proof	proof	NOUN
ejpam-5560	112	36	is	be	AUX
ejpam-5560	112	37	obvious	obvious	ADJ
ejpam-5560	112	38	.	.	PUNCT
ejpam-5560	113	1	2	2	NUM
ejpam-5560	113	2	⇒	⇒	NOUN
ejpam-5560	113	3	3	3	NUM
ejpam-5560	113	4	|	|	ADV
ejpam-5560	113	5	let	let	VERB
ejpam-5560	113	6	’s	’s	NOUN
ejpam-5560	113	7	pose	pose	VERB
ejpam-5560	113	8	u	u	NOUN
ejpam-5560	113	9	=	=	PUNCT
ejpam-5560	113	10	{	{	PUNCT
ejpam-5560	113	11	λ	λ	X
ejpam-5560	113	12	>	>	X
ejpam-5560	113	13	ω1	ω1	PROPN
ejpam-5560	113	14	:	:	PUNCT
ejpam-5560	113	15	l(k)(λ	l(k)(λ	X
ejpam-5560	113	16	)	)	PUNCT
ejpam-5560	113	17	̸=	̸=	NOUN
ejpam-5560	113	18	0	0	NUM
ejpam-5560	113	19	}	}	PUNCT
ejpam-5560	113	20	(=	(=	NOUN
ejpam-5560	113	21	]	]	PUNCT
ejpam-5560	113	22	ω1,+∞	ω1,+∞	PROPN
ejpam-5560	113	23	[	[	NOUN
ejpam-5560	113	24	)	)	PUNCT
ejpam-5560	113	25	and	and	CCONJ
ejpam-5560	113	26	v	v	X
ejpam-5560	113	27	=	=	SYM
ejpam-5560	113	28	{	{	PUNCT
ejpam-5560	113	29	λ	λ	X
ejpam-5560	113	30	∈	∈	NOUN
ejpam-5560	113	31	u	u	NOUN
ejpam-5560	113	32	:	:	PUNCT
ejpam-5560	113	33	for	for	ADP
ejpam-5560	113	34	all	all	DET
ejpam-5560	113	35	y	y	PROPN
ejpam-5560	113	36	∈	∈	PROPN
ejpam-5560	113	37	r(c	r(c	PROPN
ejpam-5560	113	38	)	)	PUNCT
ejpam-5560	113	39	,	,	PUNCT
ejpam-5560	113	40	lim	lim	PROPN
ejpam-5560	113	41	n→+∞	n→+∞	PROPN
ejpam-5560	113	42	(	(	PUNCT
ejpam-5560	113	43	λ2i	λ2i	X
ejpam-5560	113	44	−an	−an	PROPN
ejpam-5560	113	45	)	)	PUNCT
ejpam-5560	113	46	−1y	−1y	NOUN
ejpam-5560	113	47	=	=	SYM
ejpam-5560	113	48	(	(	PUNCT
ejpam-5560	113	49	λ2i	λ2i	X
ejpam-5560	113	50	−a)−1y	−a)−1y	X
ejpam-5560	113	51	}	}	PUNCT
ejpam-5560	113	52	.	.	PUNCT
ejpam-5560	114	1	according	accord	VERB
ejpam-5560	114	2	to	to	ADP
ejpam-5560	114	3	the	the	DET
ejpam-5560	114	4	statements	statement	NOUN
ejpam-5560	114	5	of	of	ADP
ejpam-5560	114	6	(	(	PUNCT
ejpam-5560	114	7	2	2	NUM
ejpam-5560	114	8	)	)	PUNCT
ejpam-5560	114	9	,	,	PUNCT
ejpam-5560	114	10	v	v	NOUN
ejpam-5560	114	11	is	be	AUX
ejpam-5560	114	12	a	a	DET
ejpam-5560	114	13	nonempty	nonempty	ADV
ejpam-5560	114	14	set	set	VERB
ejpam-5560	114	15	.	.	PUNCT
ejpam-5560	115	1	let	let	AUX
ejpam-5560	115	2	be	be	AUX
ejpam-5560	115	3	λ	λ	INTJ
ejpam-5560	115	4	∈	∈	NOUN
ejpam-5560	115	5	v	v	ADP
ejpam-5560	115	6	fixed	fix	VERB
ejpam-5560	115	7	and	and	CCONJ
ejpam-5560	115	8	n	n	CCONJ
ejpam-5560	115	9	∈	∈	PROPN
ejpam-5560	115	10	n	n	CCONJ
ejpam-5560	115	11	,	,	PUNCT
ejpam-5560	115	12	then	then	ADV
ejpam-5560	115	13	for	for	ADP
ejpam-5560	115	14	µ	µ	NOUN
ejpam-5560	115	15	in	in	ADP
ejpam-5560	115	16	the	the	DET
ejpam-5560	115	17	open	open	ADJ
ejpam-5560	115	18	set	set	NOUN
ejpam-5560	115	19	oλ	oλ	NOUN
ejpam-5560	115	20	,	,	PUNCT
ejpam-5560	115	21	where	where	SCONJ
ejpam-5560	115	22	oλ	oλ	X
ejpam-5560	115	23	:	:	PUNCT
ejpam-5560	115	24	=	=	SYM
ejpam-5560	115	25	{	{	PUNCT
ejpam-5560	115	26	µ	µ	X
ejpam-5560	115	27	∈	∈	X
ejpam-5560	115	28	u	u	NOUN
ejpam-5560	115	29	:	:	PUNCT
ejpam-5560	115	30	∥	∥	X
ejpam-5560	115	31	(	(	PUNCT
ejpam-5560	115	32	µ2	µ2	PROPN
ejpam-5560	115	33	−	−	PROPN
ejpam-5560	115	34	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	115	35	−an	−an	PROPN
ejpam-5560	115	36	)	)	PUNCT
ejpam-5560	115	37	−1	−1	NOUN
ejpam-5560	115	38	∥	∥	NOUN
ejpam-5560	115	39	<	<	X
ejpam-5560	115	40	1	1	NUM
ejpam-5560	115	41	4	4	NUM
ejpam-5560	115	42	}	}	PUNCT
ejpam-5560	115	43	,	,	PUNCT
ejpam-5560	115	44	we	we	PRON
ejpam-5560	115	45	have	have	VERB
ejpam-5560	115	46	∥	∥	NUM
ejpam-5560	115	47	(	(	PUNCT
ejpam-5560	115	48	µ2	µ2	PROPN
ejpam-5560	115	49	−	−	PROPN
ejpam-5560	115	50	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	115	51	−an	−an	PROPN
ejpam-5560	115	52	)	)	PUNCT
ejpam-5560	115	53	−1	−1	NOUN
ejpam-5560	115	54	∥	∥	NOUN
ejpam-5560	115	55	<	<	X
ejpam-5560	115	56	1	1	NUM
ejpam-5560	115	57	4	4	NUM
ejpam-5560	115	58	<	<	SYM
ejpam-5560	115	59	1	1	NUM
ejpam-5560	116	1	so	so	ADV
ejpam-5560	116	2	i	i	PRON
ejpam-5560	116	3	−	−	PROPN
ejpam-5560	117	1	(	(	PUNCT
ejpam-5560	117	2	µ2	µ2	PROPN
ejpam-5560	117	3	−	−	PROPN
ejpam-5560	117	4	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	117	5	−an	−an	PROPN
ejpam-5560	117	6	)	)	PUNCT
ejpam-5560	117	7	−1	−1	NOUN
ejpam-5560	117	8	is	be	AUX
ejpam-5560	117	9	invertible	invertible	ADJ
ejpam-5560	117	10	,	,	PUNCT
ejpam-5560	117	11	the	the	DET
ejpam-5560	117	12	series	series	NOUN
ejpam-5560	117	13	∑	∑	PROPN
ejpam-5560	117	14	k≥0	k≥0	PROPN
ejpam-5560	117	15	(	(	PUNCT
ejpam-5560	117	16	(	(	PUNCT
ejpam-5560	117	17	µ2	µ2	NOUN
ejpam-5560	117	18	−	−	PROPN
ejpam-5560	117	19	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	117	20	−an	−an	PROPN
ejpam-5560	117	21	)	)	PUNCT
ejpam-5560	117	22	−1	−1	NOUN
ejpam-5560	117	23	)	)	PUNCT
ejpam-5560	118	1	k	k	X
ejpam-5560	118	2	is	be	AUX
ejpam-5560	118	3	uniformly	uniformly	ADV
ejpam-5560	118	4	convergent	convergent	ADJ
ejpam-5560	118	5	and	and	CCONJ
ejpam-5560	118	6	(	(	PUNCT
ejpam-5560	118	7	i	i	PRON
ejpam-5560	118	8	−	−	PROPN
ejpam-5560	119	1	(	(	PUNCT
ejpam-5560	119	2	µ2	µ2	PROPN
ejpam-5560	119	3	−	−	PROPN
ejpam-5560	119	4	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	119	5	−an	−an	NOUN
ejpam-5560	119	6	)	)	PUNCT
ejpam-5560	119	7	−1)−1	−1)−1	NOUN
ejpam-5560	119	8	=	=	PUNCT
ejpam-5560	120	1	+	+	ADJ
ejpam-5560	120	2	∞∑	∞∑	ADJ
ejpam-5560	120	3	k=0	k=0	PROPN
ejpam-5560	120	4	{	{	PUNCT
ejpam-5560	120	5	(	(	PUNCT
ejpam-5560	120	6	µ2	µ2	PROPN
ejpam-5560	120	7	−	−	PROPN
ejpam-5560	120	8	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	120	9	−an	−an	NOUN
ejpam-5560	120	10	)	)	PUNCT
ejpam-5560	120	11	−1}k	−1}k	NOUN
ejpam-5560	120	12	.	.	PUNCT
ejpam-5560	121	1	y.	y.	PROPN
ejpam-5560	121	2	bajjou	bajjou	PROPN
ejpam-5560	121	3	,	,	PUNCT
ejpam-5560	121	4	a.	a.	PROPN
ejpam-5560	121	5	el	el	PROPN
ejpam-5560	121	6	amrani	amrani	PROPN
ejpam-5560	121	7	,	,	PUNCT
ejpam-5560	121	8	a.	a.	PROPN
ejpam-5560	121	9	blali	blali	PROPN
ejpam-5560	121	10	/	/	SYM
ejpam-5560	121	11	eur	eur	PROPN
ejpam-5560	121	12	.	.	PUNCT
ejpam-5560	122	1	j.	j.	PROPN
ejpam-5560	122	2	pure	pure	PROPN
ejpam-5560	122	3	appl	appl	PROPN
ejpam-5560	122	4	.	.	PROPN
ejpam-5560	122	5	math	math	PROPN
ejpam-5560	122	6	,	,	PUNCT
ejpam-5560	122	7	18	18	NUM
ejpam-5560	122	8	(	(	PUNCT
ejpam-5560	122	9	1	1	NUM
ejpam-5560	122	10	)	)	PUNCT
ejpam-5560	122	11	(	(	PUNCT
ejpam-5560	122	12	2025	2025	NUM
ejpam-5560	122	13	)	)	PUNCT
ejpam-5560	122	14	,	,	PUNCT
ejpam-5560	122	15	5560	5560	NUM
ejpam-5560	122	16	7	7	NUM
ejpam-5560	122	17	of	of	ADP
ejpam-5560	122	18	15	15	NUM
ejpam-5560	122	19	but	but	CCONJ
ejpam-5560	122	20	µ2i	µ2i	ADJ
ejpam-5560	122	21	−an	−an	NOUN
ejpam-5560	123	1	=	=	PUNCT
ejpam-5560	123	2	(	(	PUNCT
ejpam-5560	123	3	µ2	µ2	PROPN
ejpam-5560	123	4	−	−	PROPN
ejpam-5560	123	5	λ2)i	λ2)i	NOUN
ejpam-5560	123	6	+	+	CCONJ
ejpam-5560	123	7	(	(	PUNCT
ejpam-5560	123	8	λ2i	λ2i	X
ejpam-5560	123	9	−an	−an	PROPN
ejpam-5560	123	10	)	)	PUNCT
ejpam-5560	123	11	=	=	SYM
ejpam-5560	123	12	(	(	PUNCT
ejpam-5560	123	13	(	(	PUNCT
ejpam-5560	123	14	µ2	µ2	NOUN
ejpam-5560	123	15	−	−	PROPN
ejpam-5560	123	16	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	123	17	−an	−an	PROPN
ejpam-5560	123	18	)	)	PUNCT
ejpam-5560	123	19	−1	−1	NOUN
ejpam-5560	124	1	+	+	CCONJ
ejpam-5560	124	2	i	i	NOUN
ejpam-5560	124	3	)	)	PUNCT
ejpam-5560	125	1	(	(	PUNCT
ejpam-5560	125	2	λ2i	λ2i	X
ejpam-5560	125	3	−an	−an	PROPN
ejpam-5560	125	4	)	)	PUNCT
ejpam-5560	125	5	=	=	SYM
ejpam-5560	125	6	(	(	PUNCT
ejpam-5560	125	7	(	(	PUNCT
ejpam-5560	125	8	i	i	PRON
ejpam-5560	125	9	−	−	PROPN
ejpam-5560	126	1	(	(	PUNCT
ejpam-5560	126	2	µ2	µ2	PROPN
ejpam-5560	126	3	−	−	PROPN
ejpam-5560	126	4	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	126	5	−an	−an	PROPN
ejpam-5560	126	6	)	)	PUNCT
ejpam-5560	126	7	−1	−1	NOUN
ejpam-5560	126	8	)	)	PUNCT
ejpam-5560	127	1	(	(	PUNCT
ejpam-5560	127	2	λ2i	λ2i	X
ejpam-5560	127	3	−an	−an	PROPN
ejpam-5560	127	4	)	)	PUNCT
ejpam-5560	127	5	,	,	PUNCT
ejpam-5560	127	6	so	so	CCONJ
ejpam-5560	127	7	(	(	PUNCT
ejpam-5560	127	8	µ2i	µ2i	PROPN
ejpam-5560	127	9	−an	−an	NOUN
ejpam-5560	127	10	)	)	PUNCT
ejpam-5560	127	11	−1	−1	NOUN
ejpam-5560	128	1	=	=	SYM
ejpam-5560	128	2	(	(	PUNCT
ejpam-5560	128	3	λ2i	λ2i	X
ejpam-5560	128	4	−an	−an	PROPN
ejpam-5560	128	5	)	)	PUNCT
ejpam-5560	128	6	−1	−1	NOUN
ejpam-5560	128	7	(	(	PUNCT
ejpam-5560	128	8	(	(	PUNCT
ejpam-5560	128	9	i	i	PRON
ejpam-5560	128	10	−	−	PROPN
ejpam-5560	129	1	(	(	PUNCT
ejpam-5560	129	2	µ2	µ2	PROPN
ejpam-5560	129	3	−	−	PROPN
ejpam-5560	129	4	λ2))(λ2i	λ2))(λ2i	PROPN
ejpam-5560	129	5	−an	−an	PROPN
ejpam-5560	129	6	)	)	PUNCT
ejpam-5560	129	7	−1	−1	NOUN
ejpam-5560	129	8	)	)	PUNCT
ejpam-5560	129	9	−1	−1	NOUN
ejpam-5560	129	10	=	=	SYM
ejpam-5560	129	11	(	(	PUNCT
ejpam-5560	129	12	λ2i	λ2i	X
ejpam-5560	129	13	−an	−an	PROPN
ejpam-5560	129	14	)	)	PUNCT
ejpam-5560	129	15	−1	−1	NOUN
ejpam-5560	130	1	+	+	PUNCT
ejpam-5560	130	2	∞∑	∞∑	PRON
ejpam-5560	130	3	k=0	k=0	PROPN
ejpam-5560	130	4	(	(	PUNCT
ejpam-5560	130	5	(	(	PUNCT
ejpam-5560	130	6	µ2	µ2	NOUN
ejpam-5560	130	7	−	−	PROPN
ejpam-5560	130	8	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	130	9	−an	−an	PROPN
ejpam-5560	130	10	)	)	PUNCT
ejpam-5560	130	11	−1	−1	NOUN
ejpam-5560	130	12	)	)	PUNCT
ejpam-5560	130	13	k	k	X
ejpam-5560	131	1	=	=	PUNCT
ejpam-5560	131	2	+	+	ADJ
ejpam-5560	131	3	∞∑	∞∑	PRON
ejpam-5560	131	4	k=0	k=0	PROPN
ejpam-5560	131	5	(	(	PUNCT
ejpam-5560	131	6	µ2	µ2	PROPN
ejpam-5560	131	7	−	−	PROPN
ejpam-5560	131	8	λ2)k	λ2)k	VERB
ejpam-5560	131	9	(	(	PUNCT
ejpam-5560	131	10	(	(	PUNCT
ejpam-5560	131	11	λ2i	λ2i	X
ejpam-5560	131	12	−an	−an	PROPN
ejpam-5560	131	13	)	)	PUNCT
ejpam-5560	131	14	−1	−1	NOUN
ejpam-5560	131	15	)	)	PUNCT
ejpam-5560	131	16	k+1	k+1	NOUN
ejpam-5560	131	17	,	,	PUNCT
ejpam-5560	131	18	and	and	CCONJ
ejpam-5560	131	19	for	for	ADP
ejpam-5560	131	20	all	all	DET
ejpam-5560	131	21	y	y	PROPN
ejpam-5560	131	22	∈	∈	PROPN
ejpam-5560	131	23	r(c	r(c	PROPN
ejpam-5560	131	24	)	)	PUNCT
ejpam-5560	131	25	lim	lim	PROPN
ejpam-5560	131	26	n→+∞	n→+∞	PROPN
ejpam-5560	131	27	(	(	PUNCT
ejpam-5560	131	28	µ2i	µ2i	PROPN
ejpam-5560	131	29	−an	−an	NOUN
ejpam-5560	131	30	)	)	PUNCT
ejpam-5560	131	31	−1y	−1y	NOUN
ejpam-5560	131	32	=	=	SYM
ejpam-5560	131	33	lim	lim	PROPN
ejpam-5560	131	34	n→+∞	n→+∞	VERB
ejpam-5560	132	1	+	+	PROPN
ejpam-5560	132	2	∞∑	∞∑	PRON
ejpam-5560	132	3	k=0	k=0	PROPN
ejpam-5560	132	4	(	(	PUNCT
ejpam-5560	132	5	µ2	µ2	PROPN
ejpam-5560	132	6	−	−	PROPN
ejpam-5560	132	7	λ2)k	λ2)k	VERB
ejpam-5560	132	8	(	(	PUNCT
ejpam-5560	132	9	(	(	PUNCT
ejpam-5560	132	10	λ2i	λ2i	X
ejpam-5560	132	11	−an	−an	PROPN
ejpam-5560	132	12	)	)	PUNCT
ejpam-5560	132	13	−1	−1	NOUN
ejpam-5560	132	14	)	)	PUNCT
ejpam-5560	132	15	k+1	k+1	X
ejpam-5560	133	1	y	y	NOUN
ejpam-5560	133	2	=	=	PUNCT
ejpam-5560	134	1	+	+	PROPN
ejpam-5560	134	2	∞∑	∞∑	ADJ
ejpam-5560	134	3	k=0	k=0	PROPN
ejpam-5560	134	4	lim	lim	PROPN
ejpam-5560	134	5	n→+∞	n→+∞	PROPN
ejpam-5560	134	6	(	(	PUNCT
ejpam-5560	134	7	µ2	µ2	PROPN
ejpam-5560	134	8	−	−	PROPN
ejpam-5560	134	9	λ2)k	λ2)k	VERB
ejpam-5560	134	10	(	(	PUNCT
ejpam-5560	134	11	(	(	PUNCT
ejpam-5560	134	12	λ2i	λ2i	X
ejpam-5560	134	13	−an	−an	PROPN
ejpam-5560	134	14	)	)	PUNCT
ejpam-5560	134	15	−1	−1	NOUN
ejpam-5560	134	16	)	)	PUNCT
ejpam-5560	135	1	k+1	k+1	X
ejpam-5560	136	1	y	y	NOUN
ejpam-5560	136	2	=	=	PUNCT
ejpam-5560	137	1	+	+	PROPN
ejpam-5560	137	2	∞∑	∞∑	PRON
ejpam-5560	137	3	k=0	k=0	PROPN
ejpam-5560	137	4	(	(	PUNCT
ejpam-5560	137	5	µ2	µ2	PROPN
ejpam-5560	137	6	−	−	PROPN
ejpam-5560	137	7	λ2)k	λ2)k	VERB
ejpam-5560	137	8	(	(	PUNCT
ejpam-5560	137	9	(	(	PUNCT
ejpam-5560	137	10	λ2i	λ2i	X
ejpam-5560	137	11	−a)−1	−a)−1	NOUN
ejpam-5560	137	12	)	)	PUNCT
ejpam-5560	137	13	k+1	k+1	X
ejpam-5560	137	14	y	y	NOUN
ejpam-5560	137	15	=	=	SYM
ejpam-5560	137	16	(	(	PUNCT
ejpam-5560	137	17	λ2i	λ2i	X
ejpam-5560	137	18	−a)−1	−a)−1	NOUN
ejpam-5560	137	19	+	+	NOUN
ejpam-5560	137	20	∞∑	∞∑	DET
ejpam-5560	137	21	k=0	k=0	PROPN
ejpam-5560	137	22	(	(	PUNCT
ejpam-5560	137	23	µ2	µ2	PROPN
ejpam-5560	137	24	−	−	PROPN
ejpam-5560	137	25	λ2	λ2	PROPN
ejpam-5560	137	26	)	)	PUNCT
ejpam-5560	137	27	(	(	PUNCT
ejpam-5560	137	28	(	(	PUNCT
ejpam-5560	137	29	λ2i	λ2i	X
ejpam-5560	137	30	−a)−1	−a)−1	NOUN
ejpam-5560	137	31	)	)	PUNCT
ejpam-5560	138	1	k	k	PROPN
ejpam-5560	138	2	y	y	PROPN
ejpam-5560	138	3	=	=	PUNCT
ejpam-5560	138	4	(	(	PUNCT
ejpam-5560	138	5	µ2i	µ2i	PROPN
ejpam-5560	138	6	−a)−1y	−a)−1y	PROPN
ejpam-5560	138	7	(	(	PUNCT
ejpam-5560	138	8	because	because	SCONJ
ejpam-5560	138	9	lim	lim	PROPN
ejpam-5560	138	10	n→+∞	n→+∞	VERB
ejpam-5560	138	11	∥	∥	PROPN
ejpam-5560	138	12	(	(	PUNCT
ejpam-5560	138	13	µ2	µ2	PROPN
ejpam-5560	138	14	−	−	PROPN
ejpam-5560	138	15	λ2)(λ2i	λ2)(λ2i	PROPN
ejpam-5560	138	16	−an	−an	PROPN
ejpam-5560	138	17	)	)	PUNCT
ejpam-5560	138	18	−1	−1	NOUN
ejpam-5560	138	19	∥	∥	X
ejpam-5560	138	20	<	<	X
ejpam-5560	138	21	1	1	NUM
ejpam-5560	138	22	)	)	PUNCT
ejpam-5560	138	23	.	.	PUNCT
ejpam-5560	139	1	so	so	ADV
ejpam-5560	139	2	we	we	PRON
ejpam-5560	139	3	can	can	AUX
ejpam-5560	139	4	conclude	conclude	VERB
ejpam-5560	139	5	that	that	PRON
ejpam-5560	139	6	for	for	ADP
ejpam-5560	139	7	all	all	DET
ejpam-5560	139	8	λ	λ	PROPN
ejpam-5560	139	9	∈	∈	NOUN
ejpam-5560	139	10	v	v	ADP
ejpam-5560	139	11	there	there	PRON
ejpam-5560	139	12	exists	exist	VERB
ejpam-5560	139	13	an	an	DET
ejpam-5560	139	14	open	open	ADJ
ejpam-5560	139	15	set	set	NOUN
ejpam-5560	139	16	oλ	oλ	ADP
ejpam-5560	139	17	such	such	ADJ
ejpam-5560	139	18	that	that	SCONJ
ejpam-5560	139	19	oλ	oλ	NOUN
ejpam-5560	139	20	⊂	⊂	PROPN
ejpam-5560	139	21	v	v	NOUN
ejpam-5560	139	22	;	;	PUNCT
ejpam-5560	139	23	therefore	therefore	ADV
ejpam-5560	139	24	v	v	NOUN
ejpam-5560	139	25	is	be	AUX
ejpam-5560	139	26	an	an	DET
ejpam-5560	139	27	open	open	ADJ
ejpam-5560	139	28	set	set	NOUN
ejpam-5560	139	29	.	.	PUNCT
ejpam-5560	140	1	let	let	AUX
ejpam-5560	140	2	be	be	AUX
ejpam-5560	140	3	(	(	PUNCT
ejpam-5560	140	4	λk)k∈n	λk)k∈n	NUM
ejpam-5560	140	5	a	a	DET
ejpam-5560	140	6	sequence	sequence	NOUN
ejpam-5560	140	7	in	in	ADP
ejpam-5560	140	8	v	v	ADP
ejpam-5560	140	9	such	such	ADJ
ejpam-5560	140	10	that	that	SCONJ
ejpam-5560	140	11	lim	lim	PROPN
ejpam-5560	140	12	k→+∞	k→+∞	PROPN
ejpam-5560	140	13	λk	λk	X
ejpam-5560	141	1	=	=	PUNCT
ejpam-5560	142	1	λ	λ	PROPN
ejpam-5560	142	2	and	and	CCONJ
ejpam-5560	142	3	λ	λ	PROPN
ejpam-5560	142	4	∈	∈	PROPN
ejpam-5560	142	5	u	u	NOUN
ejpam-5560	142	6	,	,	PUNCT
ejpam-5560	142	7	let	let	VERB
ejpam-5560	142	8	’s	’s	NOUN
ejpam-5560	142	9	show	show	VERB
ejpam-5560	142	10	that	that	SCONJ
ejpam-5560	142	11	λ	λ	PROPN
ejpam-5560	142	12	∈	∈	PROPN
ejpam-5560	142	13	v.	v.	ADP
ejpam-5560	142	14	like	like	INTJ
ejpam-5560	142	15	for	for	ADP
ejpam-5560	142	16	n	n	PRON
ejpam-5560	142	17	∈	∈	PROPN
ejpam-5560	142	18	n	n	CCONJ
ejpam-5560	142	19	,	,	PUNCT
ejpam-5560	142	20	the	the	DET
ejpam-5560	142	21	open	open	ADJ
ejpam-5560	142	22	set	set	NOUN
ejpam-5560	142	23	o′	o′	PROPN
ejpam-5560	142	24	λ	λ	X
ejpam-5560	142	25	:	:	PUNCT
ejpam-5560	142	26	=	=	SYM
ejpam-5560	142	27	{	{	PUNCT
ejpam-5560	142	28	µ	µ	X
ejpam-5560	142	29	∈	∈	X
ejpam-5560	142	30	u	u	NOUN
ejpam-5560	142	31	:	:	PUNCT
ejpam-5560	142	32	∥	∥	X
ejpam-5560	142	33	(	(	PUNCT
ejpam-5560	142	34	µ2−λ2)(µ2i−an	µ2−λ2)(µ2i−an	NUM
ejpam-5560	142	35	)	)	PUNCT
ejpam-5560	142	36	−1	−1	NOUN
ejpam-5560	142	37	∥	∥	NOUN
ejpam-5560	142	38	<	<	X
ejpam-5560	142	39	1	1	NUM
ejpam-5560	142	40	4	4	NUM
ejpam-5560	142	41	}	}	PUNCT
ejpam-5560	142	42	contains	contain	VERB
ejpam-5560	142	43	λ	λ	NOUN
ejpam-5560	142	44	therfore	therfore	ADJ
ejpam-5560	142	45	there	there	PRON
ejpam-5560	142	46	exists	exist	VERB
ejpam-5560	142	47	λk0	λk0	NOUN
ejpam-5560	142	48	∈	∈	PROPN
ejpam-5560	142	49	u	u	NOUN
ejpam-5560	142	50	such	such	ADJ
ejpam-5560	142	51	that	that	SCONJ
ejpam-5560	142	52	λk0	λk0	NOUN
ejpam-5560	142	53	∈	∈	PRON
ejpam-5560	142	54	o′	o′	X
ejpam-5560	142	55	λ	λ	X
ejpam-5560	142	56	;	;	PUNCT
ejpam-5560	142	57	but	but	CCONJ
ejpam-5560	142	58	(	(	PUNCT
ejpam-5560	142	59	λ	λ	NOUN
ejpam-5560	142	60	2i−an	2i−an	NUM
ejpam-5560	142	61	)	)	PUNCT
ejpam-5560	142	62	−1	−1	NOUN
ejpam-5560	143	1	=	=	PUNCT
ejpam-5560	144	1	+	+	ADP
ejpam-5560	144	2	∞∑	∞∑	DET
ejpam-5560	144	3	k=0	k=0	PROPN
ejpam-5560	144	4	(	(	PUNCT
ejpam-5560	144	5	(	(	PUNCT
ejpam-5560	144	6	λ2	λ2	NOUN
ejpam-5560	144	7	−	−	PROPN
ejpam-5560	144	8	λ2	λ2	PROPN
ejpam-5560	144	9	k0	k0	PROPN
ejpam-5560	144	10	)	)	PUNCT
ejpam-5560	144	11	k(λ2	k(λ2	NOUN
ejpam-5560	144	12	k0i	k0i	PROPN
ejpam-5560	144	13	−an	−an	PROPN
ejpam-5560	144	14	)	)	PUNCT
ejpam-5560	144	15	−1	−1	NOUN
ejpam-5560	144	16	)	)	PUNCT
ejpam-5560	145	1	k+1	k+1	X
ejpam-5560	145	2	whose	whose	DET
ejpam-5560	145	3	series	series	NOUN
ejpam-5560	145	4	converges	converge	VERB
ejpam-5560	145	5	uniformly	uniformly	ADV
ejpam-5560	145	6	on	on	ADP
ejpam-5560	145	7	o′	o′	X
ejpam-5560	145	8	λ	λ	NOUN
ejpam-5560	145	9	and	and	CCONJ
ejpam-5560	145	10	as	as	ADP
ejpam-5560	145	11	the	the	DET
ejpam-5560	145	12	function	function	NOUN
ejpam-5560	145	13	β	β	X
ejpam-5560	145	14	7−→	7−→	NOUN
ejpam-5560	145	15	(	(	PUNCT
ejpam-5560	145	16	β2i	β2i	PROPN
ejpam-5560	145	17	−	−	PROPN
ejpam-5560	145	18	an	an	PRON
ejpam-5560	145	19	)	)	PUNCT
ejpam-5560	145	20	−1	−1	NOUN
ejpam-5560	145	21	is	be	AUX
ejpam-5560	145	22	continuous	continuous	ADJ
ejpam-5560	145	23	from	from	ADP
ejpam-5560	145	24	]	]	PUNCT
ejpam-5560	145	25	ω1,+∞	ω1,+∞	PROPN
ejpam-5560	145	26	[	[	PUNCT
ejpam-5560	145	27	to	to	ADP
ejpam-5560	145	28	b(e	b(e	PROPN
ejpam-5560	145	29	)	)	PUNCT
ejpam-5560	146	1	then	then	ADV
ejpam-5560	146	2	lim	lim	PROPN
ejpam-5560	146	3	n→+∞	n→+∞	PROPN
ejpam-5560	146	4	(	(	PUNCT
ejpam-5560	146	5	λ2i	λ2i	X
ejpam-5560	146	6	−an	−an	PROPN
ejpam-5560	146	7	)	)	PUNCT
ejpam-5560	146	8	−1	−1	NOUN
ejpam-5560	147	1	=	=	PROPN
ejpam-5560	147	2	lim	lim	PROPN
ejpam-5560	147	3	n→+∞	n→+∞	VERB
ejpam-5560	147	4	+	+	PROPN
ejpam-5560	147	5	∞∑	∞∑	ADJ
ejpam-5560	147	6	k=0	k=0	PROPN
ejpam-5560	147	7	(	(	PUNCT
ejpam-5560	147	8	(	(	PUNCT
ejpam-5560	147	9	λ2	λ2	NOUN
ejpam-5560	147	10	−	−	PROPN
ejpam-5560	147	11	λ2	λ2	PROPN
ejpam-5560	147	12	k0	k0	PROPN
ejpam-5560	147	13	)	)	PUNCT
ejpam-5560	147	14	k(λ2	k(λ2	NOUN
ejpam-5560	147	15	k0i	k0i	PROPN
ejpam-5560	147	16	−an	−an	PROPN
ejpam-5560	147	17	)	)	PUNCT
ejpam-5560	147	18	−1	−1	NOUN
ejpam-5560	147	19	)	)	PUNCT
ejpam-5560	147	20	k+1	k+1	X
ejpam-5560	147	21	y.	y.	PROPN
ejpam-5560	147	22	bajjou	bajjou	PROPN
ejpam-5560	147	23	,	,	PUNCT
ejpam-5560	147	24	a.	a.	PROPN
ejpam-5560	147	25	el	el	PROPN
ejpam-5560	147	26	amrani	amrani	PROPN
ejpam-5560	147	27	,	,	PUNCT
ejpam-5560	147	28	a.	a.	PROPN
ejpam-5560	147	29	blali	blali	PROPN
ejpam-5560	147	30	/	/	SYM
ejpam-5560	147	31	eur	eur	PROPN
ejpam-5560	147	32	.	.	PUNCT
ejpam-5560	148	1	j.	j.	PROPN
ejpam-5560	148	2	pure	pure	PROPN
ejpam-5560	148	3	appl	appl	PROPN
ejpam-5560	148	4	.	.	PROPN
ejpam-5560	148	5	math	math	PROPN
ejpam-5560	148	6	,	,	PUNCT
ejpam-5560	148	7	18	18	NUM
ejpam-5560	148	8	(	(	PUNCT
ejpam-5560	148	9	1	1	NUM
ejpam-5560	148	10	)	)	PUNCT
ejpam-5560	148	11	(	(	PUNCT
ejpam-5560	148	12	2025	2025	NUM
ejpam-5560	148	13	)	)	PUNCT
ejpam-5560	148	14	,	,	PUNCT
ejpam-5560	148	15	5560	5560	NUM
ejpam-5560	148	16	8	8	NUM
ejpam-5560	148	17	of	of	ADP
ejpam-5560	148	18	15	15	NUM
ejpam-5560	148	19	=	=	SYM
ejpam-5560	149	1	+	+	ADP
ejpam-5560	149	2	∞∑	∞∑	ADJ
ejpam-5560	149	3	k=0	k=0	PROPN
ejpam-5560	149	4	lim	lim	PROPN
ejpam-5560	149	5	n→+∞	n→+∞	PROPN
ejpam-5560	149	6	(	(	PUNCT
ejpam-5560	149	7	λ2	λ2	NOUN
ejpam-5560	149	8	−	−	PROPN
ejpam-5560	149	9	λ2	λ2	PROPN
ejpam-5560	149	10	k0	k0	PROPN
ejpam-5560	149	11	)	)	PUNCT
ejpam-5560	150	1	k	k	PROPN
ejpam-5560	150	2	(	(	PUNCT
ejpam-5560	150	3	(	(	PUNCT
ejpam-5560	150	4	λ2	λ2	PROPN
ejpam-5560	150	5	k0i	k0i	PROPN
ejpam-5560	150	6	−an	−an	PROPN
ejpam-5560	150	7	)	)	PUNCT
ejpam-5560	150	8	−1	−1	NOUN
ejpam-5560	150	9	)	)	PUNCT
ejpam-5560	150	10	k+1	k+1	X
ejpam-5560	151	1	=	=	PUNCT
ejpam-5560	151	2	+	+	ADJ
ejpam-5560	151	3	∞∑	∞∑	ADJ
ejpam-5560	151	4	k=0	k=0	PROPN
ejpam-5560	151	5	(	(	PUNCT
ejpam-5560	151	6	λ2	λ2	NOUN
ejpam-5560	151	7	−	−	PROPN
ejpam-5560	151	8	λ2	λ2	PROPN
ejpam-5560	151	9	k0	k0	PROPN
ejpam-5560	151	10	)	)	PUNCT
ejpam-5560	151	11	k	k	PROPN
ejpam-5560	152	1	(	(	PUNCT
ejpam-5560	152	2	(	(	PUNCT
ejpam-5560	152	3	λ2	λ2	NOUN
ejpam-5560	152	4	k0i	k0i	NOUN
ejpam-5560	152	5	−a)−1	−a)−1	NOUN
ejpam-5560	152	6	)	)	PUNCT
ejpam-5560	152	7	k+1	k+1	X
ejpam-5560	152	8	=	=	SYM
ejpam-5560	152	9	(	(	PUNCT
ejpam-5560	152	10	λ2i	λ2i	NOUN
ejpam-5560	152	11	−a)−1	−a)−1	NOUN
ejpam-5560	152	12	,	,	PUNCT
ejpam-5560	152	13	the	the	DET
ejpam-5560	152	14	last	last	ADJ
ejpam-5560	152	15	equality	equality	NOUN
ejpam-5560	152	16	is	be	AUX
ejpam-5560	152	17	due	due	ADJ
ejpam-5560	152	18	to	to	ADP
ejpam-5560	152	19	the	the	DET
ejpam-5560	152	20	following	follow	VERB
ejpam-5560	152	21	inequality	inequality	NOUN
ejpam-5560	152	22	lim	lim	PROPN
ejpam-5560	152	23	n→+∞	n→+∞	VERB
ejpam-5560	152	24	∥	∥	PROPN
ejpam-5560	152	25	(	(	PUNCT
ejpam-5560	152	26	λ2	λ2	NOUN
ejpam-5560	152	27	−	−	PROPN
ejpam-5560	152	28	λ2	λ2	PROPN
ejpam-5560	152	29	k0)(λ	k0)(λ	PROPN
ejpam-5560	152	30	2	2	NUM
ejpam-5560	152	31	k0i	k0i	PROPN
ejpam-5560	152	32	−an	−an	PROPN
ejpam-5560	152	33	)	)	PUNCT
ejpam-5560	152	34	−1	−1	NOUN
ejpam-5560	152	35	∥≤	∥≤	VERB
ejpam-5560	152	36	1	1	NUM
ejpam-5560	152	37	4	4	NUM
ejpam-5560	152	38	<	<	X
ejpam-5560	152	39	1	1	NUM
ejpam-5560	152	40	,	,	PUNCT
ejpam-5560	152	41	so	so	ADV
ejpam-5560	152	42	λ	λ	X
ejpam-5560	152	43	∈	∈	PROPN
ejpam-5560	153	1	v.	v.	CCONJ
ejpam-5560	153	2	therefore	therefore	ADV
ejpam-5560	153	3	v	v	NOUN
ejpam-5560	153	4	is	be	AUX
ejpam-5560	153	5	relatively	relatively	ADV
ejpam-5560	153	6	closed	close	VERB
ejpam-5560	153	7	from	from	ADP
ejpam-5560	153	8	u.	u.	NOUN
ejpam-5560	153	9	finally	finally	ADV
ejpam-5560	153	10	the	the	DET
ejpam-5560	153	11	set	set	NOUN
ejpam-5560	153	12	v	v	NOUN
ejpam-5560	153	13	is	be	AUX
ejpam-5560	153	14	both	both	CCONJ
ejpam-5560	153	15	an	an	DET
ejpam-5560	153	16	open	open	ADJ
ejpam-5560	153	17	and	and	CCONJ
ejpam-5560	153	18	a	a	DET
ejpam-5560	153	19	closed	closed	NOUN
ejpam-5560	153	20	of	of	ADP
ejpam-5560	153	21	the	the	DET
ejpam-5560	153	22	connected	connect	VERB
ejpam-5560	153	23	set	set	NOUN
ejpam-5560	153	24	u	u	NOUN
ejpam-5560	153	25	,	,	PUNCT
ejpam-5560	153	26	whence	whence	NOUN
ejpam-5560	153	27	v	v	NOUN
ejpam-5560	153	28	=	=	PUNCT
ejpam-5560	153	29	u.	u.	NOUN
ejpam-5560	153	30	3	3	NUM
ejpam-5560	153	31	⇒	⇒	NOUN
ejpam-5560	153	32	4	4	NUM
ejpam-5560	153	33	|	|	ADV
ejpam-5560	153	34	obvious	obvious	ADJ
ejpam-5560	153	35	.	.	PUNCT
ejpam-5560	154	1	4	4	NUM
ejpam-5560	154	2	⇒	⇒	NOUN
ejpam-5560	154	3	5	5	NUM
ejpam-5560	154	4	|	|	ADV
ejpam-5560	154	5	suppose	suppose	VERB
ejpam-5560	154	6	that	that	SCONJ
ejpam-5560	154	7	the	the	DET
ejpam-5560	154	8	conditions	condition	NOUN
ejpam-5560	154	9	of	of	ADP
ejpam-5560	154	10	statement	statement	NOUN
ejpam-5560	154	11	4	4	NUM
ejpam-5560	154	12	are	be	AUX
ejpam-5560	154	13	satisfied	satisfied	ADJ
ejpam-5560	154	14	.	.	PUNCT
ejpam-5560	155	1	let	let	VERB
ejpam-5560	155	2	x	x	SYM
ejpam-5560	155	3	∈	∈	PROPN
ejpam-5560	155	4	e	e	NOUN
ejpam-5560	155	5	be	be	AUX
ejpam-5560	155	6	fixed	fix	VERB
ejpam-5560	155	7	.	.	PUNCT
ejpam-5560	156	1	we	we	PRON
ejpam-5560	156	2	define	define	VERB
ejpam-5560	156	3	,	,	PUNCT
ejpam-5560	156	4	for	for	ADP
ejpam-5560	156	5	each	each	DET
ejpam-5560	156	6	n	n	PRON
ejpam-5560	156	7	∈	∈	PROPN
ejpam-5560	156	8	n	n	CCONJ
ejpam-5560	156	9	,	,	PUNCT
ejpam-5560	156	10	the	the	DET
ejpam-5560	156	11	following	follow	VERB
ejpam-5560	156	12	functions	function	NOUN
ejpam-5560	156	13	:	:	PUNCT
ejpam-5560	156	14	fn	fn	X
ejpam-5560	156	15	:	:	PUNCT
ejpam-5560	156	16	r+	r+	NOUN
ejpam-5560	156	17	→	→	SYM
ejpam-5560	156	18	e	e	X
ejpam-5560	156	19	,	,	PUNCT
ejpam-5560	156	20	t	t	PROPN
ejpam-5560	156	21	7→	7→	NUM
ejpam-5560	156	22	cn(t)x	cn(t)x	PROPN
ejpam-5560	156	23	.	.	PUNCT
ejpam-5560	157	1	f	f	PROPN
ejpam-5560	157	2	:	:	PUNCT
ejpam-5560	157	3	r+	r+	X
ejpam-5560	157	4	→	→	SYM
ejpam-5560	157	5	l∞(e	l∞(e	NOUN
ejpam-5560	157	6	)	)	PUNCT
ejpam-5560	157	7	,	,	PUNCT
ejpam-5560	157	8	t	t	PROPN
ejpam-5560	157	9	7→	7→	NUM
ejpam-5560	157	10	(	(	PUNCT
ejpam-5560	157	11	fn(t))n∈n	fn(t))n∈n	PROPN
ejpam-5560	157	12	.	.	PROPN
ejpam-5560	157	13	fn	fn	PROPN
ejpam-5560	157	14	:]	:]	PROPN
ejpam-5560	157	15	ω1,+∞[→	ω1,+∞[→	PROPN
ejpam-5560	157	16	e	e	NOUN
ejpam-5560	157	17	,	,	PUNCT
ejpam-5560	157	18	λ	λ	PROPN
ejpam-5560	157	19	7→	7→	PROPN
ejpam-5560	157	20	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	157	21	2	2	NUM
ejpam-5560	157	22	,	,	PUNCT
ejpam-5560	157	23	an)x	an)x	PROPN
ejpam-5560	157	24	.	.	PUNCT
ejpam-5560	158	1	f	f	PROPN
ejpam-5560	158	2	:]	:]	PUNCT
ejpam-5560	158	3	ω1,+∞[→	ω1,+∞[→	PROPN
ejpam-5560	158	4	l∞(e	l∞(e	NOUN
ejpam-5560	158	5	)	)	PUNCT
ejpam-5560	158	6	,	,	PUNCT
ejpam-5560	158	7	λ	λ	PROPN
ejpam-5560	158	8	7→	7→	NUM
ejpam-5560	158	9	(	(	PUNCT
ejpam-5560	158	10	fn(λ)n∈n	fn(λ)n∈n	NOUN
ejpam-5560	158	11	)	)	PUNCT
ejpam-5560	158	12	.	.	PUNCT
ejpam-5560	159	1	gn	gn	PROPN
ejpam-5560	159	2	:	:	PUNCT
ejpam-5560	159	3	r+	r+	X
ejpam-5560	159	4	→	→	SYM
ejpam-5560	159	5	e	e	X
ejpam-5560	159	6	,	,	PUNCT
ejpam-5560	159	7	t	t	PROPN
ejpam-5560	159	8	7→	7→	NUM
ejpam-5560	160	1	∫	∫	PROPN
ejpam-5560	161	1	t	t	NOUN
ejpam-5560	161	2	0	0	NUM
ejpam-5560	161	3	(	(	PUNCT
ejpam-5560	161	4	t−	t−	PROPN
ejpam-5560	161	5	s)fn(s)ds	s)fn(s)ds	PROPN
ejpam-5560	161	6	.	.	PUNCT
ejpam-5560	162	1	g	g	NOUN
ejpam-5560	162	2	:	:	PUNCT
ejpam-5560	162	3	r+	r+	X
ejpam-5560	162	4	→	→	SYM
ejpam-5560	162	5	e	e	X
ejpam-5560	162	6	,	,	PUNCT
ejpam-5560	162	7	t	t	PROPN
ejpam-5560	162	8	7→	7→	NUM
ejpam-5560	162	9	(	(	PUNCT
ejpam-5560	162	10	gn(t))n∈n	gn(t))n∈n	NOUN
ejpam-5560	162	11	.	.	PUNCT
ejpam-5560	163	1	(	(	PUNCT
ejpam-5560	163	2	i	i	NOUN
ejpam-5560	163	3	)	)	PUNCT
ejpam-5560	163	4	•	•	ADP
ejpam-5560	163	5	a	a	X
ejpam-5560	163	6	)	)	PUNCT
ejpam-5560	163	7	f	f	PROPN
ejpam-5560	163	8	is	be	AUX
ejpam-5560	163	9	well	well	ADV
ejpam-5560	163	10	defined	define	VERB
ejpam-5560	163	11	.	.	PUNCT
ejpam-5560	164	1	let	let	VERB
ejpam-5560	164	2	t	t	NOUN
ejpam-5560	164	3	be	be	AUX
ejpam-5560	164	4	a	a	DET
ejpam-5560	164	5	positive	positive	ADJ
ejpam-5560	164	6	real	real	NOUN
ejpam-5560	164	7	.	.	PUNCT
ejpam-5560	165	1	we	we	PRON
ejpam-5560	165	2	have	have	VERB
ejpam-5560	165	3	for	for	ADP
ejpam-5560	165	4	all	all	PRON
ejpam-5560	165	5	n	n	PRON
ejpam-5560	165	6	∈	∈	PROPN
ejpam-5560	165	7	n	n	CCONJ
ejpam-5560	165	8	,	,	PUNCT
ejpam-5560	165	9	∥	∥	PROPN
ejpam-5560	165	10	fn(t	fn(t	X
ejpam-5560	165	11	)	)	PUNCT
ejpam-5560	165	12	∥≤	∥≤	PROPN
ejpam-5560	165	13	m	m	VERB
ejpam-5560	165	14	∥	∥	NOUN
ejpam-5560	165	15	x	x	PUNCT
ejpam-5560	165	16	∥	∥	NUM
ejpam-5560	165	17	eω1	eω1	NOUN
ejpam-5560	165	18	t	t	NOUN
ejpam-5560	165	19	,	,	PUNCT
ejpam-5560	165	20	so	so	ADV
ejpam-5560	165	21	for	for	ADP
ejpam-5560	165	22	all	all	DET
ejpam-5560	165	23	t	t	PROPN
ejpam-5560	165	24	≥	≥	NOUN
ejpam-5560	165	25	0	0	NUM
ejpam-5560	165	26	∥	∥	PRON
ejpam-5560	165	27	(	(	PUNCT
ejpam-5560	165	28	fn(t))n∈n	fn(t))n∈n	PROPN
ejpam-5560	165	29	∥∞≤	∥∞≤	PROPN
ejpam-5560	165	30	m	m	VERB
ejpam-5560	165	31	∥	∥	NOUN
ejpam-5560	165	32	x	x	SYM
ejpam-5560	165	33	∥	∥	NOUN
ejpam-5560	165	34	eω1	eω1	NOUN
ejpam-5560	165	35	t	t	NOUN
ejpam-5560	165	36	<	<	X
ejpam-5560	165	37	+	+	NOUN
ejpam-5560	165	38	∞	∞	PROPN
ejpam-5560	165	39	,	,	PUNCT
ejpam-5560	165	40	therfore	therfore	ADP
ejpam-5560	165	41	the	the	DET
ejpam-5560	165	42	function	function	NOUN
ejpam-5560	165	43	f	f	PROPN
ejpam-5560	165	44	is	be	AUX
ejpam-5560	165	45	well	well	ADV
ejpam-5560	165	46	defined	define	VERB
ejpam-5560	165	47	,	,	PUNCT
ejpam-5560	165	48	and	and	CCONJ
ejpam-5560	165	49	since	since	SCONJ
ejpam-5560	165	50	the	the	DET
ejpam-5560	165	51	sequence	sequence	NOUN
ejpam-5560	165	52	(	(	PUNCT
ejpam-5560	165	53	fn)n∈n	fn)n∈n	NUM
ejpam-5560	165	54	is	be	AUX
ejpam-5560	165	55	equicontinuous	equicontinuous	ADJ
ejpam-5560	165	56	,	,	PUNCT
ejpam-5560	165	57	the	the	DET
ejpam-5560	165	58	function	function	NOUN
ejpam-5560	165	59	f	f	PROPN
ejpam-5560	165	60	is	be	AUX
ejpam-5560	165	61	continuous	continuous	ADJ
ejpam-5560	165	62	.	.	PUNCT
ejpam-5560	166	1	•	•	NUM
ejpam-5560	166	2	b	b	X
ejpam-5560	166	3	)	)	PUNCT
ejpam-5560	166	4	f	f	PROPN
ejpam-5560	166	5	has	have	VERB
ejpam-5560	166	6	value	value	NOUN
ejpam-5560	166	7	in	in	ADP
ejpam-5560	166	8	c(e	c(e	NOUN
ejpam-5560	166	9	)	)	PUNCT
ejpam-5560	166	10	.	.	PUNCT
ejpam-5560	167	1	let	let	VERB
ejpam-5560	167	2	λ	λ	PROPN
ejpam-5560	167	3	in	in	ADP
ejpam-5560	167	4	]	]	PUNCT
ejpam-5560	167	5	ω1,+∞	ω1,+∞	PROPN
ejpam-5560	167	6	[	[	NOUN
ejpam-5560	167	7	.	.	PUNCT
ejpam-5560	168	1	we	we	PRON
ejpam-5560	168	2	now	now	ADV
ejpam-5560	168	3	have	have	AUX
ejpam-5560	168	4	theorem	theorem	VERB
ejpam-5560	168	5	1	1	NUM
ejpam-5560	168	6	,	,	PUNCT
ejpam-5560	168	7	for	for	ADP
ejpam-5560	168	8	all	all	DET
ejpam-5560	168	9	n	n	PRON
ejpam-5560	168	10	∈	∈	PROPN
ejpam-5560	168	11	n	n	CCONJ
ejpam-5560	168	12	,	,	PUNCT
ejpam-5560	168	13	fn(λ	fn(λ	NUM
ejpam-5560	168	14	)	)	PUNCT
ejpam-5560	169	1	=	=	PUNCT
ejpam-5560	169	2	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	169	3	2	2	NUM
ejpam-5560	169	4	,	,	PUNCT
ejpam-5560	169	5	an)x	an)x	PROPN
ejpam-5560	169	6	=	=	SYM
ejpam-5560	169	7	∫	∫	PROPN
ejpam-5560	170	1	+	+	NUM
ejpam-5560	170	2	∞	∞	PROPN
ejpam-5560	170	3	0	0	NUM
ejpam-5560	170	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	170	5	=	=	PUNCT
ejpam-5560	171	1	∫	∫	PROPN
ejpam-5560	172	1	+	+	NUM
ejpam-5560	172	2	∞	∞	PROPN
ejpam-5560	172	3	0	0	PUNCT
ejpam-5560	172	4	e−λtfn(t)dt	e−λtfn(t)dt	ADV
ejpam-5560	173	1	,	,	PUNCT
ejpam-5560	173	2	y.	y.	PROPN
ejpam-5560	173	3	bajjou	bajjou	PROPN
ejpam-5560	173	4	,	,	PUNCT
ejpam-5560	173	5	a.	a.	PROPN
ejpam-5560	173	6	el	el	PROPN
ejpam-5560	173	7	amrani	amrani	PROPN
ejpam-5560	173	8	,	,	PUNCT
ejpam-5560	173	9	a.	a.	PROPN
ejpam-5560	173	10	blali	blali	PROPN
ejpam-5560	173	11	/	/	SYM
ejpam-5560	173	12	eur	eur	PROPN
ejpam-5560	173	13	.	.	PUNCT
ejpam-5560	174	1	j.	j.	PROPN
ejpam-5560	174	2	pure	pure	PROPN
ejpam-5560	174	3	appl	appl	PROPN
ejpam-5560	174	4	.	.	PROPN
ejpam-5560	174	5	math	math	PROPN
ejpam-5560	174	6	,	,	PUNCT
ejpam-5560	174	7	18	18	NUM
ejpam-5560	174	8	(	(	PUNCT
ejpam-5560	174	9	1	1	NUM
ejpam-5560	174	10	)	)	PUNCT
ejpam-5560	174	11	(	(	PUNCT
ejpam-5560	174	12	2025	2025	NUM
ejpam-5560	174	13	)	)	PUNCT
ejpam-5560	174	14	,	,	PUNCT
ejpam-5560	174	15	5560	5560	NUM
ejpam-5560	174	16	9	9	NUM
ejpam-5560	174	17	of	of	ADP
ejpam-5560	174	18	15	15	NUM
ejpam-5560	174	19	so	so	ADV
ejpam-5560	174	20	for	for	ADP
ejpam-5560	174	21	all	all	PRON
ejpam-5560	174	22	n	n	PRON
ejpam-5560	174	23	∈	∈	PROPN
ejpam-5560	174	24	n	n	CCONJ
ejpam-5560	174	25	,	,	PUNCT
ejpam-5560	174	26	∥	∥	PROPN
ejpam-5560	174	27	fn(λ	fn(λ	NOUN
ejpam-5560	174	28	)	)	PUNCT
ejpam-5560	174	29	∥≤	∥≤	VERB
ejpam-5560	174	30	m∥x∥	m∥x∥	PROPN
ejpam-5560	174	31	λ−ω	λ−ω	NOUN
ejpam-5560	174	32	,	,	PUNCT
ejpam-5560	174	33	therefore	therefore	ADV
ejpam-5560	174	34	∥	∥	PROPN
ejpam-5560	174	35	f	f	X
ejpam-5560	174	36	(	(	PUNCT
ejpam-5560	174	37	λ	λ	NOUN
ejpam-5560	174	38	)	)	PUNCT
ejpam-5560	174	39	∥∞	∥∞	NOUN
ejpam-5560	174	40	=	=	SYM
ejpam-5560	174	41	∥	∥	NOUN
ejpam-5560	174	42	(	(	PUNCT
ejpam-5560	174	43	fn(λ))n∈n	fn(λ))n∈n	NOUN
ejpam-5560	174	44	∥∞	∥∞	ADJ
ejpam-5560	175	1	≤	≤	NUM
ejpam-5560	175	2	m	m	VERB
ejpam-5560	175	3	∥	∥	NUM
ejpam-5560	175	4	x	x	PUNCT
ejpam-5560	175	5	∥	∥	X
ejpam-5560	175	6	λ−	λ−	PROPN
ejpam-5560	175	7	ω1	ω1	PROPN
ejpam-5560	175	8	<	<	X
ejpam-5560	175	9	+	+	PROPN
ejpam-5560	175	10	∞	∞	PROPN
ejpam-5560	175	11	,	,	PUNCT
ejpam-5560	175	12	and	and	CCONJ
ejpam-5560	175	13	by	by	ADP
ejpam-5560	175	14	hypothesis	hypothesis	NOUN
ejpam-5560	175	15	lim	lim	PROPN
ejpam-5560	175	16	n→+∞	n→+∞	PROPN
ejpam-5560	175	17	fn(λ	fn(λ	PROPN
ejpam-5560	175	18	)	)	PUNCT
ejpam-5560	176	1	=	=	VERB
ejpam-5560	176	2	lim	lim	PROPN
ejpam-5560	176	3	n→+∞	n→+∞	VERB
ejpam-5560	176	4	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	176	5	2	2	NUM
ejpam-5560	176	6	,	,	PUNCT
ejpam-5560	176	7	an)x	an)x	PROPN
ejpam-5560	176	8	=	=	SYM
ejpam-5560	176	9	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	176	10	2	2	NUM
ejpam-5560	176	11	,	,	PUNCT
ejpam-5560	176	12	a)x	a)x	NUM
ejpam-5560	176	13	which	which	PRON
ejpam-5560	176	14	give	give	VERB
ejpam-5560	176	15	f	f	PROPN
ejpam-5560	176	16	(	(	PUNCT
ejpam-5560	176	17	λ	λ	NOUN
ejpam-5560	176	18	)	)	PUNCT
ejpam-5560	176	19	∈	∈	PROPN
ejpam-5560	176	20	c(e	c(e	NOUN
ejpam-5560	176	21	)	)	PUNCT
ejpam-5560	176	22	.	.	PUNCT
ejpam-5560	177	1	•	•	NUM
ejpam-5560	177	2	c	c	X
ejpam-5560	177	3	)	)	PUNCT
ejpam-5560	178	1	f	f	PROPN
ejpam-5560	178	2	∈	∈	PROPN
ejpam-5560	178	3	c∞(]ω1,+∞	c∞(]ω1,+∞	VERB
ejpam-5560	178	4	[	[	X
ejpam-5560	178	5	,	,	PUNCT
ejpam-5560	178	6	l∞(e	l∞(e	NOUN
ejpam-5560	178	7	)	)	PUNCT
ejpam-5560	178	8	)	)	PUNCT
ejpam-5560	178	9	and	and	CCONJ
ejpam-5560	178	10	for	for	ADP
ejpam-5560	178	11	all	all	DET
ejpam-5560	178	12	k	k	PROPN
ejpam-5560	178	13	∈	∈	PROPN
ejpam-5560	178	14	n	n	X
ejpam-5560	178	15	for	for	ADP
ejpam-5560	178	16	all	all	DET
ejpam-5560	178	17	λ	λ	PROPN
ejpam-5560	178	18	>	>	X
ejpam-5560	178	19	ω1	ω1	PROPN
ejpam-5560	178	20	f	f	PROPN
ejpam-5560	178	21	(	(	PUNCT
ejpam-5560	178	22	k)(λ	k)(λ	NOUN
ejpam-5560	178	23	)	)	PUNCT
ejpam-5560	178	24	∈	∈	PROPN
ejpam-5560	178	25	c(e	c(e	NOUN
ejpam-5560	178	26	)	)	PUNCT
ejpam-5560	178	27	.	.	PUNCT
ejpam-5560	179	1	let	let	VERB
ejpam-5560	179	2	t	t	NOUN
ejpam-5560	179	3	and	and	CCONJ
ejpam-5560	179	4	h	h	NOUN
ejpam-5560	179	5	be	be	AUX
ejpam-5560	179	6	a	a	DET
ejpam-5560	179	7	positive	positive	ADJ
ejpam-5560	179	8	reals	real	NOUN
ejpam-5560	179	9	.	.	PUNCT
ejpam-5560	180	1	for	for	ADP
ejpam-5560	180	2	all	all	DET
ejpam-5560	180	3	n	n	PRON
ejpam-5560	180	4	∈	∈	NOUN
ejpam-5560	180	5	n	n	CCONJ
ejpam-5560	180	6	we	we	PRON
ejpam-5560	180	7	have	have	VERB
ejpam-5560	180	8	∥	∥	PRON
ejpam-5560	180	9	gn(t	gn(t	X
ejpam-5560	180	10	)	)	PUNCT
ejpam-5560	180	11	∥	∥	PUNCT
ejpam-5560	180	12	≤	≤	NUM
ejpam-5560	181	1	∫	∫	PROPN
ejpam-5560	181	2	t	t	NOUN
ejpam-5560	181	3	0	0	NUM
ejpam-5560	181	4	(	(	PUNCT
ejpam-5560	181	5	t−	t−	PROPN
ejpam-5560	181	6	s	s	PART
ejpam-5560	181	7	)	)	PUNCT
ejpam-5560	181	8	∥	∥	NOUN
ejpam-5560	181	9	fn(s	fn(	NOUN
ejpam-5560	181	10	)	)	PUNCT
ejpam-5560	181	11	∥	∥	PUNCT
ejpam-5560	182	1	ds	ds	ADJ
ejpam-5560	182	2	≤	≤	NUM
ejpam-5560	182	3	m	m	VERB
ejpam-5560	182	4	∥	∥	X
ejpam-5560	182	5	x	x	PUNCT
ejpam-5560	182	6	∥	∥	NOUN
ejpam-5560	182	7	ω	ω	NUM
ejpam-5560	182	8	teωt	teωt	NOUN
ejpam-5560	182	9	≤	≤	NUM
ejpam-5560	182	10	m	m	VERB
ejpam-5560	182	11	∥	∥	X
ejpam-5560	182	12	x	x	PUNCT
ejpam-5560	182	13	∥	∥	PUNCT
ejpam-5560	182	14	ω	ω	NUM
ejpam-5560	182	15	e(ω+1)t	e(ω+1)t	PROPN
ejpam-5560	182	16	≤	≤	NUM
ejpam-5560	182	17	m	m	VERB
ejpam-5560	182	18	∥	∥	NUM
ejpam-5560	182	19	x	x	PUNCT
ejpam-5560	182	20	∥	∥	NOUN
ejpam-5560	182	21	ω	ω	NUM
ejpam-5560	182	22	eω1	eω1	NOUN
ejpam-5560	182	23	t.	t.	ADJ
ejpam-5560	182	24	so	so	ADV
ejpam-5560	182	25	∥	∥	PUNCT
ejpam-5560	182	26	g(t	g(t	PROPN
ejpam-5560	182	27	)	)	PUNCT
ejpam-5560	183	1	∥∞=∥	∥∞=∥	PROPN
ejpam-5560	183	2	(	(	PUNCT
ejpam-5560	183	3	gn(t))n∈n	gn(t))n∈n	NOUN
ejpam-5560	183	4	∥∞≤	∥∞≤	PROPN
ejpam-5560	183	5	m∥x∥	m∥x∥	PROPN
ejpam-5560	183	6	ω	ω	NUM
ejpam-5560	183	7	eω1	eω1	VERB
ejpam-5560	183	8	t	t	NOUN
ejpam-5560	183	9	<	<	X
ejpam-5560	184	1	+	+	X
ejpam-5560	184	2	∞	∞	PROPN
ejpam-5560	184	3	which	which	PRON
ejpam-5560	184	4	gives	give	VERB
ejpam-5560	184	5	that	that	DET
ejpam-5560	184	6	g(t	g(t	PROPN
ejpam-5560	184	7	)	)	PUNCT
ejpam-5560	184	8	∈	∈	PROPN
ejpam-5560	184	9	l∞(e	l∞(e	NOUN
ejpam-5560	184	10	)	)	PUNCT
ejpam-5560	184	11	.	.	PUNCT
ejpam-5560	185	1	and	and	CCONJ
ejpam-5560	185	2	for	for	ADP
ejpam-5560	185	3	all	all	PRON
ejpam-5560	185	4	n	n	PRON
ejpam-5560	185	5	∈	∈	NOUN
ejpam-5560	185	6	n	n	CCONJ
ejpam-5560	185	7	:	:	PUNCT
ejpam-5560	185	8	∥	∥	NUM
ejpam-5560	185	9	gn(t+	gn(t+	PROPN
ejpam-5560	185	10	h)−	h)−	PROPN
ejpam-5560	185	11	gn(t	gn(t	PUNCT
ejpam-5560	185	12	)	)	PUNCT
ejpam-5560	185	13	∥	∥	X
ejpam-5560	185	14	=	=	PUNCT
ejpam-5560	186	1	∥	∥	NUM
ejpam-5560	186	2	∫	∫	NOUN
ejpam-5560	186	3	t+h	t+h	X
ejpam-5560	186	4	t	t	PROPN
ejpam-5560	186	5	(	(	PUNCT
ejpam-5560	186	6	t−	t−	PROPN
ejpam-5560	186	7	s)fn(s)ds+	s)fn(s)ds+	PROPN
ejpam-5560	186	8	h	h	NOUN
ejpam-5560	186	9	∫	∫	PROPN
ejpam-5560	186	10	t+h	t+h	NUM
ejpam-5560	186	11	0	0	NUM
ejpam-5560	186	12	fn(s)ds	fn(s)ds	VERB
ejpam-5560	186	13	∥	∥	PUNCT
ejpam-5560	186	14	≤	≤	NUM
ejpam-5560	186	15	h	h	NOUN
ejpam-5560	186	16	{	{	PUNCT
ejpam-5560	186	17	∫	∫	PROPN
ejpam-5560	186	18	t+h	t+h	X
ejpam-5560	186	19	t	t	PROPN
ejpam-5560	186	20	∥	∥	NUM
ejpam-5560	186	21	fn(s	fn(s	X
ejpam-5560	186	22	)	)	PUNCT
ejpam-5560	186	23	∥	∥	PUNCT
ejpam-5560	186	24	ds+	ds+	ADJ
ejpam-5560	186	25	∫	∫	PROPN
ejpam-5560	186	26	t+h	t+h	NUM
ejpam-5560	186	27	0	0	NUM
ejpam-5560	186	28	∥	∥	X
ejpam-5560	186	29	fn(s	fn(	NOUN
ejpam-5560	186	30	)	)	PUNCT
ejpam-5560	186	31	∥	∥	PUNCT
ejpam-5560	186	32	ds	ds	ADJ
ejpam-5560	186	33	}	}	PUNCT
ejpam-5560	186	34	≤	≤	NOUN
ejpam-5560	186	35	2hm	2hm	NOUN
ejpam-5560	186	36	∥	∥	PUNCT
ejpam-5560	186	37	x	x	PUNCT
ejpam-5560	186	38	∥	∥	PUNCT
ejpam-5560	186	39	ω1	ω1	X
ejpam-5560	186	40	eω1(t+h	eω1(t+h	ADJ
ejpam-5560	186	41	)	)	PUNCT
ejpam-5560	186	42	.	.	PUNCT
ejpam-5560	187	1	so	so	ADV
ejpam-5560	187	2	∥	∥	NUM
ejpam-5560	187	3	g(t+	g(t+	ADJ
ejpam-5560	187	4	h)−	h)−	PROPN
ejpam-5560	187	5	g(t	g(t	PROPN
ejpam-5560	187	6	)	)	PUNCT
ejpam-5560	187	7	∥≤	∥≤	VERB
ejpam-5560	187	8	2hm∥x∥	2hm∥x∥	NUM
ejpam-5560	187	9	ω	ω	NUM
ejpam-5560	187	10	eω(t+h	eω(t+h	PROPN
ejpam-5560	187	11	)	)	PUNCT
ejpam-5560	187	12	,	,	PUNCT
ejpam-5560	187	13	from	from	ADP
ejpam-5560	187	14	where	where	SCONJ
ejpam-5560	187	15	g	g	PROPN
ejpam-5560	187	16	is	be	AUX
ejpam-5560	187	17	continuous	continuous	ADJ
ejpam-5560	187	18	at	at	ADP
ejpam-5560	187	19	t.	t.	PROPN
ejpam-5560	188	1	so	so	SCONJ
ejpam-5560	188	2	the	the	DET
ejpam-5560	188	3	function	function	NOUN
ejpam-5560	188	4	g	g	NOUN
ejpam-5560	188	5	is	be	AUX
ejpam-5560	188	6	well	well	ADV
ejpam-5560	188	7	defined	define	VERB
ejpam-5560	188	8	and	and	CCONJ
ejpam-5560	188	9	continuous	continuous	ADJ
ejpam-5560	188	10	.	.	PUNCT
ejpam-5560	189	1	on	on	ADP
ejpam-5560	189	2	the	the	DET
ejpam-5560	189	3	other	other	ADJ
ejpam-5560	189	4	hand	hand	NOUN
ejpam-5560	189	5	,	,	PUNCT
ejpam-5560	189	6	the	the	DET
ejpam-5560	189	7	function	function	NOUN
ejpam-5560	189	8	i	i	PROPN
ejpam-5560	189	9	d	d	PROPN
ejpam-5560	189	10	:	:	PUNCT
ejpam-5560	189	11	r+	r+	NOUN
ejpam-5560	189	12	→	→	SYM
ejpam-5560	189	13	r+	r+	X
ejpam-5560	189	14	,	,	PUNCT
ejpam-5560	189	15	t	t	PROPN
ejpam-5560	189	16	7→	7→	NUM
ejpam-5560	189	17	t	t	NOUN
ejpam-5560	189	18	is	be	AUX
ejpam-5560	189	19	continuous	continuous	ADJ
ejpam-5560	189	20	and	and	CCONJ
ejpam-5560	189	21	for	for	ADP
ejpam-5560	189	22	all	all	DET
ejpam-5560	189	23	λ	λ	PROPN
ejpam-5560	189	24	>	>	X
ejpam-5560	189	25	0	0	NUM
ejpam-5560	190	1	we	we	PRON
ejpam-5560	190	2	have	have	VERB
ejpam-5560	190	3	l(id)(λ	l(id)(λ	NOUN
ejpam-5560	190	4	)	)	PUNCT
ejpam-5560	191	1	=	=	PUNCT
ejpam-5560	191	2	∫	∫	PROPN
ejpam-5560	192	1	+	+	NUM
ejpam-5560	192	2	∞	∞	NOUN
ejpam-5560	192	3	0	0	NUM
ejpam-5560	192	4	e−λssds	e−λssds	NOUN
ejpam-5560	193	1	=	=	SYM
ejpam-5560	193	2	∫	∫	PROPN
ejpam-5560	194	1	+	+	NUM
ejpam-5560	194	2	∞	∞	PROPN
ejpam-5560	194	3	0	0	PUNCT
ejpam-5560	194	4	se−λsds	se−λsds	NOUN
ejpam-5560	194	5	=	=	SYM
ejpam-5560	194	6	l(id)(λ	l(id)(λ	PROPN
ejpam-5560	194	7	)	)	PUNCT
ejpam-5560	194	8	=	=	SYM
ejpam-5560	195	1	1	1	NUM
ejpam-5560	195	2	λ2	λ2	NOUN
ejpam-5560	195	3	,	,	PUNCT
ejpam-5560	195	4	then	then	ADV
ejpam-5560	195	5	the	the	DET
ejpam-5560	195	6	proposition	proposition	NOUN
ejpam-5560	195	7	1.6.4	1.6.4	NUM
ejpam-5560	195	8	from	from	ADP
ejpam-5560	195	9	[	[	X
ejpam-5560	195	10	1	1	NUM
ejpam-5560	195	11	]	]	PUNCT
ejpam-5560	195	12	give	give	VERB
ejpam-5560	195	13	l(id	l(id	PROPN
ejpam-5560	195	14	∗	∗	NOUN
ejpam-5560	195	15	f)(λ	f)(λ	NOUN
ejpam-5560	195	16	)	)	PUNCT
ejpam-5560	195	17	exists	exist	VERB
ejpam-5560	195	18	for	for	ADP
ejpam-5560	195	19	all	all	DET
ejpam-5560	195	20	λ	λ	PROPN
ejpam-5560	195	21	>	>	X
ejpam-5560	195	22	ω1	ω1	PROPN
ejpam-5560	195	23	and	and	CCONJ
ejpam-5560	195	24	l(id	l(id	PROPN
ejpam-5560	195	25	∗	∗	NOUN
ejpam-5560	195	26	f)(λ	f)(λ	NOUN
ejpam-5560	195	27	)	)	PUNCT
ejpam-5560	195	28	=	=	SYM
ejpam-5560	195	29	l(id)(λ)l(f)(λ	l(id)(λ)l(f)(λ	PROPN
ejpam-5560	195	30	)	)	PUNCT
ejpam-5560	195	31	y.	y.	PROPN
ejpam-5560	195	32	bajjou	bajjou	PROPN
ejpam-5560	195	33	,	,	PUNCT
ejpam-5560	195	34	a.	a.	PROPN
ejpam-5560	195	35	el	el	PROPN
ejpam-5560	195	36	amrani	amrani	PROPN
ejpam-5560	195	37	,	,	PUNCT
ejpam-5560	195	38	a.	a.	PROPN
ejpam-5560	195	39	blali	blali	PROPN
ejpam-5560	195	40	/	/	SYM
ejpam-5560	195	41	eur	eur	PROPN
ejpam-5560	195	42	.	.	PUNCT
ejpam-5560	196	1	j.	j.	PROPN
ejpam-5560	196	2	pure	pure	PROPN
ejpam-5560	196	3	appl	appl	PROPN
ejpam-5560	196	4	.	.	PROPN
ejpam-5560	196	5	math	math	PROPN
ejpam-5560	196	6	,	,	PUNCT
ejpam-5560	196	7	18	18	NUM
ejpam-5560	196	8	(	(	PUNCT
ejpam-5560	196	9	1	1	NUM
ejpam-5560	196	10	)	)	PUNCT
ejpam-5560	196	11	(	(	PUNCT
ejpam-5560	196	12	2025	2025	NUM
ejpam-5560	196	13	)	)	PUNCT
ejpam-5560	196	14	,	,	PUNCT
ejpam-5560	196	15	5560	5560	NUM
ejpam-5560	196	16	10	10	NUM
ejpam-5560	196	17	of	of	ADP
ejpam-5560	196	18	15	15	NUM
ejpam-5560	196	19	=	=	SYM
ejpam-5560	196	20	1	1	NUM
ejpam-5560	196	21	λ2	λ2	NOUN
ejpam-5560	196	22	l(f)(λ	l(f)(λ	NOUN
ejpam-5560	196	23	)	)	PUNCT
ejpam-5560	196	24	=	=	SYM
ejpam-5560	197	1	1	1	NUM
ejpam-5560	197	2	λ2	λ2	NOUN
ejpam-5560	197	3	∫	∫	PROPN
ejpam-5560	198	1	+	+	ADJ
ejpam-5560	198	2	∞	∞	NOUN
ejpam-5560	198	3	0	0	NUM
ejpam-5560	198	4	e−λtf(t)dt	e−λtf(t)dt	PUNCT
ejpam-5560	198	5	=	=	SYM
ejpam-5560	198	6	1	1	NUM
ejpam-5560	198	7	λ2	λ2	NOUN
ejpam-5560	198	8	∫	∫	PROPN
ejpam-5560	199	1	+	+	ADJ
ejpam-5560	199	2	∞	∞	PROPN
ejpam-5560	199	3	0	0	PUNCT
ejpam-5560	200	1	(	(	PUNCT
ejpam-5560	200	2	e−λtfn(t))n∈ndt	e−λtfn(t))n∈ndt	PROPN
ejpam-5560	200	3	=	=	SYM
ejpam-5560	200	4	1	1	NUM
ejpam-5560	200	5	λ2	λ2	NOUN
ejpam-5560	200	6	(	(	PUNCT
ejpam-5560	200	7	∫	∫	PROPN
ejpam-5560	201	1	+	+	NOUN
ejpam-5560	201	2	∞	∞	NOUN
ejpam-5560	201	3	0	0	PUNCT
ejpam-5560	202	1	e−λtfn(t)dt)n∈n	e−λtfn(t)dt)n∈n	PUNCT
ejpam-5560	202	2	=	=	SYM
ejpam-5560	202	3	1	1	NUM
ejpam-5560	202	4	λ2	λ2	NOUN
ejpam-5560	202	5	(	(	PUNCT
ejpam-5560	202	6	fn(λ)n∈n	fn(λ)n∈n	NOUN
ejpam-5560	202	7	=	=	SYM
ejpam-5560	202	8	1	1	NUM
ejpam-5560	202	9	λ2	λ2	NOUN
ejpam-5560	202	10	f	f	X
ejpam-5560	202	11	(	(	PUNCT
ejpam-5560	202	12	λ	λ	NOUN
ejpam-5560	202	13	)	)	PUNCT
ejpam-5560	202	14	,	,	PUNCT
ejpam-5560	202	15	but	but	CCONJ
ejpam-5560	202	16	l(id	l(id	PROPN
ejpam-5560	202	17	∗	∗	NOUN
ejpam-5560	202	18	f)(λ	f)(λ	NOUN
ejpam-5560	202	19	)	)	PUNCT
ejpam-5560	202	20	=	=	PUNCT
ejpam-5560	203	1	∫	∫	PROPN
ejpam-5560	204	1	+	+	NUM
ejpam-5560	204	2	∞	∞	PROPN
ejpam-5560	204	3	0	0	NUM
ejpam-5560	204	4	e−λt(id	e−λt(id	PROPN
ejpam-5560	204	5	∗	∗	NOUN
ejpam-5560	204	6	f)(t)dt	f)(t)dt	NOUN
ejpam-5560	204	7	=	=	PUNCT
ejpam-5560	204	8	∫	∫	PROPN
ejpam-5560	205	1	+	+	NUM
ejpam-5560	205	2	∞	∞	PROPN
ejpam-5560	205	3	0	0	NUM
ejpam-5560	205	4	e−λt	e−λt	PROPN
ejpam-5560	205	5	∫	∫	PROPN
ejpam-5560	205	6	t	t	PROPN
ejpam-5560	205	7	0	0	NUM
ejpam-5560	205	8	(	(	PUNCT
ejpam-5560	205	9	t−	t−	DET
ejpam-5560	205	10	s)f(s)dsdt	s)f(s)dsdt	NOUN
ejpam-5560	205	11	=	=	SYM
ejpam-5560	205	12	∫	∫	PROPN
ejpam-5560	206	1	+	+	ADJ
ejpam-5560	206	2	∞	∞	PROPN
ejpam-5560	206	3	0	0	NUM
ejpam-5560	206	4	e−λtg(t)dt	e−λtg(t)dt	PROPN
ejpam-5560	206	5	=	=	SYM
ejpam-5560	206	6	l(g)(λ	l(g)(λ	PROPN
ejpam-5560	206	7	)	)	PUNCT
ejpam-5560	206	8	from	from	ADP
ejpam-5560	206	9	which	which	PRON
ejpam-5560	206	10	follows	follow	VERB
ejpam-5560	206	11	the	the	DET
ejpam-5560	206	12	equality	equality	NOUN
ejpam-5560	206	13	f	f	X
ejpam-5560	206	14	(	(	PUNCT
ejpam-5560	206	15	λ	λ	NOUN
ejpam-5560	206	16	)	)	PUNCT
ejpam-5560	206	17	=	=	SYM
ejpam-5560	206	18	λ2l(g)(λ	λ2l(g)(λ	NOUN
ejpam-5560	206	19	)	)	PUNCT
ejpam-5560	206	20	,	,	PUNCT
ejpam-5560	206	21	according	accord	VERB
ejpam-5560	206	22	to	to	ADP
ejpam-5560	206	23	theorem	theorem	ADJ
ejpam-5560	206	24	1.5.1	1.5.1	NUM
ejpam-5560	206	25	of	of	ADP
ejpam-5560	206	26	[	[	X
ejpam-5560	206	27	1	1	NUM
ejpam-5560	206	28	]	]	PUNCT
ejpam-5560	206	29	,	,	PUNCT
ejpam-5560	206	30	l(g	l(g	PROPN
ejpam-5560	206	31	)	)	PUNCT
ejpam-5560	206	32	(	(	PUNCT
ejpam-5560	206	33	so	so	ADV
ejpam-5560	206	34	f	f	X
ejpam-5560	206	35	)	)	PUNCT
ejpam-5560	206	36	is	be	AUX
ejpam-5560	206	37	infinitely	infinitely	ADV
ejpam-5560	206	38	differentiable	differentiable	ADJ
ejpam-5560	206	39	on	on	ADP
ejpam-5560	206	40	]	]	PUNCT
ejpam-5560	206	41	ω1,+∞	ω1,+∞	PROPN
ejpam-5560	206	42	[	[	PUNCT
ejpam-5560	206	43	and	and	CCONJ
ejpam-5560	206	44	since	since	SCONJ
ejpam-5560	206	45	c(e	c(e	NOUN
ejpam-5560	206	46	)	)	PUNCT
ejpam-5560	206	47	is	be	AUX
ejpam-5560	206	48	closed	close	VERB
ejpam-5560	206	49	of	of	ADP
ejpam-5560	206	50	l∞(e	l∞(e	NOUN
ejpam-5560	206	51	)	)	PUNCT
ejpam-5560	206	52	then	then	ADV
ejpam-5560	206	53	for	for	ADP
ejpam-5560	206	54	all	all	DET
ejpam-5560	206	55	k	k	PROPN
ejpam-5560	206	56	∈	∈	PROPN
ejpam-5560	206	57	n	n	CCONJ
ejpam-5560	206	58	,	,	PUNCT
ejpam-5560	206	59	for	for	ADP
ejpam-5560	206	60	all	all	DET
ejpam-5560	206	61	λ	λ	PRON
ejpam-5560	206	62	∈]ω1,+∞	∈]ω1,+∞	ADJ
ejpam-5560	206	63	[	[	X
ejpam-5560	206	64	,	,	PUNCT
ejpam-5560	206	65	f	f	PROPN
ejpam-5560	206	66	(	(	PUNCT
ejpam-5560	206	67	k)(λ	k)(λ	NOUN
ejpam-5560	206	68	)	)	PUNCT
ejpam-5560	206	69	∈	∈	PROPN
ejpam-5560	206	70	c(e	c(e	NOUN
ejpam-5560	206	71	)	)	PUNCT
ejpam-5560	206	72	.	.	PUNCT
ejpam-5560	207	1	•	•	NUM
ejpam-5560	207	2	d	d	X
ejpam-5560	207	3	)	)	PUNCT
ejpam-5560	208	1	lim	lim	PROPN
ejpam-5560	208	2	n→+∞	n→+∞	PROPN
ejpam-5560	208	3	cn(t)xdt	cn(t)xdt	PROPN
ejpam-5560	208	4	=	=	PUNCT
ejpam-5560	208	5	c(t)x	c(t)x	PROPN
ejpam-5560	208	6	.	.	PUNCT
ejpam-5560	209	1	we	we	PRON
ejpam-5560	209	2	have	have	VERB
ejpam-5560	209	3	for	for	ADP
ejpam-5560	209	4	all	all	DET
ejpam-5560	209	5	t	t	PROPN
ejpam-5560	209	6	>	>	X
ejpam-5560	209	7	0	0	NUM
ejpam-5560	209	8	,	,	PUNCT
ejpam-5560	209	9	there	there	PRON
ejpam-5560	209	10	exist	exist	VERB
ejpam-5560	209	11	kt	kt	PROPN
ejpam-5560	209	12	∈	∈	PROPN
ejpam-5560	209	13	n	n	CCONJ
ejpam-5560	209	14	:	:	PUNCT
ejpam-5560	209	15	for	for	ADP
ejpam-5560	209	16	all	all	DET
ejpam-5560	209	17	k	k	PROPN
ejpam-5560	209	18	≥	≥	X
ejpam-5560	209	19	kt	kt	PROPN
ejpam-5560	209	20	,	,	PUNCT
ejpam-5560	209	21	(	(	PUNCT
ejpam-5560	209	22	−1)k	−1)k	PROPN
ejpam-5560	209	23	1	1	NUM
ejpam-5560	209	24	k	k	NOUN
ejpam-5560	209	25	!	!	PUNCT
ejpam-5560	210	1	(	(	PUNCT
ejpam-5560	210	2	k	k	PROPN
ejpam-5560	210	3	t	t	PROPN
ejpam-5560	210	4	)	)	PUNCT
ejpam-5560	210	5	k+1f	k+1f	PROPN
ejpam-5560	210	6	(	(	PUNCT
ejpam-5560	210	7	k	k	NOUN
ejpam-5560	210	8	)	)	PUNCT
ejpam-5560	210	9	(	(	PUNCT
ejpam-5560	210	10	k	k	PROPN
ejpam-5560	210	11	t	t	PROPN
ejpam-5560	210	12	)	)	PUNCT
ejpam-5560	210	13	∈	∈	PROPN
ejpam-5560	210	14	c(e	c(e	NOUN
ejpam-5560	210	15	)	)	PUNCT
ejpam-5560	210	16	,	,	PUNCT
ejpam-5560	210	17	it	it	PRON
ejpam-5560	210	18	is	be	AUX
ejpam-5560	210	19	that	that	SCONJ
ejpam-5560	210	20	for	for	ADP
ejpam-5560	210	21	all	all	DET
ejpam-5560	210	22	t	t	PROPN
ejpam-5560	210	23	>	>	X
ejpam-5560	210	24	0	0	PUNCT
ejpam-5560	211	1	there	there	PRON
ejpam-5560	211	2	is	be	VERB
ejpam-5560	211	3	kt	kt	PROPN
ejpam-5560	211	4	∈	∈	PROPN
ejpam-5560	211	5	n	n	PRON
ejpam-5560	211	6	such	such	ADJ
ejpam-5560	211	7	that	that	SCONJ
ejpam-5560	211	8	(	(	PUNCT
ejpam-5560	211	9	(	(	PUNCT
ejpam-5560	211	10	−1)k	−1)k	PROPN
ejpam-5560	211	11	1	1	NUM
ejpam-5560	211	12	k	k	NOUN
ejpam-5560	211	13	!	!	PUNCT
ejpam-5560	212	1	(	(	PUNCT
ejpam-5560	212	2	k	k	PROPN
ejpam-5560	212	3	t	t	PROPN
ejpam-5560	212	4	)	)	PUNCT
ejpam-5560	212	5	k+1f	k+1f	PROPN
ejpam-5560	212	6	(	(	PUNCT
ejpam-5560	212	7	k	k	NOUN
ejpam-5560	212	8	)	)	PUNCT
ejpam-5560	212	9	(	(	PUNCT
ejpam-5560	212	10	k	k	PROPN
ejpam-5560	212	11	t	t	PROPN
ejpam-5560	212	12	)	)	PUNCT
ejpam-5560	212	13	)	)	PUNCT
ejpam-5560	212	14	k≥kt	k≥kt	PROPN
ejpam-5560	212	15	is	be	AUX
ejpam-5560	212	16	a	a	DET
ejpam-5560	212	17	sequence	sequence	NOUN
ejpam-5560	212	18	of	of	ADP
ejpam-5560	212	19	elements	element	NOUN
ejpam-5560	212	20	of	of	ADP
ejpam-5560	212	21	c(e	c(e	NOUN
ejpam-5560	212	22	)	)	PUNCT
ejpam-5560	212	23	.	.	PUNCT
ejpam-5560	213	1	f	f	PROPN
ejpam-5560	213	2	is	be	AUX
ejpam-5560	213	3	continuous	continuous	ADJ
ejpam-5560	213	4	on	on	ADP
ejpam-5560	213	5	r+	r+	X
ejpam-5560	213	6	,	,	PUNCT
ejpam-5560	213	7	so	so	ADV
ejpam-5560	213	8	each	each	DET
ejpam-5560	213	9	t	t	PROPN
ejpam-5560	213	10	>	>	X
ejpam-5560	213	11	0	0	PUNCT
ejpam-5560	213	12	is	be	AUX
ejpam-5560	213	13	a	a	DET
ejpam-5560	213	14	lebesgue	lebesgue	ADJ
ejpam-5560	213	15	point	point	NOUN
ejpam-5560	213	16	of	of	ADP
ejpam-5560	213	17	f	f	PROPN
ejpam-5560	213	18	,	,	PUNCT
ejpam-5560	213	19	the	the	DET
ejpam-5560	213	20	post	post	ADJ
ejpam-5560	213	21	-	-	ADJ
ejpam-5560	213	22	widder	widder	ADJ
ejpam-5560	213	23	theorem	theorem	NOUN
ejpam-5560	213	24	(	(	PUNCT
ejpam-5560	213	25	see	see	INTJ
ejpam-5560	213	26	theorem	theorem	VERB
ejpam-5560	213	27	1.7.7	1.7.7	NUM
ejpam-5560	213	28	of	of	ADP
ejpam-5560	213	29	[	[	X
ejpam-5560	213	30	1	1	NUM
ejpam-5560	213	31	]	]	PUNCT
ejpam-5560	213	32	)	)	PUNCT
ejpam-5560	213	33	give	give	VERB
ejpam-5560	213	34	for	for	ADP
ejpam-5560	213	35	t	t	PROPN
ejpam-5560	213	36	>	>	X
ejpam-5560	213	37	0	0	PUNCT
ejpam-5560	213	38	f(t	f(t	NOUN
ejpam-5560	213	39	)	)	PUNCT
ejpam-5560	213	40	=	=	SYM
ejpam-5560	213	41	lim	lim	PROPN
ejpam-5560	213	42	k→+∞	k→+∞	PROPN
ejpam-5560	213	43	(	(	PUNCT
ejpam-5560	213	44	−1)k	−1)k	PROPN
ejpam-5560	213	45	1	1	NUM
ejpam-5560	213	46	k	k	NOUN
ejpam-5560	213	47	!	!	PUNCT
ejpam-5560	214	1	(	(	PUNCT
ejpam-5560	214	2	k	k	PROPN
ejpam-5560	214	3	t	t	PROPN
ejpam-5560	214	4	)	)	PUNCT
ejpam-5560	214	5	k+1f̂	k+1f̂	PROPN
ejpam-5560	214	6	(	(	PUNCT
ejpam-5560	214	7	k	k	NOUN
ejpam-5560	214	8	)	)	PUNCT
ejpam-5560	214	9	(	(	PUNCT
ejpam-5560	214	10	k	k	PROPN
ejpam-5560	214	11	t	t	PROPN
ejpam-5560	214	12	)	)	PUNCT
ejpam-5560	215	1	=	=	SYM
ejpam-5560	215	2	lim	lim	PROPN
ejpam-5560	215	3	k→+∞	k→+∞	PROPN
ejpam-5560	215	4	(	(	PUNCT
ejpam-5560	215	5	−1)k	−1)k	PROPN
ejpam-5560	215	6	1	1	NUM
ejpam-5560	215	7	k	k	NOUN
ejpam-5560	215	8	!	!	PUNCT
ejpam-5560	216	1	(	(	PUNCT
ejpam-5560	216	2	k	k	PROPN
ejpam-5560	216	3	t	t	PROPN
ejpam-5560	216	4	)	)	PUNCT
ejpam-5560	216	5	k+1f	k+1f	PROPN
ejpam-5560	216	6	(	(	PUNCT
ejpam-5560	216	7	k	k	NOUN
ejpam-5560	216	8	)	)	PUNCT
ejpam-5560	216	9	(	(	PUNCT
ejpam-5560	216	10	k	k	PROPN
ejpam-5560	216	11	t	t	PROPN
ejpam-5560	216	12	)	)	PUNCT
ejpam-5560	216	13	.	.	PUNCT
ejpam-5560	217	1	but	but	CCONJ
ejpam-5560	217	2	c(e	c(e	NOUN
ejpam-5560	217	3	)	)	PUNCT
ejpam-5560	217	4	is	be	AUX
ejpam-5560	217	5	closed	close	VERB
ejpam-5560	217	6	then	then	ADV
ejpam-5560	217	7	f(t	f(t	NOUN
ejpam-5560	217	8	)	)	PUNCT
ejpam-5560	218	1	=	=	NOUN
ejpam-5560	218	2	(	(	PUNCT
ejpam-5560	218	3	fn(t))n∈n	fn(t))n∈n	PROPN
ejpam-5560	218	4	∈	∈	PROPN
ejpam-5560	218	5	c(e	c(e	NOUN
ejpam-5560	218	6	)	)	PUNCT
ejpam-5560	218	7	therefore	therefore	ADV
ejpam-5560	218	8	lim	lim	PROPN
ejpam-5560	218	9	n→+∞	n→+∞	PROPN
ejpam-5560	218	10	fn(t	fn(t	X
ejpam-5560	218	11	)	)	PUNCT
ejpam-5560	218	12	exist	exist	VERB
ejpam-5560	218	13	and	and	CCONJ
ejpam-5560	218	14	this	this	DET
ejpam-5560	218	15	y.	y.	PROPN
ejpam-5560	218	16	bajjou	bajjou	PROPN
ejpam-5560	218	17	,	,	PUNCT
ejpam-5560	218	18	a.	a.	PROPN
ejpam-5560	218	19	el	el	PROPN
ejpam-5560	218	20	amrani	amrani	PROPN
ejpam-5560	218	21	,	,	PUNCT
ejpam-5560	218	22	a.	a.	PROPN
ejpam-5560	218	23	blali	blali	PROPN
ejpam-5560	218	24	/	/	SYM
ejpam-5560	218	25	eur	eur	PROPN
ejpam-5560	218	26	.	.	PUNCT
ejpam-5560	219	1	j.	j.	PROPN
ejpam-5560	219	2	pure	pure	PROPN
ejpam-5560	219	3	appl	appl	PROPN
ejpam-5560	219	4	.	.	PROPN
ejpam-5560	219	5	math	math	PROPN
ejpam-5560	219	6	,	,	PUNCT
ejpam-5560	219	7	18	18	NUM
ejpam-5560	219	8	(	(	PUNCT
ejpam-5560	219	9	1	1	NUM
ejpam-5560	219	10	)	)	PUNCT
ejpam-5560	219	11	(	(	PUNCT
ejpam-5560	219	12	2025	2025	NUM
ejpam-5560	219	13	)	)	PUNCT
ejpam-5560	219	14	,	,	PUNCT
ejpam-5560	219	15	5560	5560	NUM
ejpam-5560	219	16	11	11	NUM
ejpam-5560	219	17	of	of	ADP
ejpam-5560	219	18	15	15	NUM
ejpam-5560	219	19	for	for	ADP
ejpam-5560	219	20	all	all	DET
ejpam-5560	219	21	t	t	NOUN
ejpam-5560	219	22	>	>	X
ejpam-5560	219	23	0	0	PROPN
ejpam-5560	220	1	but	but	CCONJ
ejpam-5560	220	2	fn(0	fn(0	PROPN
ejpam-5560	220	3	)	)	PUNCT
ejpam-5560	220	4	=	=	SYM
ejpam-5560	220	5	cn(0	cn(0	NOUN
ejpam-5560	220	6	)	)	PUNCT
ejpam-5560	220	7	)	)	PUNCT
ejpam-5560	221	1	=	=	PUNCT
ejpam-5560	221	2	0	0	NUM
ejpam-5560	221	3	,	,	PUNCT
ejpam-5560	221	4	then	then	ADV
ejpam-5560	221	5	if	if	SCONJ
ejpam-5560	221	6	we	we	PRON
ejpam-5560	221	7	noted	note	VERB
ejpam-5560	221	8	by	by	ADP
ejpam-5560	221	9	h	h	PROPN
ejpam-5560	221	10	the	the	DET
ejpam-5560	221	11	function	function	NOUN
ejpam-5560	221	12	h	h	NOUN
ejpam-5560	221	13	:	:	PUNCT
ejpam-5560	221	14	r+	r+	X
ejpam-5560	221	15	→	→	SYM
ejpam-5560	221	16	e	e	X
ejpam-5560	221	17	,	,	PUNCT
ejpam-5560	221	18	t	t	PROPN
ejpam-5560	221	19	7→	7→	NUM
ejpam-5560	221	20	h(t	h(t	NUM
ejpam-5560	221	21	)	)	PUNCT
ejpam-5560	222	1	=	=	PRON
ejpam-5560	222	2	{	{	PUNCT
ejpam-5560	222	3	lim	lim	PROPN
ejpam-5560	222	4	k→+∞	k→+∞	PROPN
ejpam-5560	222	5	fn(t	fn(t	PUNCT
ejpam-5560	222	6	)	)	PUNCT
ejpam-5560	222	7	,	,	PUNCT
ejpam-5560	222	8	t	t	PROPN
ejpam-5560	222	9	>	>	X
ejpam-5560	222	10	0	0	NUM
ejpam-5560	222	11	;	;	PUNCT
ejpam-5560	222	12	0	0	NUM
ejpam-5560	222	13	,	,	PUNCT
ejpam-5560	222	14	t=0	t=0	X
ejpam-5560	222	15	.	.	PUNCT
ejpam-5560	223	1	then	then	ADV
ejpam-5560	223	2	(	(	PUNCT
ejpam-5560	223	3	fn)n∈n	fn)n∈n	NUM
ejpam-5560	223	4	is	be	AUX
ejpam-5560	223	5	a	a	DET
ejpam-5560	223	6	sequence	sequence	NOUN
ejpam-5560	223	7	of	of	ADP
ejpam-5560	223	8	equicontinuous	equicontinuous	ADJ
ejpam-5560	223	9	functions	function	NOUN
ejpam-5560	223	10	which	which	PRON
ejpam-5560	223	11	converges	converge	VERB
ejpam-5560	223	12	pointwise	pointwise	VERB
ejpam-5560	223	13	to	to	ADP
ejpam-5560	223	14	h	h	NOUN
ejpam-5560	223	15	,	,	PUNCT
ejpam-5560	223	16	then	then	ADV
ejpam-5560	223	17	h	h	NOUN
ejpam-5560	223	18	is	be	AUX
ejpam-5560	223	19	continuous	continuous	ADJ
ejpam-5560	223	20	in	in	ADP
ejpam-5560	223	21	r+	r+	X
ejpam-5560	223	22	.	.	PUNCT
ejpam-5560	224	1	the	the	DET
ejpam-5560	224	2	convergence	convergence	NOUN
ejpam-5560	224	3	dominate	dominate	VERB
ejpam-5560	224	4	theorem	theorem	NOUN
ejpam-5560	224	5	give	give	VERB
ejpam-5560	224	6	that	that	SCONJ
ejpam-5560	224	7	lim	lim	PROPN
ejpam-5560	224	8	n→+∞	n→+∞	VERB
ejpam-5560	224	9	∫	∫	PROPN
ejpam-5560	225	1	+	+	PROPN
ejpam-5560	225	2	∞	∞	PROPN
ejpam-5560	225	3	0	0	NUM
ejpam-5560	225	4	e−λtcn(t)xdt	e−λtcn(t)xdt	NOUN
ejpam-5560	225	5	=	=	SYM
ejpam-5560	225	6	∫	∫	PROPN
ejpam-5560	226	1	+	+	NUM
ejpam-5560	226	2	∞	∞	PROPN
ejpam-5560	226	3	0	0	NUM
ejpam-5560	227	1	e−λth(t)dt	e−λth(t)dt	PROPN
ejpam-5560	227	2	,	,	PUNCT
ejpam-5560	227	3	but	but	CCONJ
ejpam-5560	227	4	lim	lim	PROPN
ejpam-5560	227	5	n→+∞	n→+∞	VERB
ejpam-5560	227	6	∫	∫	PROPN
ejpam-5560	228	1	+	+	PROPN
ejpam-5560	228	2	∞	∞	PROPN
ejpam-5560	228	3	0	0	NUM
ejpam-5560	228	4	e−λtcn(t)xdt	e−λtcn(t)xdt	PROPN
ejpam-5560	228	5	=	=	PROPN
ejpam-5560	228	6	lim	lim	PROPN
ejpam-5560	228	7	n→+∞	n→+∞	VERB
ejpam-5560	228	8	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	228	9	2	2	NUM
ejpam-5560	228	10	,	,	PUNCT
ejpam-5560	228	11	an)x	an)x	PROPN
ejpam-5560	228	12	=	=	SYM
ejpam-5560	228	13	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	228	14	2	2	NUM
ejpam-5560	228	15	,	,	PUNCT
ejpam-5560	228	16	a)x	a)x	X
ejpam-5560	228	17	,	,	PUNCT
ejpam-5560	228	18	then	then	ADV
ejpam-5560	228	19	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	228	20	2	2	NUM
ejpam-5560	228	21	,	,	PUNCT
ejpam-5560	228	22	a)x	a)x	PUNCT
ejpam-5560	228	23	=	=	PUNCT
ejpam-5560	229	1	∫	∫	PROPN
ejpam-5560	230	1	+	+	NUM
ejpam-5560	230	2	∞	∞	PROPN
ejpam-5560	230	3	0	0	NUM
ejpam-5560	231	1	e−λth(t)dt	e−λth(t)dt	PROPN
ejpam-5560	231	2	,	,	PUNCT
ejpam-5560	231	3	but	but	CCONJ
ejpam-5560	231	4	{	{	PUNCT
ejpam-5560	231	5	λ2	λ2	NOUN
ejpam-5560	231	6	:	:	PUNCT
ejpam-5560	231	7	λ	λ	X
ejpam-5560	231	8	>	>	X
ejpam-5560	231	9	ω1	ω1	PROPN
ejpam-5560	231	10	and	and	CCONJ
ejpam-5560	231	11	l(k)(λ	l(k)(λ	NUM
ejpam-5560	231	12	)	)	PUNCT
ejpam-5560	231	13	̸=	̸=	NOUN
ejpam-5560	231	14	0	0	NUM
ejpam-5560	231	15	}	}	PUNCT
ejpam-5560	231	16	⊂	⊂	PRON
ejpam-5560	231	17	ρc(a	ρc(a	NOUN
ejpam-5560	231	18	)	)	PUNCT
ejpam-5560	231	19	,	,	PUNCT
ejpam-5560	231	20	then	then	ADV
ejpam-5560	231	21	by	by	ADP
ejpam-5560	231	22	the	the	DET
ejpam-5560	231	23	properties	property	NOUN
ejpam-5560	231	24	1.(b	1.(b	NUM
ejpam-5560	231	25	)	)	PUNCT
ejpam-5560	231	26	and	and	CCONJ
ejpam-5560	231	27	1.(c	1.(c	NUM
ejpam-5560	231	28	)	)	PUNCT
ejpam-5560	231	29	,	,	PUNCT
ejpam-5560	231	30	we	we	PRON
ejpam-5560	231	31	can	can	AUX
ejpam-5560	231	32	deduce	deduce	VERB
ejpam-5560	231	33	that	that	SCONJ
ejpam-5560	231	34	h	h	NOUN
ejpam-5560	231	35	is	be	AUX
ejpam-5560	231	36	k	k	ADJ
ejpam-5560	231	37	-	-	ADJ
ejpam-5560	231	38	convoluted	convoluted	ADJ
ejpam-5560	231	39	c	c	NOUN
ejpam-5560	231	40	-	-	ADJ
ejpam-5560	231	41	cosine	cosine	ADJ
ejpam-5560	231	42	function	function	NOUN
ejpam-5560	231	43	generated	generate	VERB
ejpam-5560	231	44	by	by	ADP
ejpam-5560	231	45	a	a	PRON
ejpam-5560	231	46	,	,	PUNCT
ejpam-5560	231	47	and	and	CCONJ
ejpam-5560	231	48	like	like	INTJ
ejpam-5560	231	49	(	(	PUNCT
ejpam-5560	231	50	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	231	51	is	be	AUX
ejpam-5560	231	52	uniquely	uniquely	ADV
ejpam-5560	231	53	determined	determine	VERB
ejpam-5560	231	54	by	by	ADP
ejpam-5560	231	55	one	one	NUM
ejpam-5560	231	56	of	of	ADP
ejpam-5560	231	57	its	its	PRON
ejpam-5560	231	58	subgenerators	subgenerator	NOUN
ejpam-5560	231	59	,	,	PUNCT
ejpam-5560	231	60	then	then	ADV
ejpam-5560	231	61	h	h	X
ejpam-5560	231	62	(	(	PUNCT
ejpam-5560	231	63	.	.	PUNCT
ejpam-5560	231	64	)	)	PUNCT
ejpam-5560	232	1	=	=	SYM
ejpam-5560	232	2	c(.)x	c(.)x	PROPN
ejpam-5560	232	3	,	,	PUNCT
ejpam-5560	232	4	it	it	PRON
ejpam-5560	232	5	is	be	AUX
ejpam-5560	232	6	lim	lim	PROPN
ejpam-5560	232	7	n→+∞	n→+∞	PROPN
ejpam-5560	232	8	cn(t)x	cn(t)x	PROPN
ejpam-5560	232	9	=	=	SYM
ejpam-5560	232	10	c(t)x	c(t)x	PROPN
ejpam-5560	232	11	,	,	PUNCT
ejpam-5560	232	12	and	and	CCONJ
ejpam-5560	232	13	this	this	PRON
ejpam-5560	232	14	for	for	ADP
ejpam-5560	232	15	all	all	DET
ejpam-5560	232	16	t	t	PROPN
ejpam-5560	232	17	≥	≥	NOUN
ejpam-5560	232	18	0	0	NUM
ejpam-5560	232	19	.	.	PUNCT
ejpam-5560	233	1	(	(	PUNCT
ejpam-5560	233	2	ii	ii	NOUN
ejpam-5560	233	3	)	)	PUNCT
ejpam-5560	233	4	let	let	VERB
ejpam-5560	233	5	h	h	NOUN
ejpam-5560	233	6	be	be	AUX
ejpam-5560	233	7	a	a	DET
ejpam-5560	233	8	compact	compact	NOUN
ejpam-5560	233	9	of	of	ADP
ejpam-5560	233	10	[	[	X
ejpam-5560	233	11	0,+∞	0,+∞	NUM
ejpam-5560	233	12	[	[	PUNCT
ejpam-5560	233	13	and	and	CCONJ
ejpam-5560	234	1	x	x	SYM
ejpam-5560	234	2	∈	∈	PROPN
ejpam-5560	234	3	e.	e.	PROPN
ejpam-5560	234	4	like	like	ADP
ejpam-5560	234	5	h	h	PROPN
ejpam-5560	234	6	⊂	⊂	PROPN
ejpam-5560	235	1	[	[	X
ejpam-5560	235	2	0	0	NUM
ejpam-5560	235	3	,	,	PUNCT
ejpam-5560	235	4	sup	sup	NOUN
ejpam-5560	235	5	(	(	PUNCT
ejpam-5560	235	6	h	h	NOUN
ejpam-5560	235	7	)	)	PUNCT
ejpam-5560	235	8	]	]	PUNCT
ejpam-5560	235	9	then	then	ADV
ejpam-5560	235	10	it	it	PRON
ejpam-5560	235	11	suffices	suffice	VERB
ejpam-5560	235	12	to	to	PART
ejpam-5560	235	13	prove	prove	VERB
ejpam-5560	235	14	that	that	SCONJ
ejpam-5560	235	15	the	the	DET
ejpam-5560	235	16	convergence	convergence	NOUN
ejpam-5560	235	17	is	be	AUX
ejpam-5560	235	18	uniform	uniform	ADJ
ejpam-5560	235	19	on	on	ADP
ejpam-5560	235	20	the	the	DET
ejpam-5560	235	21	compact	compact	ADJ
ejpam-5560	235	22	[	[	X
ejpam-5560	235	23	0	0	NUM
ejpam-5560	235	24	,	,	PUNCT
ejpam-5560	235	25	sup(h	sup(h	PROPN
ejpam-5560	235	26	)	)	PUNCT
ejpam-5560	235	27	]	]	PUNCT
ejpam-5560	235	28	.	.	PUNCT
ejpam-5560	236	1	for	for	ADP
ejpam-5560	236	2	that	that	PRON
ejpam-5560	236	3	let	let	VERB
ejpam-5560	236	4	ε	ε	PROPN
ejpam-5560	236	5	>	>	X
ejpam-5560	236	6	0	0	PROPN
ejpam-5560	236	7	,	,	PUNCT
ejpam-5560	236	8	(	(	PUNCT
ejpam-5560	236	9	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	236	10	is	be	AUX
ejpam-5560	236	11	equicontinuous	equicontinuous	ADJ
ejpam-5560	236	12	at	at	ADV
ejpam-5560	236	13	all	all	ADV
ejpam-5560	236	14	t	t	NOUN
ejpam-5560	236	15	∈	∈	PROPN
ejpam-5560	237	1	[	[	X
ejpam-5560	237	2	0,+∞	0,+∞	NUM
ejpam-5560	237	3	[	[	PUNCT
ejpam-5560	237	4	so	so	ADV
ejpam-5560	237	5	(	(	PUNCT
ejpam-5560	237	6	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	237	7	is	be	AUX
ejpam-5560	237	8	equicontinuous	equicontinuous	ADJ
ejpam-5560	237	9	in	in	ADP
ejpam-5560	237	10	[	[	X
ejpam-5560	237	11	0	0	NUM
ejpam-5560	237	12	,	,	PUNCT
ejpam-5560	237	13	sup(h	sup(h	PROPN
ejpam-5560	237	14	)	)	PUNCT
ejpam-5560	237	15	]	]	PUNCT
ejpam-5560	237	16	which	which	PRON
ejpam-5560	237	17	is	be	AUX
ejpam-5560	237	18	compact	compact	ADJ
ejpam-5560	237	19	,	,	PUNCT
ejpam-5560	237	20	then	then	ADV
ejpam-5560	237	21	(	(	PUNCT
ejpam-5560	237	22	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	237	23	is	be	AUX
ejpam-5560	237	24	uniformly	uniformly	ADV
ejpam-5560	237	25	equicontinuous	equicontinuous	ADJ
ejpam-5560	237	26	in	in	ADP
ejpam-5560	237	27	[	[	X
ejpam-5560	237	28	0	0	NUM
ejpam-5560	237	29	,	,	PUNCT
ejpam-5560	237	30	sup(h	sup(h	PROPN
ejpam-5560	237	31	)	)	PUNCT
ejpam-5560	237	32	]	]	PUNCT
ejpam-5560	237	33	which	which	PRON
ejpam-5560	237	34	implies	imply	VERB
ejpam-5560	237	35	the	the	DET
ejpam-5560	237	36	existence	existence	NOUN
ejpam-5560	237	37	of	of	ADP
ejpam-5560	237	38	η	η	PROPN
ejpam-5560	237	39	>	>	X
ejpam-5560	237	40	0	0	NUM
ejpam-5560	237	41	such	such	ADJ
ejpam-5560	237	42	that	that	PRON
ejpam-5560	237	43	(	(	PUNCT
ejpam-5560	237	44	∀s	∀s	PROPN
ejpam-5560	237	45	,	,	PUNCT
ejpam-5560	237	46	t	t	PROPN
ejpam-5560	237	47	≥	≥	NUM
ejpam-5560	237	48	0	0	NUM
ejpam-5560	237	49	)	)	PUNCT
ejpam-5560	237	50	|	|	ADV
ejpam-5560	237	51	t−	t−	PROPN
ejpam-5560	237	52	s	s	VERB
ejpam-5560	237	53	|	|	NOUN
ejpam-5560	237	54	<	<	X
ejpam-5560	237	55	η	η	PROPN
ejpam-5560	237	56	=	=	PROPN
ejpam-5560	237	57	⇒	⇒	X
ejpam-5560	237	58	(	(	PUNCT
ejpam-5560	237	59	∀n	∀n	NUM
ejpam-5560	237	60	∈	∈	PROPN
ejpam-5560	237	61	n	n	CCONJ
ejpam-5560	237	62	)	)	PUNCT
ejpam-5560	237	63	∥	∥	NOUN
ejpam-5560	237	64	cn(t)x−	cn(t)x−	NOUN
ejpam-5560	237	65	cn(s)x	cn(s)x	VERB
ejpam-5560	237	66	∥	∥	X
ejpam-5560	237	67	<	<	X
ejpam-5560	237	68	ε	ε	PROPN
ejpam-5560	237	69	3	3	NUM
ejpam-5560	237	70	.	.	PUNCT
ejpam-5560	238	1	(	(	PUNCT
ejpam-5560	238	2	4	4	NUM
ejpam-5560	238	3	)	)	PUNCT
ejpam-5560	238	4	for	for	ADP
ejpam-5560	238	5	n0	n0	X
ejpam-5560	238	6	=	=	SYM
ejpam-5560	238	7	⌊	⌊	PROPN
ejpam-5560	238	8	sup(h	sup(h	PROPN
ejpam-5560	238	9	)	)	PUNCT
ejpam-5560	238	10	η	η	PROPN
ejpam-5560	238	11	⌋+1	⌋+1	PROPN
ejpam-5560	238	12	∈	∈	PROPN
ejpam-5560	238	13	n∗	n∗	PROPN
ejpam-5560	238	14	,	,	PUNCT
ejpam-5560	238	15	we	we	PRON
ejpam-5560	238	16	have	have	VERB
ejpam-5560	238	17	sup(h	sup(h	PROPN
ejpam-5560	238	18	)	)	PUNCT
ejpam-5560	238	19	n0	n0	X
ejpam-5560	238	20	<	<	X
ejpam-5560	238	21	η	η	PROPN
ejpam-5560	238	22	(	(	PUNCT
ejpam-5560	238	23	is	be	AUX
ejpam-5560	238	24	therefore	therefore	ADV
ejpam-5560	238	25	for	for	ADP
ejpam-5560	238	26	all	all	DET
ejpam-5560	238	27	n	n	PRON
ejpam-5560	238	28	≥	≥	NOUN
ejpam-5560	238	29	n0	n0	PROPN
ejpam-5560	238	30	,	,	PUNCT
ejpam-5560	238	31	sup(h	sup(h	PROPN
ejpam-5560	238	32	)	)	PUNCT
ejpam-5560	239	1	n	n	CCONJ
ejpam-5560	239	2	≤	≤	NOUN
ejpam-5560	239	3	sup(h	sup(h	PROPN
ejpam-5560	239	4	)	)	PUNCT
ejpam-5560	239	5	n0	n0	X
ejpam-5560	239	6	<	<	X
ejpam-5560	239	7	η	η	PROPN
ejpam-5560	239	8	)	)	PUNCT
ejpam-5560	239	9	.	.	PUNCT
ejpam-5560	240	1	for	for	ADP
ejpam-5560	240	2	all	all	PRON
ejpam-5560	240	3	i	i	PRON
ejpam-5560	240	4	∈	∈	PROPN
ejpam-5560	240	5	{	{	PUNCT
ejpam-5560	240	6	0	0	NUM
ejpam-5560	240	7	,	,	PUNCT
ejpam-5560	240	8	...	...	PUNCT
ejpam-5560	240	9	,	,	PUNCT
ejpam-5560	240	10	n0	n0	X
ejpam-5560	240	11	}	}	PUNCT
ejpam-5560	240	12	,	,	PUNCT
ejpam-5560	240	13	ti	ti	X
ejpam-5560	240	14	=	=	SYM
ejpam-5560	240	15	i	i	PROPN
ejpam-5560	240	16	n0	n0	X
ejpam-5560	240	17	sup(h	sup(h	PROPN
ejpam-5560	240	18	)	)	PUNCT
ejpam-5560	240	19	∈	∈	PROPN
ejpam-5560	241	1	[	[	X
ejpam-5560	241	2	0	0	NUM
ejpam-5560	241	3	,	,	PUNCT
ejpam-5560	241	4	sup(h	sup(h	PROPN
ejpam-5560	241	5	)	)	PUNCT
ejpam-5560	241	6	]	]	PUNCT
ejpam-5560	241	7	.	.	PUNCT
ejpam-5560	242	1	so	so	ADV
ejpam-5560	242	2	for	for	ADP
ejpam-5560	242	3	each	each	DET
ejpam-5560	242	4	t	t	NOUN
ejpam-5560	242	5	∈	∈	PROPN
ejpam-5560	243	1	[	[	X
ejpam-5560	243	2	0	0	NUM
ejpam-5560	243	3	,	,	PUNCT
ejpam-5560	243	4	sup(h	sup(h	PROPN
ejpam-5560	243	5	)	)	PUNCT
ejpam-5560	243	6	]	]	PUNCT
ejpam-5560	243	7	there	there	PRON
ejpam-5560	243	8	is	be	VERB
ejpam-5560	243	9	i	i	PROPN
ejpam-5560	243	10	∈	∈	PROPN
ejpam-5560	243	11	{	{	PUNCT
ejpam-5560	243	12	0	0	NUM
ejpam-5560	243	13	,	,	PUNCT
ejpam-5560	243	14	...	...	PUNCT
ejpam-5560	243	15	,	,	PUNCT
ejpam-5560	243	16	n0	n0	ADJ
ejpam-5560	243	17	−	−	NOUN
ejpam-5560	243	18	1	1	NUM
ejpam-5560	243	19	}	}	PUNCT
ejpam-5560	243	20	such	such	ADJ
ejpam-5560	243	21	that	that	SCONJ
ejpam-5560	243	22	ti	ti	PROPN
ejpam-5560	243	23	≤	≤	X
ejpam-5560	243	24	t	t	PROPN
ejpam-5560	243	25	≤	≤	NUM
ejpam-5560	243	26	ti+1	ti+1	NOUN
ejpam-5560	243	27	.	.	PUNCT
ejpam-5560	244	1	for	for	ADP
ejpam-5560	244	2	all	all	PRON
ejpam-5560	244	3	i	i	PRON
ejpam-5560	244	4	∈	∈	PROPN
ejpam-5560	244	5	{	{	PUNCT
ejpam-5560	244	6	1	1	NUM
ejpam-5560	244	7	,	,	PUNCT
ejpam-5560	244	8	...	...	PUNCT
ejpam-5560	244	9	,	,	PUNCT
ejpam-5560	244	10	n0	n0	X
ejpam-5560	244	11	}	}	PUNCT
ejpam-5560	244	12	,	,	PUNCT
ejpam-5560	244	13	(	(	PUNCT
ejpam-5560	244	14	cn(ti)x)n∈n	cn(ti)x)n∈n	NOUN
ejpam-5560	244	15	is	be	AUX
ejpam-5560	244	16	a	a	DET
ejpam-5560	244	17	cauchy	cauchy	ADJ
ejpam-5560	244	18	sequence	sequence	NOUN
ejpam-5560	244	19	since	since	SCONJ
ejpam-5560	244	20	it	it	PRON
ejpam-5560	244	21	is	be	AUX
ejpam-5560	244	22	convergent	convergent	ADJ
ejpam-5560	244	23	,	,	PUNCT
ejpam-5560	244	24	therefore	therefore	ADV
ejpam-5560	244	25	there	there	PRON
ejpam-5560	244	26	exist	exist	VERB
ejpam-5560	244	27	mi	mi	PROPN
ejpam-5560	244	28	∈	∈	PROPN
ejpam-5560	244	29	n∗	n∗	NOUN
ejpam-5560	244	30	such	such	ADJ
ejpam-5560	244	31	that	that	PRON
ejpam-5560	244	32	for	for	ADP
ejpam-5560	244	33	all	all	DET
ejpam-5560	244	34	n	n	CCONJ
ejpam-5560	244	35	,	,	PUNCT
ejpam-5560	244	36	m	m	VERB
ejpam-5560	244	37	≥	≥	NOUN
ejpam-5560	244	38	mi	mi	NOUN
ejpam-5560	244	39	∥	∥	X
ejpam-5560	244	40	cn(ti)x−	cn(ti)x−	PROPN
ejpam-5560	244	41	cm(ti)x	cm(ti)x	VERB
ejpam-5560	244	42	∥≤	∥≤	PROPN
ejpam-5560	244	43	ε	ε	PROPN
ejpam-5560	244	44	3	3	NUM
ejpam-5560	244	45	.	.	PUNCT
ejpam-5560	245	1	if	if	SCONJ
ejpam-5560	245	2	we	we	PRON
ejpam-5560	245	3	posed	pose	VERB
ejpam-5560	245	4	n0	n0	X
ejpam-5560	245	5	=	=	SYM
ejpam-5560	245	6	max	max	PROPN
ejpam-5560	245	7	0≤i≤n0	0≤i≤n0	PROPN
ejpam-5560	245	8	{	{	PUNCT
ejpam-5560	245	9	mi	mi	PROPN
ejpam-5560	245	10	}	}	PUNCT
ejpam-5560	245	11	,	,	PUNCT
ejpam-5560	245	12	then	then	ADV
ejpam-5560	245	13	for	for	ADP
ejpam-5560	245	14	all	all	DET
ejpam-5560	245	15	m	m	PROPN
ejpam-5560	245	16	,	,	PUNCT
ejpam-5560	245	17	n	n	PRON
ejpam-5560	245	18	≥	≥	NOUN
ejpam-5560	245	19	n0	n0	NUM
ejpam-5560	245	20	and	and	CCONJ
ejpam-5560	245	21	all	all	DET
ejpam-5560	245	22	t	t	NOUN
ejpam-5560	245	23	∈	∈	PROPN
ejpam-5560	246	1	[	[	X
ejpam-5560	246	2	0	0	NUM
ejpam-5560	246	3	,	,	PUNCT
ejpam-5560	246	4	sup(h	sup(h	PROPN
ejpam-5560	246	5	)	)	PUNCT
ejpam-5560	246	6	]	]	PUNCT
ejpam-5560	246	7	,	,	PUNCT
ejpam-5560	246	8	there	there	PRON
ejpam-5560	246	9	exist	exist	VERB
ejpam-5560	246	10	i0	i0	PROPN
ejpam-5560	246	11	∈	∈	PROPN
ejpam-5560	246	12	{	{	PUNCT
ejpam-5560	246	13	0	0	NUM
ejpam-5560	246	14	,	,	PUNCT
ejpam-5560	246	15	...	...	PUNCT
ejpam-5560	246	16	,	,	PUNCT
ejpam-5560	246	17	n0	n0	ADJ
ejpam-5560	246	18	−	−	NOUN
ejpam-5560	246	19	1	1	NUM
ejpam-5560	246	20	}	}	PUNCT
ejpam-5560	246	21	such	such	ADJ
ejpam-5560	246	22	that	that	SCONJ
ejpam-5560	246	23	ti0	ti0	PROPN
ejpam-5560	246	24	≤	≤	X
ejpam-5560	246	25	t	t	PROPN
ejpam-5560	246	26	≤	≤	NUM
ejpam-5560	246	27	ti0	ti0	PROPN
ejpam-5560	246	28	+	+	NOUN
ejpam-5560	246	29	1	1	NUM
ejpam-5560	246	30	,	,	PUNCT
ejpam-5560	246	31	and	and	CCONJ
ejpam-5560	246	32	then	then	ADV
ejpam-5560	246	33	if	if	SCONJ
ejpam-5560	246	34	an	an	PRON
ejpam-5560	246	35	,	,	PUNCT
ejpam-5560	246	36	m	m	NOUN
ejpam-5560	246	37	=	=	ADJ
ejpam-5560	246	38	∥	∥	NOUN
ejpam-5560	246	39	cn(t)x−	cn(t)x−	NOUN
ejpam-5560	246	40	cm(t)x	cm(t)x	PRON
ejpam-5560	246	41	∥	∥	NOUN
ejpam-5560	246	42	we	we	PRON
ejpam-5560	246	43	have	have	VERB
ejpam-5560	246	44	an	an	DET
ejpam-5560	246	45	,	,	PUNCT
ejpam-5560	246	46	m	m	NOUN
ejpam-5560	246	47	=	=	SYM
ejpam-5560	246	48	∥	∥	PROPN
ejpam-5560	246	49	cn(t)x−	cn(t)x−	NOUN
ejpam-5560	246	50	cn(ti0)x+	cn(ti0)x+	NOUN
ejpam-5560	246	51	cn(ti0)x−	cn(ti0)x−	NUM
ejpam-5560	246	52	cm(ti0)x+	cm(ti0)x+	NOUN
ejpam-5560	246	53	cm(ti0)x−	cm(ti0)x−	NOUN
ejpam-5560	246	54	cm(t)x	cm(t)x	PROPN
ejpam-5560	246	55	∥	∥	PROPN
ejpam-5560	246	56	y.	y.	NOUN
ejpam-5560	246	57	bajjou	bajjou	PROPN
ejpam-5560	246	58	,	,	PUNCT
ejpam-5560	246	59	a.	a.	PROPN
ejpam-5560	246	60	el	el	PROPN
ejpam-5560	246	61	amrani	amrani	PROPN
ejpam-5560	246	62	,	,	PUNCT
ejpam-5560	246	63	a.	a.	PROPN
ejpam-5560	246	64	blali	blali	PROPN
ejpam-5560	246	65	/	/	SYM
ejpam-5560	246	66	eur	eur	PROPN
ejpam-5560	246	67	.	.	PUNCT
ejpam-5560	247	1	j.	j.	PROPN
ejpam-5560	247	2	pure	pure	PROPN
ejpam-5560	247	3	appl	appl	PROPN
ejpam-5560	247	4	.	.	PROPN
ejpam-5560	247	5	math	math	PROPN
ejpam-5560	247	6	,	,	PUNCT
ejpam-5560	247	7	18	18	NUM
ejpam-5560	247	8	(	(	PUNCT
ejpam-5560	247	9	1	1	NUM
ejpam-5560	247	10	)	)	PUNCT
ejpam-5560	247	11	(	(	PUNCT
ejpam-5560	247	12	2025	2025	NUM
ejpam-5560	247	13	)	)	PUNCT
ejpam-5560	247	14	,	,	PUNCT
ejpam-5560	247	15	5560	5560	NUM
ejpam-5560	247	16	12	12	NUM
ejpam-5560	247	17	of	of	ADP
ejpam-5560	247	18	15	15	NUM
ejpam-5560	247	19	≤	≤	NUM
ejpam-5560	247	20	∥	∥	PUNCT
ejpam-5560	247	21	cn(t)x−	cn(t)x−	NOUN
ejpam-5560	247	22	cn(ti0)x	cn(ti0)x	VERB
ejpam-5560	247	23	∥	∥	X
ejpam-5560	248	1	+	+	CCONJ
ejpam-5560	248	2	∥	∥	PRON
ejpam-5560	249	1	cn(ti0)x−	cn(ti0)x−	NOUN
ejpam-5560	249	2	cm(ti0)x	cm(ti0)x	VERB
ejpam-5560	249	3	∥	∥	PRON
ejpam-5560	249	4	+	+	CCONJ
ejpam-5560	249	5	∥	∥	PRON
ejpam-5560	249	6	cm(ti0)x−	cm(ti0)x−	X
ejpam-5560	249	7	cm(t)x	cm(t)x	PROPN
ejpam-5560	249	8	∥	∥	PUNCT
ejpam-5560	249	9	≤	≤	NUM
ejpam-5560	249	10	ε	ε	PROPN
ejpam-5560	249	11	3	3	NUM
ejpam-5560	249	12	+	+	CCONJ
ejpam-5560	249	13	∥	∥	PRON
ejpam-5560	249	14	cn(ti0)x−	cn(ti0)x−	NOUN
ejpam-5560	249	15	cm(ti0)x	cm(ti0)x	VERB
ejpam-5560	249	16	∥	∥	PRON
ejpam-5560	249	17	+	+	CCONJ
ejpam-5560	249	18	∥	∥	PRON
ejpam-5560	249	19	cm(ti0)x−	cm(ti0)x−	X
ejpam-5560	249	20	cm(t)x	cm(t)x	PROPN
ejpam-5560	249	21	∥	∥	PROPN
ejpam-5560	249	22	(	(	PUNCT
ejpam-5560	249	23	because	because	SCONJ
ejpam-5560	249	24	|	|	ADV
ejpam-5560	249	25	t−	t−	PRON
ejpam-5560	249	26	ti0	ti0	NOUN
ejpam-5560	249	27	|	|	CCONJ
ejpam-5560	249	28	<	<	X
ejpam-5560	249	29	η	η	NOUN
ejpam-5560	249	30	)	)	PUNCT
ejpam-5560	249	31	≤	≤	PUNCT
ejpam-5560	249	32	ε	ε	PROPN
ejpam-5560	249	33	3	3	NUM
ejpam-5560	249	34	+	+	CCONJ
ejpam-5560	249	35	ε	ε	PROPN
ejpam-5560	249	36	3	3	NUM
ejpam-5560	249	37	+	+	CCONJ
ejpam-5560	249	38	∥	∥	PRON
ejpam-5560	249	39	cm(ti0)x−	cm(ti0)x−	X
ejpam-5560	249	40	cm(t)x	cm(t)x	PROPN
ejpam-5560	249	41	∥	∥	X
ejpam-5560	249	42	(	(	PUNCT
ejpam-5560	249	43	because	because	SCONJ
ejpam-5560	249	44	m	m	PROPN
ejpam-5560	249	45	≥	≥	PROPN
ejpam-5560	249	46	n0	n0	NUM
ejpam-5560	249	47	≥	≥	PROPN
ejpam-5560	249	48	mi	mi	PROPN
ejpam-5560	249	49	)	)	PUNCT
ejpam-5560	249	50	≤	≤	PUNCT
ejpam-5560	249	51	ε	ε	PROPN
ejpam-5560	249	52	3	3	NUM
ejpam-5560	249	53	+	+	CCONJ
ejpam-5560	249	54	ε	ε	PROPN
ejpam-5560	249	55	3	3	NUM
ejpam-5560	249	56	+	+	CCONJ
ejpam-5560	249	57	ε	ε	PROPN
ejpam-5560	249	58	3	3	NUM
ejpam-5560	249	59	(	(	PUNCT
ejpam-5560	249	60	because	because	SCONJ
ejpam-5560	249	61	|	|	ADV
ejpam-5560	249	62	t−	t−	PRON
ejpam-5560	249	63	ti0	ti0	NOUN
ejpam-5560	249	64	|	|	CCONJ
ejpam-5560	249	65	<	<	X
ejpam-5560	249	66	η	η	NOUN
ejpam-5560	249	67	)	)	PUNCT
ejpam-5560	249	68	≤	≤	PUNCT
ejpam-5560	249	69	ε	ε	PROPN
ejpam-5560	249	70	.	.	PUNCT
ejpam-5560	250	1	so	so	ADV
ejpam-5560	250	2	the	the	DET
ejpam-5560	250	3	uniform	uniform	PROPN
ejpam-5560	250	4	cauchy	cauchy	PROPN
ejpam-5560	250	5	criterion	criterion	NOUN
ejpam-5560	250	6	implies	imply	VERB
ejpam-5560	250	7	that	that	SCONJ
ejpam-5560	250	8	(	(	PUNCT
ejpam-5560	250	9	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	250	10	converge	converge	VERB
ejpam-5560	250	11	uniformly	uniformly	ADV
ejpam-5560	250	12	on	on	ADP
ejpam-5560	250	13	h	h	NOUN
ejpam-5560	250	14	towards	towards	ADP
ejpam-5560	250	15	c(.)x	c(.)x	PROPN
ejpam-5560	250	16	)	)	PUNCT
ejpam-5560	250	17	.	.	PUNCT
ejpam-5560	251	1	5	5	NUM
ejpam-5560	251	2	⇒	⇒	NOUN
ejpam-5560	251	3	1	1	NUM
ejpam-5560	251	4	|	|	ADV
ejpam-5560	251	5	let	let	VERB
ejpam-5560	251	6	x	x	X
ejpam-5560	251	7	∈	∈	PROPN
ejpam-5560	251	8	e	e	NOUN
ejpam-5560	251	9	;	;	PUNCT
ejpam-5560	251	10	like	like	INTJ
ejpam-5560	251	11	(	(	PUNCT
ejpam-5560	251	12	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	251	13	converge	converge	VERB
ejpam-5560	251	14	uniformly	uniformly	ADV
ejpam-5560	251	15	of	of	ADP
ejpam-5560	251	16	any	any	DET
ejpam-5560	251	17	compact	compact	NOUN
ejpam-5560	251	18	in	in	ADP
ejpam-5560	251	19	[	[	X
ejpam-5560	251	20	0,+∞	0,+∞	NUM
ejpam-5560	251	21	[	[	PUNCT
ejpam-5560	251	22	then	then	ADV
ejpam-5560	251	23	(	(	PUNCT
ejpam-5560	251	24	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	251	25	is	be	AUX
ejpam-5560	251	26	equicontinuous	equicontinuous	ADJ
ejpam-5560	251	27	in	in	ADP
ejpam-5560	251	28	[	[	X
ejpam-5560	251	29	0,+∞	0,+∞	PROPN
ejpam-5560	252	1	[	[	X
ejpam-5560	252	2	.	.	PUNCT
ejpam-5560	252	3	let	let	VERB
ejpam-5560	252	4	λ	λ	PROPN
ejpam-5560	252	5	>	>	X
ejpam-5560	252	6	ω1	ω1	PROPN
ejpam-5560	252	7	,	,	PUNCT
ejpam-5560	252	8	then	then	ADV
ejpam-5560	252	9	for	for	ADP
ejpam-5560	252	10	all	all	DET
ejpam-5560	252	11	n	n	DET
ejpam-5560	252	12	∈	∈	PROPN
ejpam-5560	252	13	n	n	CCONJ
ejpam-5560	252	14	,	,	PUNCT
ejpam-5560	252	15	we	we	PRON
ejpam-5560	252	16	have	have	VERB
ejpam-5560	252	17	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	NOUN
ejpam-5560	252	18	2	2	NUM
ejpam-5560	252	19	,	,	PUNCT
ejpam-5560	253	1	an)x	an)x	PROPN
ejpam-5560	253	2	=	=	SYM
ejpam-5560	253	3	∫	∫	PROPN
ejpam-5560	254	1	+	+	NUM
ejpam-5560	254	2	∞	∞	PROPN
ejpam-5560	254	3	0	0	NUM
ejpam-5560	255	1	e−λtcn(t)dt	e−λtcn(t)dt	NOUN
ejpam-5560	255	2	.	.	PUNCT
ejpam-5560	256	1	the	the	DET
ejpam-5560	256	2	convergence	convergence	NOUN
ejpam-5560	256	3	dominate	dominate	VERB
ejpam-5560	256	4	theorem	theorem	NOUN
ejpam-5560	256	5	give	give	VERB
ejpam-5560	256	6	that	that	SCONJ
ejpam-5560	256	7	lim	lim	PROPN
ejpam-5560	256	8	n→+∞	n→+∞	PROPN
ejpam-5560	256	9	λl(k)(λ)(λ)rc(λ	λl(k)(λ)(λ)rc(λ	PUNCT
ejpam-5560	256	10	2	2	NUM
ejpam-5560	256	11	,	,	PUNCT
ejpam-5560	256	12	an)x	an)x	PROPN
ejpam-5560	257	1	=	=	PROPN
ejpam-5560	257	2	lim	lim	PROPN
ejpam-5560	257	3	n→+∞	n→+∞	VERB
ejpam-5560	257	4	∫	∫	PROPN
ejpam-5560	258	1	+	+	PROPN
ejpam-5560	258	2	∞	∞	PROPN
ejpam-5560	258	3	0	0	NUM
ejpam-5560	258	4	e−λtcn(t)xdt	e−λtcn(t)xdt	NOUN
ejpam-5560	258	5	=	=	SYM
ejpam-5560	258	6	∫	∫	PROPN
ejpam-5560	259	1	+	+	NUM
ejpam-5560	259	2	∞	∞	PROPN
ejpam-5560	259	3	0	0	NUM
ejpam-5560	259	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	259	5	=	=	PUNCT
ejpam-5560	259	6	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	259	7	2	2	NUM
ejpam-5560	259	8	,	,	PUNCT
ejpam-5560	259	9	a)x	a)x	PUNCT
ejpam-5560	259	10	.	.	PUNCT
ejpam-5560	260	1	corollary	corollary	ADJ
ejpam-5560	260	2	1	1	NUM
ejpam-5560	260	3	.	.	PUNCT
ejpam-5560	261	1	let	let	VERB
ejpam-5560	261	2	(	(	PUNCT
ejpam-5560	261	3	c(t))t≥0	c(t))t≥0	NOUN
ejpam-5560	261	4	be	be	AUX
ejpam-5560	261	5	an	an	DET
ejpam-5560	261	6	α−times	α−time	NOUN
ejpam-5560	261	7	integrated	integrate	VERB
ejpam-5560	261	8	cosine	cosine	NOUN
ejpam-5560	261	9	function	function	NOUN
ejpam-5560	261	10	(	(	PUNCT
ejpam-5560	261	11	for	for	ADP
ejpam-5560	261	12	some	some	DET
ejpam-5560	261	13	α	α	PRON
ejpam-5560	261	14	≥	≥	NOUN
ejpam-5560	261	15	0	0	NUM
ejpam-5560	261	16	)	)	PUNCT
ejpam-5560	261	17	with	with	ADP
ejpam-5560	261	18	generator	generator	PROPN
ejpam-5560	261	19	a	a	NOUN
ejpam-5560	261	20	,	,	PUNCT
ejpam-5560	261	21	and	and	CCONJ
ejpam-5560	261	22	for	for	ADP
ejpam-5560	261	23	each	each	DET
ejpam-5560	261	24	n	n	PRON
ejpam-5560	261	25	∈	∈	PROPN
ejpam-5560	261	26	n	n	CCONJ
ejpam-5560	261	27	,	,	PUNCT
ejpam-5560	261	28	let	let	VERB
ejpam-5560	261	29	(	(	PUNCT
ejpam-5560	261	30	cn(t))t≥0	cn(t))t≥0	PROPN
ejpam-5560	261	31	an	an	PRON
ejpam-5560	261	32	α−times	α−time	NOUN
ejpam-5560	261	33	integrated	integrate	VERB
ejpam-5560	261	34	cosine	cosine	NOUN
ejpam-5560	261	35	function	function	NOUN
ejpam-5560	261	36	with	with	ADP
ejpam-5560	261	37	generator	generator	NOUN
ejpam-5560	261	38	(	(	PUNCT
ejpam-5560	261	39	an	an	PRON
ejpam-5560	261	40	,	,	PUNCT
ejpam-5560	261	41	d(an	d(an	NOUN
ejpam-5560	261	42	)	)	PUNCT
ejpam-5560	261	43	)	)	PUNCT
ejpam-5560	261	44	such	such	ADJ
ejpam-5560	261	45	that	that	SCONJ
ejpam-5560	261	46	:	:	PUNCT
ejpam-5560	261	47	there	there	PRON
ejpam-5560	261	48	exist	exist	VERB
ejpam-5560	261	49	ω	ω	NUM
ejpam-5560	261	50	≥	≥	NOUN
ejpam-5560	261	51	0	0	NUM
ejpam-5560	261	52	,	,	PUNCT
ejpam-5560	261	53	there	there	PRON
ejpam-5560	261	54	exist	exist	VERB
ejpam-5560	261	55	m	m	VERB
ejpam-5560	261	56	>	>	X
ejpam-5560	261	57	0	0	NUM
ejpam-5560	262	1	:	:	PUNCT
ejpam-5560	262	2	for	for	ADP
ejpam-5560	262	3	all	all	DET
ejpam-5560	262	4	t	t	PROPN
ejpam-5560	262	5	≥	≥	NOUN
ejpam-5560	262	6	0	0	NUM
ejpam-5560	262	7	,	,	PUNCT
ejpam-5560	262	8	for	for	ADP
ejpam-5560	262	9	all	all	DET
ejpam-5560	262	10	x	x	SYM
ejpam-5560	262	11	∈	∈	PROPN
ejpam-5560	262	12	e	e	NOUN
ejpam-5560	262	13	,	,	PUNCT
ejpam-5560	262	14	∥	∥	X
ejpam-5560	262	15	c(t)x	c(t)x	PROPN
ejpam-5560	262	16	)	)	PUNCT
ejpam-5560	262	17	∥≤	∥≤	NOUN
ejpam-5560	262	18	meωt	meωt	NOUN
ejpam-5560	262	19	and	and	CCONJ
ejpam-5560	262	20	for	for	ADP
ejpam-5560	262	21	all	all	DET
ejpam-5560	262	22	n	n	PRON
ejpam-5560	262	23	∈	∈	PROPN
ejpam-5560	262	24	n	n	CCONJ
ejpam-5560	262	25	)	)	PUNCT
ejpam-5560	262	26	∥	∥	NOUN
ejpam-5560	262	27	cn(t)x	cn(t)x	NOUN
ejpam-5560	262	28	)	)	PUNCT
ejpam-5560	262	29	∥≤	∥≤	PROPN
ejpam-5560	262	30	meωt	meωt	NOUN
ejpam-5560	262	31	.	.	PUNCT
ejpam-5560	263	1	then	then	ADV
ejpam-5560	263	2	if	if	SCONJ
ejpam-5560	263	3	we	we	PRON
ejpam-5560	263	4	put	put	VERB
ejpam-5560	263	5	ω1	ω1	PROPN
ejpam-5560	263	6	=	=	PUNCT
ejpam-5560	263	7	max(ω	max(ω	NOUN
ejpam-5560	263	8	+	+	CCONJ
ejpam-5560	263	9	1	1	NUM
ejpam-5560	263	10	,	,	PUNCT
ejpam-5560	263	11	abs(k	abs(k	PROPN
ejpam-5560	263	12	)	)	PUNCT
ejpam-5560	263	13	)	)	PUNCT
ejpam-5560	263	14	,	,	PUNCT
ejpam-5560	263	15	the	the	DET
ejpam-5560	263	16	following	follow	VERB
ejpam-5560	263	17	statements	statement	NOUN
ejpam-5560	263	18	are	be	AUX
ejpam-5560	263	19	equivalent	equivalent	ADJ
ejpam-5560	263	20	:	:	PUNCT
ejpam-5560	263	21	(	(	PUNCT
ejpam-5560	263	22	i	i	NOUN
ejpam-5560	263	23	)	)	PUNCT
ejpam-5560	263	24	there	there	PRON
ejpam-5560	263	25	exist	exist	VERB
ejpam-5560	263	26	λ0	λ0	NOUN
ejpam-5560	263	27	>	>	X
ejpam-5560	263	28	ω1	ω1	PROPN
ejpam-5560	263	29	such	such	ADJ
ejpam-5560	263	30	that	that	PRON
ejpam-5560	263	31	for	for	ADP
ejpam-5560	263	32	all	all	DET
ejpam-5560	263	33	x	x	SYM
ejpam-5560	263	34	∈	∈	PROPN
ejpam-5560	263	35	e	e	NOUN
ejpam-5560	263	36	,	,	PUNCT
ejpam-5560	263	37	lim	lim	PROPN
ejpam-5560	263	38	n→+∞	n→+∞	VERB
ejpam-5560	263	39	r(λ2	r(λ2	NOUN
ejpam-5560	263	40	0	0	NUM
ejpam-5560	263	41	,	,	PUNCT
ejpam-5560	263	42	an)x	an)x	PROPN
ejpam-5560	263	43	=	=	SYM
ejpam-5560	263	44	r(λ2	r(λ2	NOUN
ejpam-5560	263	45	0	0	NUM
ejpam-5560	263	46	,	,	PUNCT
ejpam-5560	263	47	a)x	a)x	PUNCT
ejpam-5560	263	48	and	and	CCONJ
ejpam-5560	263	49	(	(	PUNCT
ejpam-5560	263	50	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	263	51	is	be	AUX
ejpam-5560	263	52	equicontinuous	equicontinuous	ADJ
ejpam-5560	263	53	.	.	PUNCT
ejpam-5560	264	1	(	(	PUNCT
ejpam-5560	264	2	ii	ii	NOUN
ejpam-5560	264	3	)	)	PUNCT
ejpam-5560	264	4	there	there	PRON
ejpam-5560	264	5	exist	exist	VERB
ejpam-5560	264	6	λ0	λ0	NOUN
ejpam-5560	264	7	>	>	X
ejpam-5560	264	8	ω1	ω1	PROPN
ejpam-5560	264	9	such	such	ADJ
ejpam-5560	264	10	that	that	PRON
ejpam-5560	264	11	for	for	ADP
ejpam-5560	264	12	all	all	DET
ejpam-5560	264	13	y	y	PROPN
ejpam-5560	264	14	∈	∈	PROPN
ejpam-5560	264	15	r(c	r(c	PROPN
ejpam-5560	264	16	)	)	PUNCT
ejpam-5560	264	17	,	,	PUNCT
ejpam-5560	264	18	lim	lim	PROPN
ejpam-5560	264	19	n→+∞	n→+∞	PROPN
ejpam-5560	264	20	(	(	PUNCT
ejpam-5560	264	21	λ2i	λ2i	X
ejpam-5560	264	22	−an	−an	PROPN
ejpam-5560	264	23	)	)	PUNCT
ejpam-5560	264	24	−1y	−1y	NOUN
ejpam-5560	264	25	=	=	SYM
ejpam-5560	264	26	(	(	PUNCT
ejpam-5560	264	27	λ2i	λ2i	X
ejpam-5560	264	28	−a)−1y	−a)−1y	PROPN
ejpam-5560	264	29	and	and	CCONJ
ejpam-5560	264	30	for	for	ADP
ejpam-5560	264	31	all	all	DET
ejpam-5560	264	32	x	x	SYM
ejpam-5560	264	33	∈	∈	PROPN
ejpam-5560	264	34	e	e	NOUN
ejpam-5560	264	35	,	,	PUNCT
ejpam-5560	264	36	(	(	PUNCT
ejpam-5560	264	37	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	264	38	is	be	AUX
ejpam-5560	264	39	equicontinuous	equicontinuous	ADJ
ejpam-5560	264	40	.	.	PUNCT
ejpam-5560	265	1	y.	y.	PROPN
ejpam-5560	265	2	bajjou	bajjou	PROPN
ejpam-5560	265	3	,	,	PUNCT
ejpam-5560	265	4	a.	a.	PROPN
ejpam-5560	265	5	el	el	PROPN
ejpam-5560	265	6	amrani	amrani	PROPN
ejpam-5560	265	7	,	,	PUNCT
ejpam-5560	265	8	a.	a.	PROPN
ejpam-5560	265	9	blali	blali	PROPN
ejpam-5560	265	10	/	/	SYM
ejpam-5560	265	11	eur	eur	PROPN
ejpam-5560	265	12	.	.	PUNCT
ejpam-5560	266	1	j.	j.	PROPN
ejpam-5560	266	2	pure	pure	PROPN
ejpam-5560	266	3	appl	appl	PROPN
ejpam-5560	266	4	.	.	PROPN
ejpam-5560	266	5	math	math	PROPN
ejpam-5560	266	6	,	,	PUNCT
ejpam-5560	266	7	18	18	NUM
ejpam-5560	266	8	(	(	PUNCT
ejpam-5560	266	9	1	1	NUM
ejpam-5560	266	10	)	)	PUNCT
ejpam-5560	266	11	(	(	PUNCT
ejpam-5560	266	12	2025	2025	NUM
ejpam-5560	266	13	)	)	PUNCT
ejpam-5560	266	14	,	,	PUNCT
ejpam-5560	266	15	5560	5560	NUM
ejpam-5560	266	16	13	13	NUM
ejpam-5560	266	17	of	of	ADP
ejpam-5560	266	18	15	15	NUM
ejpam-5560	266	19	(	(	PUNCT
ejpam-5560	266	20	iii	iii	NOUN
ejpam-5560	266	21	)	)	PUNCT
ejpam-5560	266	22	for	for	ADP
ejpam-5560	266	23	all	all	DET
ejpam-5560	266	24	t	t	PROPN
ejpam-5560	266	25	≥	≥	NOUN
ejpam-5560	266	26	0	0	PUNCT
ejpam-5560	266	27	and	and	CCONJ
ejpam-5560	266	28	x	x	SYM
ejpam-5560	266	29	∈	∈	PROPN
ejpam-5560	266	30	e	e	NOUN
ejpam-5560	266	31	,	,	PUNCT
ejpam-5560	266	32	lim	lim	PROPN
ejpam-5560	266	33	n→+∞	n→+∞	PROPN
ejpam-5560	266	34	cn(t)x	cn(t)x	PROPN
ejpam-5560	266	35	=	=	SYM
ejpam-5560	266	36	c(t)x	c(t)x	PROPN
ejpam-5560	266	37	,	,	PUNCT
ejpam-5560	266	38	the	the	DET
ejpam-5560	266	39	convergence	convergence	NOUN
ejpam-5560	266	40	is	be	AUX
ejpam-5560	266	41	uniform	uniform	ADJ
ejpam-5560	266	42	on	on	ADP
ejpam-5560	266	43	any	any	DET
ejpam-5560	266	44	compact	compact	NOUN
ejpam-5560	266	45	of	of	ADP
ejpam-5560	266	46	[	[	X
ejpam-5560	266	47	0,+∞	0,+∞	PROPN
ejpam-5560	266	48	[	[	X
ejpam-5560	266	49	.	.	PUNCT
ejpam-5560	266	50	proof	proof	NOUN
ejpam-5560	266	51	.	.	PUNCT
ejpam-5560	267	1	let	let	VERB
ejpam-5560	267	2	α	α	PRON
ejpam-5560	267	3	≥	≥	NOUN
ejpam-5560	267	4	0	0	NUM
ejpam-5560	267	5	.	.	PUNCT
ejpam-5560	268	1	then	then	ADV
ejpam-5560	268	2	if	if	SCONJ
ejpam-5560	268	3	k(t	k(t	NOUN
ejpam-5560	268	4	)	)	PUNCT
ejpam-5560	268	5	=	=	SYM
ejpam-5560	268	6	tα−1	tα−1	NOUN
ejpam-5560	268	7	γ(α	γ(α	NOUN
ejpam-5560	268	8	)	)	PUNCT
ejpam-5560	268	9	and	and	CCONJ
ejpam-5560	268	10	c	c	X
ejpam-5560	268	11	=	=	SYM
ejpam-5560	268	12	i	i	PROPN
ejpam-5560	268	13	,	,	PUNCT
ejpam-5560	268	14	then	then	ADV
ejpam-5560	268	15	the	the	DET
ejpam-5560	268	16	α−times	α−time	NOUN
ejpam-5560	268	17	integrated	integrated	ADJ
ejpam-5560	268	18	cosine	cosine	NOUN
ejpam-5560	268	19	function	function	NOUN
ejpam-5560	268	20	is	be	AUX
ejpam-5560	268	21	a	a	DET
ejpam-5560	268	22	k	k	ADV
ejpam-5560	268	23	-	-	ADJ
ejpam-5560	268	24	convoluted	convoluted	ADJ
ejpam-5560	268	25	c	c	NOUN
ejpam-5560	268	26	-	-	ADJ
ejpam-5560	268	27	cosine	cosine	ADJ
ejpam-5560	268	28	function	function	NOUN
ejpam-5560	268	29	on	on	ADP
ejpam-5560	268	30	e	e	NOUN
ejpam-5560	268	31	,	,	PUNCT
ejpam-5560	268	32	thus	thus	ADV
ejpam-5560	268	33	theorem	theorem	VERB
ejpam-5560	268	34	1	1	NUM
ejpam-5560	268	35	gives	give	VERB
ejpam-5560	268	36	the	the	DET
ejpam-5560	268	37	results	result	NOUN
ejpam-5560	268	38	.	.	PUNCT
ejpam-5560	269	1	corollary	corollary	ADJ
ejpam-5560	269	2	2	2	NUM
ejpam-5560	269	3	.	.	PUNCT
ejpam-5560	270	1	let	let	VERB
ejpam-5560	270	2	(	(	PUNCT
ejpam-5560	270	3	c(t))t≥0	c(t))t≥0	NOUN
ejpam-5560	270	4	be	be	AUX
ejpam-5560	270	5	a	a	DET
ejpam-5560	270	6	k−convoluted	k−convoluted	PROPN
ejpam-5560	270	7	c−cosine	c−cosine	NOUN
ejpam-5560	270	8	function	function	NOUN
ejpam-5560	270	9	with	with	ADP
ejpam-5560	270	10	subgenerator	subgenerator	NOUN
ejpam-5560	270	11	a	a	NOUN
ejpam-5560	270	12	and	and	CCONJ
ejpam-5560	270	13	for	for	ADP
ejpam-5560	270	14	each	each	DET
ejpam-5560	270	15	n	n	PRON
ejpam-5560	270	16	∈	∈	PROPN
ejpam-5560	270	17	n	n	ADV
ejpam-5560	270	18	let	let	VERB
ejpam-5560	270	19	(	(	PUNCT
ejpam-5560	270	20	cn(t))t≥0	cn(t))t≥0	PROPN
ejpam-5560	270	21	a	a	DET
ejpam-5560	270	22	k−convoluted	k−convoluted	PROPN
ejpam-5560	270	23	c−cosine	c−cosine	PROPN
ejpam-5560	270	24	function	function	NOUN
ejpam-5560	270	25	with	with	ADP
ejpam-5560	270	26	subgenerators	subgenerator	NOUN
ejpam-5560	270	27	(	(	PUNCT
ejpam-5560	270	28	an	an	PRON
ejpam-5560	270	29	,	,	PUNCT
ejpam-5560	270	30	d(an	d(an	NOUN
ejpam-5560	270	31	)	)	PUNCT
ejpam-5560	270	32	)	)	PUNCT
ejpam-5560	270	33	such	such	ADJ
ejpam-5560	270	34	that	that	SCONJ
ejpam-5560	270	35	there	there	PRON
ejpam-5560	270	36	exist	exist	VERB
ejpam-5560	270	37	ω	ω	NUM
ejpam-5560	270	38	≥	≥	NOUN
ejpam-5560	270	39	0	0	NUM
ejpam-5560	270	40	,	,	PUNCT
ejpam-5560	270	41	there	there	PRON
ejpam-5560	270	42	exist	exist	VERB
ejpam-5560	270	43	m	m	VERB
ejpam-5560	270	44	>	>	X
ejpam-5560	270	45	0	0	NUM
ejpam-5560	271	1	:	:	PUNCT
ejpam-5560	271	2	for	for	ADP
ejpam-5560	271	3	all	all	DET
ejpam-5560	271	4	t	t	PROPN
ejpam-5560	271	5	,	,	PUNCT
ejpam-5560	271	6	h	h	PROPN
ejpam-5560	271	7	≥	≥	NOUN
ejpam-5560	271	8	0	0	NUM
ejpam-5560	271	9	,	,	PUNCT
ejpam-5560	271	10	∥	∥	X
ejpam-5560	271	11	c(t+	c(t+	NOUN
ejpam-5560	271	12	h)−	h)−	PROPN
ejpam-5560	271	13	c(t	c(t	PROPN
ejpam-5560	271	14	)	)	PUNCT
ejpam-5560	271	15	∥≤	∥≤	PROPN
ejpam-5560	271	16	mheω(t+h	mheω(t+h	NOUN
ejpam-5560	271	17	)	)	PUNCT
ejpam-5560	271	18	and	and	CCONJ
ejpam-5560	271	19	for	for	ADP
ejpam-5560	271	20	all	all	DET
ejpam-5560	271	21	n	n	PRON
ejpam-5560	271	22	∈	∈	PROPN
ejpam-5560	271	23	n	n	CCONJ
ejpam-5560	271	24	,	,	PUNCT
ejpam-5560	271	25	∥	∥	NUM
ejpam-5560	271	26	cn(t+	cn(t+	NUM
ejpam-5560	271	27	h)−	h)−	PROPN
ejpam-5560	271	28	cn(t	cn(t	PUNCT
ejpam-5560	271	29	)	)	PUNCT
ejpam-5560	271	30	∥≤	∥≤	PROPN
ejpam-5560	271	31	mheω(t+h	mheω(t+h	NOUN
ejpam-5560	271	32	)	)	PUNCT
ejpam-5560	271	33	.	.	PUNCT
ejpam-5560	272	1	then	then	ADV
ejpam-5560	272	2	if	if	SCONJ
ejpam-5560	272	3	we	we	PRON
ejpam-5560	272	4	put	put	VERB
ejpam-5560	272	5	ω1	ω1	PROPN
ejpam-5560	272	6	=	=	PUNCT
ejpam-5560	272	7	max(ω	max(ω	NOUN
ejpam-5560	272	8	+	+	CCONJ
ejpam-5560	272	9	1	1	NUM
ejpam-5560	272	10	,	,	PUNCT
ejpam-5560	272	11	abs(k	abs(k	PROPN
ejpam-5560	272	12	)	)	PUNCT
ejpam-5560	272	13	)	)	PUNCT
ejpam-5560	272	14	,	,	PUNCT
ejpam-5560	272	15	the	the	DET
ejpam-5560	272	16	following	follow	VERB
ejpam-5560	272	17	statements	statement	NOUN
ejpam-5560	272	18	are	be	AUX
ejpam-5560	272	19	equivalent	equivalent	ADJ
ejpam-5560	272	20	:	:	PUNCT
ejpam-5560	272	21	(	(	PUNCT
ejpam-5560	272	22	i	i	NOUN
ejpam-5560	272	23	)	)	PUNCT
ejpam-5560	272	24	there	there	PRON
ejpam-5560	272	25	exist	exist	VERB
ejpam-5560	272	26	λ0	λ0	NOUN
ejpam-5560	272	27	>	>	X
ejpam-5560	272	28	ω1	ω1	PROPN
ejpam-5560	272	29	such	such	ADJ
ejpam-5560	272	30	that	that	DET
ejpam-5560	272	31	l(k)(λ0	l(k)(λ0	NOUN
ejpam-5560	272	32	)	)	PUNCT
ejpam-5560	272	33	̸=	̸=	PROPN
ejpam-5560	272	34	0	0	NUM
ejpam-5560	272	35	and	and	CCONJ
ejpam-5560	272	36	for	for	ADP
ejpam-5560	272	37	all	all	DET
ejpam-5560	272	38	x	x	SYM
ejpam-5560	272	39	∈	∈	PROPN
ejpam-5560	272	40	e	e	NOUN
ejpam-5560	272	41	,	,	PUNCT
ejpam-5560	272	42	lim	lim	PROPN
ejpam-5560	272	43	n→+∞	n→+∞	PROPN
ejpam-5560	272	44	rc(λ	rc(λ	PUNCT
ejpam-5560	272	45	2	2	NUM
ejpam-5560	272	46	0	0	NUM
ejpam-5560	272	47	,	,	PUNCT
ejpam-5560	272	48	an)x	an)x	PROPN
ejpam-5560	272	49	=	=	PUNCT
ejpam-5560	272	50	rc(λ	rc(λ	PUNCT
ejpam-5560	272	51	2	2	NUM
ejpam-5560	272	52	0	0	NUM
ejpam-5560	272	53	,	,	PUNCT
ejpam-5560	272	54	a)x	a)x	PUNCT
ejpam-5560	272	55	.	.	PUNCT
ejpam-5560	273	1	(	(	PUNCT
ejpam-5560	273	2	ii	ii	NOUN
ejpam-5560	273	3	)	)	PUNCT
ejpam-5560	273	4	there	there	PRON
ejpam-5560	273	5	exist	exist	VERB
ejpam-5560	273	6	λ0	λ0	NOUN
ejpam-5560	273	7	>	>	X
ejpam-5560	273	8	ω1	ω1	PROPN
ejpam-5560	273	9	such	such	ADJ
ejpam-5560	273	10	that	that	DET
ejpam-5560	273	11	l(k)(λ0	l(k)(λ0	NOUN
ejpam-5560	273	12	)	)	PUNCT
ejpam-5560	273	13	̸=	̸=	PROPN
ejpam-5560	273	14	0	0	NUM
ejpam-5560	273	15	and	and	CCONJ
ejpam-5560	273	16	for	for	ADP
ejpam-5560	273	17	all	all	DET
ejpam-5560	273	18	y	y	PROPN
ejpam-5560	273	19	∈	∈	PROPN
ejpam-5560	273	20	r(c	r(c	PROPN
ejpam-5560	273	21	)	)	PUNCT
ejpam-5560	273	22	,	,	PUNCT
ejpam-5560	273	23	lim	lim	PROPN
ejpam-5560	273	24	n→+∞	n→+∞	PROPN
ejpam-5560	273	25	(	(	PUNCT
ejpam-5560	273	26	λ2i	λ2i	X
ejpam-5560	273	27	−an	−an	PROPN
ejpam-5560	273	28	)	)	PUNCT
ejpam-5560	273	29	−1y	−1y	NOUN
ejpam-5560	273	30	=	=	SYM
ejpam-5560	273	31	(	(	PUNCT
ejpam-5560	273	32	λ2i	λ2i	X
ejpam-5560	273	33	−a)−1y	−a)−1y	X
ejpam-5560	273	34	.	.	PUNCT
ejpam-5560	274	1	(	(	PUNCT
ejpam-5560	274	2	iii	iii	NOUN
ejpam-5560	274	3	)	)	PUNCT
ejpam-5560	274	4	for	for	ADP
ejpam-5560	274	5	all	all	DET
ejpam-5560	274	6	λ	λ	PROPN
ejpam-5560	274	7	>	>	X
ejpam-5560	274	8	ω1	ω1	PROPN
ejpam-5560	274	9	such	such	ADJ
ejpam-5560	274	10	that	that	SCONJ
ejpam-5560	274	11	l(k)(λ	l(k)(λ	NOUN
ejpam-5560	274	12	)	)	PUNCT
ejpam-5560	274	13	̸=	̸=	PROPN
ejpam-5560	274	14	0	0	NUM
ejpam-5560	274	15	)	)	PUNCT
ejpam-5560	274	16	,	,	PUNCT
ejpam-5560	274	17	for	for	ADP
ejpam-5560	274	18	all	all	DET
ejpam-5560	274	19	y	y	PROPN
ejpam-5560	274	20	∈	∈	PROPN
ejpam-5560	274	21	r(c	r(c	PROPN
ejpam-5560	274	22	)	)	PUNCT
ejpam-5560	274	23	,	,	PUNCT
ejpam-5560	274	24	lim	lim	PROPN
ejpam-5560	274	25	n→+∞	n→+∞	PROPN
ejpam-5560	274	26	(	(	PUNCT
ejpam-5560	274	27	λ2i	λ2i	X
ejpam-5560	274	28	−an	−an	PROPN
ejpam-5560	274	29	)	)	PUNCT
ejpam-5560	274	30	−1y	−1y	NOUN
ejpam-5560	274	31	=	=	SYM
ejpam-5560	274	32	(	(	PUNCT
ejpam-5560	274	33	λ2i	λ2i	X
ejpam-5560	274	34	−a)−1y	−a)−1y	X
ejpam-5560	274	35	.	.	PUNCT
ejpam-5560	275	1	(	(	PUNCT
ejpam-5560	275	2	iv	iv	X
ejpam-5560	275	3	)	)	PUNCT
ejpam-5560	275	4	for	for	ADP
ejpam-5560	275	5	all	all	DET
ejpam-5560	275	6	λ	λ	PROPN
ejpam-5560	275	7	>	>	X
ejpam-5560	275	8	ω1	ω1	PROPN
ejpam-5560	275	9	such	such	ADJ
ejpam-5560	275	10	that	that	SCONJ
ejpam-5560	275	11	k(λ	k(λ	NOUN
ejpam-5560	275	12	)	)	PUNCT
ejpam-5560	275	13	̸=	̸=	PROPN
ejpam-5560	275	14	0	0	NUM
ejpam-5560	275	15	,	,	PUNCT
ejpam-5560	275	16	for	for	ADP
ejpam-5560	275	17	all	all	DET
ejpam-5560	275	18	x	x	SYM
ejpam-5560	275	19	∈	∈	PROPN
ejpam-5560	275	20	e	e	NOUN
ejpam-5560	275	21	,	,	PUNCT
ejpam-5560	275	22	lim	lim	PROPN
ejpam-5560	275	23	n→+∞	n→+∞	PROPN
ejpam-5560	275	24	rc(λ	rc(λ	PUNCT
ejpam-5560	275	25	2	2	NUM
ejpam-5560	275	26	,	,	PUNCT
ejpam-5560	275	27	an)x	an)x	PROPN
ejpam-5560	275	28	=	=	PUNCT
ejpam-5560	275	29	rc(λ	rc(λ	PUNCT
ejpam-5560	275	30	2	2	NUM
ejpam-5560	275	31	,	,	PUNCT
ejpam-5560	275	32	a)x	a)x	PUNCT
ejpam-5560	275	33	.	.	PUNCT
ejpam-5560	276	1	(	(	PUNCT
ejpam-5560	276	2	v	v	NOUN
ejpam-5560	276	3	)	)	PUNCT
ejpam-5560	276	4	for	for	ADP
ejpam-5560	276	5	all	all	DET
ejpam-5560	276	6	t	t	PROPN
ejpam-5560	276	7	≥	≥	NOUN
ejpam-5560	276	8	0	0	NUM
ejpam-5560	276	9	and	and	CCONJ
ejpam-5560	276	10	all	all	DET
ejpam-5560	276	11	x	x	SYM
ejpam-5560	276	12	∈	∈	PROPN
ejpam-5560	276	13	e	e	NOUN
ejpam-5560	276	14	,	,	PUNCT
ejpam-5560	276	15	lim	lim	PROPN
ejpam-5560	276	16	n→+∞	n→+∞	PROPN
ejpam-5560	276	17	cn(t)x	cn(t)x	PROPN
ejpam-5560	276	18	=	=	SYM
ejpam-5560	276	19	c(t)x	c(t)x	PROPN
ejpam-5560	276	20	,	,	PUNCT
ejpam-5560	276	21	the	the	DET
ejpam-5560	276	22	convergence	convergence	NOUN
ejpam-5560	276	23	is	be	AUX
ejpam-5560	276	24	uniform	uniform	ADJ
ejpam-5560	276	25	on	on	ADP
ejpam-5560	276	26	any	any	DET
ejpam-5560	276	27	compact	compact	NOUN
ejpam-5560	276	28	of	of	ADP
ejpam-5560	276	29	[	[	X
ejpam-5560	276	30	0,+∞	0,+∞	PROPN
ejpam-5560	276	31	[	[	X
ejpam-5560	276	32	.	.	PUNCT
ejpam-5560	277	1	proof	proof	NOUN
ejpam-5560	277	2	.	.	PUNCT
ejpam-5560	278	1	the	the	DET
ejpam-5560	278	2	condition	condition	NOUN
ejpam-5560	278	3	there	there	ADV
ejpam-5560	278	4	exist	exist	AUX
ejpam-5560	278	5	(	(	PUNCT
ejpam-5560	278	6	ω	ω	PROPN
ejpam-5560	278	7	,	,	PUNCT
ejpam-5560	278	8	m	m	NOUN
ejpam-5560	278	9	)	)	PUNCT
ejpam-5560	278	10	∈	∈	PROPN
ejpam-5560	278	11	r+×r+	r+×r+	PROPN
ejpam-5560	278	12	∗	∗	NOUN
ejpam-5560	278	13	,	,	PUNCT
ejpam-5560	278	14	for	for	ADP
ejpam-5560	278	15	all	all	DET
ejpam-5560	278	16	n	n	DET
ejpam-5560	278	17	∈	∈	PROPN
ejpam-5560	278	18	n	n	CCONJ
ejpam-5560	278	19	,	,	PUNCT
ejpam-5560	278	20	for	for	ADP
ejpam-5560	278	21	all	all	DET
ejpam-5560	278	22	t	t	PROPN
ejpam-5560	278	23	,	,	PUNCT
ejpam-5560	278	24	h	h	PROPN
ejpam-5560	278	25	≥	≥	NOUN
ejpam-5560	278	26	0	0	NUM
ejpam-5560	278	27	∥	∥	NUM
ejpam-5560	278	28	cn(t+h)−cn(t	cn(t+h)−cn(t	NOUN
ejpam-5560	278	29	)	)	PUNCT
ejpam-5560	278	30	∥≤	∥≤	PROPN
ejpam-5560	278	31	mheω(t+h	mheω(t+h	NOUN
ejpam-5560	278	32	)	)	PUNCT
ejpam-5560	278	33	implie	implie	VERB
ejpam-5560	278	34	that	that	PRON
ejpam-5560	278	35	for	for	ADP
ejpam-5560	278	36	t	t	NOUN
ejpam-5560	278	37	=	=	SYM
ejpam-5560	278	38	0	0	PUNCT
ejpam-5560	278	39	and	and	CCONJ
ejpam-5560	278	40	h	h	PROPN
ejpam-5560	278	41	≥	≥	NOUN
ejpam-5560	278	42	0	0	NUM
ejpam-5560	278	43	,	,	PUNCT
ejpam-5560	278	44	∥	∥	X
ejpam-5560	278	45	cn(h	cn(h	NUM
ejpam-5560	278	46	)	)	PUNCT
ejpam-5560	278	47	)	)	PUNCT
ejpam-5560	279	1	∥≤	∥≤	VERB
ejpam-5560	279	2	mheωh	mheωh	NOUN
ejpam-5560	279	3	≤	≤	NUM
ejpam-5560	279	4	me(ω+1)h	me(ω+1)h	NOUN
ejpam-5560	279	5	≤	≤	ADJ
ejpam-5560	279	6	meω1h	meω1h	NOUN
ejpam-5560	279	7	and	and	CCONJ
ejpam-5560	279	8	for	for	ADP
ejpam-5560	279	9	all	all	DET
ejpam-5560	279	10	x	x	SYM
ejpam-5560	279	11	∈	∈	PROPN
ejpam-5560	279	12	e	e	NOUN
ejpam-5560	279	13	,	,	PUNCT
ejpam-5560	279	14	(	(	PUNCT
ejpam-5560	279	15	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	279	16	is	be	AUX
ejpam-5560	279	17	equicontinuous	equicontinuous	ADJ
ejpam-5560	279	18	,	,	PUNCT
ejpam-5560	279	19	then	then	ADV
ejpam-5560	279	20	theorem	theorem	VERB
ejpam-5560	279	21	1	1	NUM
ejpam-5560	279	22	gives	give	VERB
ejpam-5560	279	23	the	the	DET
ejpam-5560	279	24	result	result	NOUN
ejpam-5560	279	25	.	.	PUNCT
ejpam-5560	280	1	y.	y.	PROPN
ejpam-5560	280	2	bajjou	bajjou	PROPN
ejpam-5560	280	3	,	,	PUNCT
ejpam-5560	280	4	a.	a.	PROPN
ejpam-5560	280	5	el	el	PROPN
ejpam-5560	280	6	amrani	amrani	PROPN
ejpam-5560	280	7	,	,	PUNCT
ejpam-5560	280	8	a.	a.	PROPN
ejpam-5560	280	9	blali	blali	PROPN
ejpam-5560	280	10	/	/	SYM
ejpam-5560	280	11	eur	eur	PROPN
ejpam-5560	280	12	.	.	PUNCT
ejpam-5560	281	1	j.	j.	PROPN
ejpam-5560	281	2	pure	pure	PROPN
ejpam-5560	281	3	appl	appl	PROPN
ejpam-5560	281	4	.	.	PROPN
ejpam-5560	281	5	math	math	PROPN
ejpam-5560	281	6	,	,	PUNCT
ejpam-5560	281	7	18	18	NUM
ejpam-5560	281	8	(	(	PUNCT
ejpam-5560	281	9	1	1	NUM
ejpam-5560	281	10	)	)	PUNCT
ejpam-5560	281	11	(	(	PUNCT
ejpam-5560	281	12	2025	2025	NUM
ejpam-5560	281	13	)	)	PUNCT
ejpam-5560	281	14	,	,	PUNCT
ejpam-5560	281	15	5560	5560	NUM
ejpam-5560	281	16	14	14	NUM
ejpam-5560	281	17	of	of	ADP
ejpam-5560	281	18	15	15	NUM
ejpam-5560	281	19	theorem	theorem	NOUN
ejpam-5560	281	20	2	2	NUM
ejpam-5560	281	21	.	.	PUNCT
ejpam-5560	281	22	suppose	suppose	VERB
ejpam-5560	281	23	that	that	SCONJ
ejpam-5560	281	24	(	(	PUNCT
ejpam-5560	281	25	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	281	26	is	be	AUX
ejpam-5560	281	27	a	a	DET
ejpam-5560	281	28	strongly	strongly	ADV
ejpam-5560	281	29	continuous	continuous	ADJ
ejpam-5560	281	30	operators	operator	NOUN
ejpam-5560	281	31	family	family	VERB
ejpam-5560	281	32	such	such	ADJ
ejpam-5560	281	33	that	that	PRON
ejpam-5560	281	34	for	for	ADP
ejpam-5560	281	35	all	all	DET
ejpam-5560	281	36	t	t	PROPN
ejpam-5560	281	37	≥	≥	NOUN
ejpam-5560	281	38	0	0	NUM
ejpam-5560	281	39	,	,	PUNCT
ejpam-5560	281	40	∥	∥	X
ejpam-5560	281	41	c(t	c(t	PROPN
ejpam-5560	281	42	)	)	PUNCT
ejpam-5560	281	43	∥≤	∥≤	PROPN
ejpam-5560	281	44	meωt	meωt	NOUN
ejpam-5560	281	45	and	and	CCONJ
ejpam-5560	281	46	cc	cc	PROPN
ejpam-5560	281	47	(	(	PUNCT
ejpam-5560	281	48	.	.	PUNCT
ejpam-5560	281	49	)	)	PUNCT
ejpam-5560	282	1	=	=	PUNCT
ejpam-5560	282	2	c(.)c	c(.)c	NOUN
ejpam-5560	282	3	.	.	PUNCT
ejpam-5560	283	1	for	for	ADP
ejpam-5560	283	2	all	all	DET
ejpam-5560	283	3	x	x	SYM
ejpam-5560	283	4	∈	∈	PROPN
ejpam-5560	283	5	e	e	NOUN
ejpam-5560	283	6	and	and	CCONJ
ejpam-5560	283	7	λ	λ	PROPN
ejpam-5560	283	8	>	>	X
ejpam-5560	283	9	ω	ω	PROPN
ejpam-5560	283	10	,	,	PUNCT
ejpam-5560	283	11	put	put	VERB
ejpam-5560	283	12	rλ2x	rλ2x	PROPN
ejpam-5560	283	13	:	:	PUNCT
ejpam-5560	283	14	=	=	SYM
ejpam-5560	283	15	1	1	NUM
ejpam-5560	283	16	λl(k)(λ	λl(k)(λ	NOUN
ejpam-5560	283	17	)	)	PUNCT
ejpam-5560	283	18	∫	∫	PROPN
ejpam-5560	284	1	+	+	PROPN
ejpam-5560	284	2	∞	∞	PROPN
ejpam-5560	284	3	0	0	NUM
ejpam-5560	284	4	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	284	5	.	.	PUNCT
ejpam-5560	285	1	for	for	ADP
ejpam-5560	285	2	each	each	DET
ejpam-5560	285	3	n	n	PRON
ejpam-5560	285	4	∈	∈	PROPN
ejpam-5560	285	5	n	n	CCONJ
ejpam-5560	285	6	,	,	PUNCT
ejpam-5560	285	7	note	note	NOUN
ejpam-5560	285	8	(	(	PUNCT
ejpam-5560	285	9	an	an	DET
ejpam-5560	285	10	,	,	PUNCT
ejpam-5560	285	11	d(an	d(an	NOUN
ejpam-5560	285	12	)	)	PUNCT
ejpam-5560	285	13	)	)	PUNCT
ejpam-5560	286	1	the	the	DET
ejpam-5560	286	2	subgenerators	subgenerator	NOUN
ejpam-5560	286	3	of	of	ADP
ejpam-5560	286	4	some	some	DET
ejpam-5560	286	5	k−convoluted	k−convoluted	PROPN
ejpam-5560	286	6	c−cosine	c−cosine	PROPN
ejpam-5560	286	7	function	function	NOUN
ejpam-5560	286	8	(	(	PUNCT
ejpam-5560	286	9	cn(t))t≥0	cn(t))t≥0	PROPN
ejpam-5560	286	10	,	,	PUNCT
ejpam-5560	286	11	such	such	ADJ
ejpam-5560	286	12	that	that	SCONJ
ejpam-5560	286	13	•	•	NUM
ejpam-5560	286	14	i	i	NOUN
ejpam-5560	286	15	)	)	PUNCT
ejpam-5560	286	16	there	there	PRON
ejpam-5560	286	17	exist	exist	VERB
ejpam-5560	286	18	ω	ω	NUM
ejpam-5560	286	19	≥	≥	NOUN
ejpam-5560	286	20	0	0	NUM
ejpam-5560	286	21	there	there	PRON
ejpam-5560	286	22	exist	exist	VERB
ejpam-5560	286	23	m	m	VERB
ejpam-5560	286	24	>	>	X
ejpam-5560	286	25	0	0	NUM
ejpam-5560	287	1	:	:	PUNCT
ejpam-5560	288	1	for	for	ADP
ejpam-5560	288	2	all	all	DET
ejpam-5560	288	3	n	n	PRON
ejpam-5560	288	4	∈	∈	PROPN
ejpam-5560	288	5	n	n	CCONJ
ejpam-5560	288	6	∥	∥	X
ejpam-5560	288	7	cn(t	cn(t	X
ejpam-5560	288	8	)	)	PUNCT
ejpam-5560	288	9	)	)	PUNCT
ejpam-5560	288	10	∥≤	∥≤	VERB
ejpam-5560	288	11	meωt	meωt	NOUN
ejpam-5560	288	12	.	.	PUNCT
ejpam-5560	289	1	•	•	NUM
ejpam-5560	289	2	ii	ii	PROPN
ejpam-5560	289	3	)	)	PUNCT
ejpam-5560	289	4	for	for	ADP
ejpam-5560	289	5	all	all	DET
ejpam-5560	289	6	x	x	SYM
ejpam-5560	289	7	∈	∈	PROPN
ejpam-5560	289	8	e	e	NOUN
ejpam-5560	289	9	)	)	PUNCT
ejpam-5560	289	10	(	(	PUNCT
ejpam-5560	289	11	cn(.)x)n∈n	cn(.)x)n∈n	PROPN
ejpam-5560	289	12	is	be	AUX
ejpam-5560	289	13	equicontinuous	equicontinuous	ADJ
ejpam-5560	289	14	.	.	PUNCT
ejpam-5560	290	1	•	•	NUM
ejpam-5560	290	2	iii	iii	X
ejpam-5560	290	3	)	)	PUNCT
ejpam-5560	290	4	there	there	PRON
ejpam-5560	290	5	exist	exist	VERB
ejpam-5560	290	6	λ	λ	PROPN
ejpam-5560	290	7	>	>	X
ejpam-5560	290	8	ω	ω	NUM
ejpam-5560	290	9	such	such	ADJ
ejpam-5560	290	10	that	that	SCONJ
ejpam-5560	290	11	lim	lim	PROPN
ejpam-5560	290	12	n→+∞	n→+∞	PROPN
ejpam-5560	290	13	rc(λ	rc(λ	PUNCT
ejpam-5560	290	14	2	2	NUM
ejpam-5560	290	15	,	,	PUNCT
ejpam-5560	290	16	an)x	an)x	PROPN
ejpam-5560	290	17	=	=	SYM
ejpam-5560	290	18	rλ2x	rλ2x	PROPN
ejpam-5560	290	19	,	,	PUNCT
ejpam-5560	290	20	r(rλ2	r(rλ2	ADJ
ejpam-5560	290	21	)	)	PUNCT
ejpam-5560	290	22	⊂	⊂	NOUN
ejpam-5560	290	23	r(c	r(c	ADJ
ejpam-5560	290	24	)	)	PUNCT
ejpam-5560	290	25	and	and	CCONJ
ejpam-5560	290	26	n(rλ2	n(rλ2	NOUN
ejpam-5560	290	27	)	)	PUNCT
ejpam-5560	290	28	=	=	PRON
ejpam-5560	290	29	{	{	PUNCT
ejpam-5560	290	30	0	0	NUM
ejpam-5560	290	31	}	}	PUNCT
ejpam-5560	290	32	.	.	PUNCT
ejpam-5560	291	1	then	then	ADV
ejpam-5560	291	2	there	there	PRON
ejpam-5560	291	3	is	be	VERB
ejpam-5560	291	4	a	a	DET
ejpam-5560	291	5	linear	linear	ADJ
ejpam-5560	291	6	operator	operator	NOUN
ejpam-5560	291	7	a	a	PRON
ejpam-5560	291	8	which	which	PRON
ejpam-5560	291	9	is	be	AUX
ejpam-5560	291	10	subgenerator	subgenerator	NOUN
ejpam-5560	291	11	of	of	ADP
ejpam-5560	291	12	a	a	DET
ejpam-5560	291	13	k−convoluted	k−convoluted	ADJ
ejpam-5560	291	14	c−	c−	ADJ
ejpam-5560	291	15	cosine	cosine	NOUN
ejpam-5560	291	16	function	function	NOUN
ejpam-5560	291	17	(	(	PUNCT
ejpam-5560	291	18	c(t))t≥0	c(t))t≥0	X
ejpam-5560	291	19	such	such	ADJ
ejpam-5560	291	20	that	that	SCONJ
ejpam-5560	291	21	for	for	ADP
ejpam-5560	291	22	all	all	DET
ejpam-5560	291	23	t	t	NOUN
ejpam-5560	291	24	⩾	⩾	NOUN
ejpam-5560	291	25	0	0	NUM
ejpam-5560	291	26	and	and	CCONJ
ejpam-5560	291	27	all	all	DET
ejpam-5560	291	28	x	x	SYM
ejpam-5560	291	29	∈	∈	PROPN
ejpam-5560	291	30	e	e	NOUN
ejpam-5560	291	31	,	,	PUNCT
ejpam-5560	291	32	lim	lim	PROPN
ejpam-5560	291	33	n→+∞	n→+∞	PROPN
ejpam-5560	291	34	cn(t)x	cn(t)x	PROPN
ejpam-5560	291	35	=	=	SYM
ejpam-5560	291	36	c(t)x	c(t)x	PROPN
ejpam-5560	291	37	,	,	PUNCT
ejpam-5560	291	38	the	the	DET
ejpam-5560	291	39	convergence	convergence	NOUN
ejpam-5560	291	40	is	be	AUX
ejpam-5560	291	41	uniform	uniform	ADJ
ejpam-5560	291	42	on	on	ADP
ejpam-5560	291	43	any	any	DET
ejpam-5560	291	44	compact	compact	NOUN
ejpam-5560	291	45	of	of	ADP
ejpam-5560	291	46	[	[	X
ejpam-5560	291	47	0,+∞	0,+∞	PROPN
ejpam-5560	291	48	[	[	X
ejpam-5560	291	49	.	.	PUNCT
ejpam-5560	291	50	proof	proof	NOUN
ejpam-5560	291	51	.	.	PUNCT
ejpam-5560	292	1	as	as	ADP
ejpam-5560	292	2	lim	lim	PROPN
ejpam-5560	292	3	n→+∞	n→+∞	PROPN
ejpam-5560	292	4	r(λ2	r(λ2	NOUN
ejpam-5560	292	5	,	,	PUNCT
ejpam-5560	292	6	an)x	an)x	PROPN
ejpam-5560	292	7	=	=	PROPN
ejpam-5560	292	8	rλ2x	rλ2x	PROPN
ejpam-5560	292	9	then	then	ADV
ejpam-5560	292	10	by	by	ADP
ejpam-5560	292	11	theorem	theorem	NOUN
ejpam-5560	292	12	1	1	NUM
ejpam-5560	292	13	and	and	CCONJ
ejpam-5560	292	14	remark	remark	NOUN
ejpam-5560	292	15	1	1	NUM
ejpam-5560	292	16	,	,	PUNCT
ejpam-5560	292	17	we	we	PRON
ejpam-5560	292	18	have	have	VERB
ejpam-5560	292	19	for	for	ADP
ejpam-5560	292	20	all	all	DET
ejpam-5560	292	21	λ	λ	PROPN
ejpam-5560	292	22	,	,	PUNCT
ejpam-5560	292	23	µ	µ	X
ejpam-5560	292	24	>	>	X
ejpam-5560	292	25	ω	ω	PROPN
ejpam-5560	292	26	and	and	CCONJ
ejpam-5560	292	27	all	all	PRON
ejpam-5560	292	28	n	n	PRON
ejpam-5560	292	29	∈	∈	PROPN
ejpam-5560	292	30	n	n	CCONJ
ejpam-5560	292	31	,	,	PUNCT
ejpam-5560	292	32	(	(	PUNCT
ejpam-5560	292	33	λ2	λ2	NOUN
ejpam-5560	292	34	−	−	PROPN
ejpam-5560	292	35	µ2)r(λ2	µ2)r(λ2	PROPN
ejpam-5560	292	36	,	,	PUNCT
ejpam-5560	292	37	an)r(µ2	an)r(µ2	PROPN
ejpam-5560	292	38	,	,	PUNCT
ejpam-5560	292	39	an	an	PRON
ejpam-5560	292	40	)	)	PUNCT
ejpam-5560	292	41	=	=	SYM
ejpam-5560	292	42	r(λ2	r(λ2	NOUN
ejpam-5560	292	43	,	,	PUNCT
ejpam-5560	292	44	an)cx−r(λ2	an)cx−r(λ2	ADJ
ejpam-5560	292	45	,	,	PUNCT
ejpam-5560	292	46	an)cx	an)cx	NOUN
ejpam-5560	292	47	,	,	PUNCT
ejpam-5560	292	48	then	then	ADV
ejpam-5560	292	49	passing	pass	VERB
ejpam-5560	292	50	to	to	ADP
ejpam-5560	292	51	the	the	DET
ejpam-5560	292	52	limit	limit	NOUN
ejpam-5560	292	53	as	as	SCONJ
ejpam-5560	292	54	n	n	PRON
ejpam-5560	292	55	tends	tend	VERB
ejpam-5560	292	56	to	to	ADP
ejpam-5560	292	57	+	+	NOUN
ejpam-5560	292	58	∞	∞	PROPN
ejpam-5560	292	59	,	,	PUNCT
ejpam-5560	292	60	we	we	PRON
ejpam-5560	292	61	get	get	VERB
ejpam-5560	292	62	for	for	ADP
ejpam-5560	292	63	all	all	DET
ejpam-5560	292	64	λ	λ	PROPN
ejpam-5560	292	65	,	,	PUNCT
ejpam-5560	292	66	µ	µ	X
ejpam-5560	292	67	>	>	X
ejpam-5560	292	68	ω	ω	PROPN
ejpam-5560	292	69	(	(	PUNCT
ejpam-5560	292	70	λ2	λ2	PROPN
ejpam-5560	292	71	−	−	PROPN
ejpam-5560	292	72	µ2)rλ2rµ2	µ2)rλ2rµ2	PROPN
ejpam-5560	292	73	=	=	PUNCT
ejpam-5560	292	74	rµ2cx−rλ2cx	rµ2cx−rλ2cx	PROPN
ejpam-5560	292	75	.	.	PUNCT
ejpam-5560	293	1	the	the	DET
ejpam-5560	293	2	remark	remark	NOUN
ejpam-5560	293	3	1	1	NUM
ejpam-5560	293	4	implies	imply	VERB
ejpam-5560	293	5	that	that	SCONJ
ejpam-5560	293	6	there	there	PRON
ejpam-5560	293	7	is	be	VERB
ejpam-5560	293	8	a	a	DET
ejpam-5560	293	9	linear	linear	ADJ
ejpam-5560	293	10	operator	operator	NOUN
ejpam-5560	293	11	a	a	DET
ejpam-5560	293	12	(	(	PUNCT
ejpam-5560	293	13	d(a	d(a	PROPN
ejpam-5560	293	14	)	)	PUNCT
ejpam-5560	293	15	=	=	SYM
ejpam-5560	293	16	r(rλ2	r(rλ2	NOUN
ejpam-5560	293	17	)	)	PUNCT
ejpam-5560	293	18	)	)	PUNCT
ejpam-5560	293	19	,	,	PUNCT
ejpam-5560	293	20	such	such	ADJ
ejpam-5560	293	21	that	that	SCONJ
ejpam-5560	293	22	rλ2x	rλ2x	PROPN
ejpam-5560	293	23	=	=	SYM
ejpam-5560	293	24	(	(	PUNCT
ejpam-5560	293	25	λ2	λ2	NOUN
ejpam-5560	293	26	−a)−1cx	−a)−1cx	NUM
ejpam-5560	293	27	=	=	SYM
ejpam-5560	293	28	rc(λ	rc(λ	PUNCT
ejpam-5560	293	29	2	2	NUM
ejpam-5560	293	30	,	,	PUNCT
ejpam-5560	293	31	a	a	PRON
ejpam-5560	293	32	)	)	PUNCT
ejpam-5560	293	33	.	.	PUNCT
ejpam-5560	294	1	by	by	ADP
ejpam-5560	294	2	definition	definition	NOUN
ejpam-5560	294	3	we	we	PRON
ejpam-5560	294	4	know	know	VERB
ejpam-5560	294	5	that	that	PRON
ejpam-5560	294	6	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	294	7	2	2	NUM
ejpam-5560	294	8	,	,	PUNCT
ejpam-5560	294	9	an)x	an)x	PROPN
ejpam-5560	294	10	=	=	SYM
ejpam-5560	294	11	∫	∫	PROPN
ejpam-5560	295	1	+	+	NUM
ejpam-5560	295	2	∞	∞	PROPN
ejpam-5560	295	3	0	0	NUM
ejpam-5560	295	4	e−λtcn(t)xdt	e−λtcn(t)xdt	PROPN
ejpam-5560	295	5	,	,	PUNCT
ejpam-5560	295	6	but	but	CCONJ
ejpam-5560	295	7	lim	lim	PROPN
ejpam-5560	295	8	n→+∞	n→+∞	VERB
ejpam-5560	295	9	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	295	10	2	2	NUM
ejpam-5560	295	11	,	,	PUNCT
ejpam-5560	295	12	an)x	an)x	PROPN
ejpam-5560	295	13	=	=	SYM
ejpam-5560	296	1	λl(k)(λ)rλ2x	λl(k)(λ)rλ2x	PROPN
ejpam-5560	296	2	=	=	SYM
ejpam-5560	296	3	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	296	4	2	2	NUM
ejpam-5560	296	5	,	,	PUNCT
ejpam-5560	296	6	a)x	a)x	X
ejpam-5560	296	7	,	,	PUNCT
ejpam-5560	296	8	by	by	ADP
ejpam-5560	296	9	the	the	DET
ejpam-5560	296	10	proof	proof	NOUN
ejpam-5560	296	11	of	of	ADP
ejpam-5560	296	12	theorem	theorem	NOUN
ejpam-5560	296	13	1	1	NUM
ejpam-5560	296	14	,	,	PUNCT
ejpam-5560	296	15	we	we	PRON
ejpam-5560	296	16	obtain	obtain	VERB
ejpam-5560	296	17	that	that	SCONJ
ejpam-5560	296	18	lim	lim	PROPN
ejpam-5560	296	19	n→+∞	n→+∞	PROPN
ejpam-5560	296	20	cn(t)x	cn(t)x	PROPN
ejpam-5560	296	21	=	=	SYM
ejpam-5560	296	22	c(t)x	c(t)x	PROPN
ejpam-5560	296	23	,	,	PUNCT
ejpam-5560	296	24	hence	hence	ADV
ejpam-5560	296	25	λl(k)(λ)rc(λ	λl(k)(λ)rc(λ	PROPN
ejpam-5560	296	26	2	2	NUM
ejpam-5560	296	27	,	,	PUNCT
ejpam-5560	296	28	a)x	a)x	PUNCT
ejpam-5560	297	1	=	=	X
ejpam-5560	297	2	∫	∫	X
ejpam-5560	297	3	+	+	ADJ
ejpam-5560	297	4	∞	∞	PROPN
ejpam-5560	297	5	0	0	NUM
ejpam-5560	297	6	e−λtc(t)xdt	e−λtc(t)xdt	PROPN
ejpam-5560	297	7	,	,	PUNCT
ejpam-5560	297	8	then	then	ADV
ejpam-5560	297	9	a	a	PRON
ejpam-5560	297	10	is	be	AUX
ejpam-5560	297	11	subgenerator	subgenerator	NOUN
ejpam-5560	297	12	of	of	ADP
ejpam-5560	297	13	k−convoluted	k−convoluted	PROPN
ejpam-5560	297	14	c−cosine	c−cosine	PROPN
ejpam-5560	297	15	function	function	NOUN
ejpam-5560	297	16	(	(	PUNCT
ejpam-5560	297	17	c(t))t≥0	c(t))t≥0	PROPN
ejpam-5560	297	18	,	,	PUNCT
ejpam-5560	297	19	such	such	ADJ
ejpam-5560	297	20	that	that	SCONJ
ejpam-5560	297	21	lim	lim	PROPN
ejpam-5560	297	22	n→+∞	n→+∞	PROPN
ejpam-5560	297	23	cn(t)x	cn(t)x	PROPN
ejpam-5560	297	24	=	=	NOUN
ejpam-5560	297	25	c(t)x	c(t)x	PROPN
ejpam-5560	297	26	for	for	ADP
ejpam-5560	297	27	all	all	DET
ejpam-5560	297	28	x	x	SYM
ejpam-5560	297	29	∈	∈	PROPN
ejpam-5560	297	30	e	e	NOUN
ejpam-5560	297	31	,	,	PUNCT
ejpam-5560	297	32	and	and	CCONJ
ejpam-5560	297	33	the	the	DET
ejpam-5560	297	34	convergence	convergence	NOUN
ejpam-5560	297	35	is	be	AUX
ejpam-5560	297	36	uniform	uniform	ADJ
ejpam-5560	297	37	on	on	ADP
ejpam-5560	297	38	any	any	DET
ejpam-5560	297	39	compact	compact	NOUN
ejpam-5560	297	40	of	of	ADP
ejpam-5560	297	41	[	[	X
ejpam-5560	297	42	0,+∞	0,+∞	PROPN
ejpam-5560	297	43	[	[	X
ejpam-5560	297	44	.	.	PUNCT
ejpam-5560	298	1	y.	y.	PROPN
ejpam-5560	298	2	bajjou	bajjou	PROPN
ejpam-5560	298	3	,	,	PUNCT
ejpam-5560	298	4	a.	a.	PROPN
ejpam-5560	298	5	el	el	PROPN
ejpam-5560	298	6	amrani	amrani	PROPN
ejpam-5560	298	7	,	,	PUNCT
ejpam-5560	298	8	a.	a.	PROPN
ejpam-5560	298	9	blali	blali	PROPN
ejpam-5560	298	10	/	/	SYM
ejpam-5560	298	11	eur	eur	PROPN
ejpam-5560	298	12	.	.	PUNCT
ejpam-5560	299	1	j.	j.	PROPN
ejpam-5560	299	2	pure	pure	PROPN
ejpam-5560	299	3	appl	appl	PROPN
ejpam-5560	299	4	.	.	PROPN
ejpam-5560	299	5	math	math	PROPN
ejpam-5560	299	6	,	,	PUNCT
ejpam-5560	299	7	18	18	NUM
ejpam-5560	299	8	(	(	PUNCT
ejpam-5560	299	9	1	1	NUM
ejpam-5560	299	10	)	)	PUNCT
ejpam-5560	299	11	(	(	PUNCT
ejpam-5560	299	12	2025	2025	NUM
ejpam-5560	299	13	)	)	PUNCT
ejpam-5560	299	14	,	,	PUNCT
ejpam-5560	299	15	5560	5560	NUM
ejpam-5560	299	16	15	15	NUM
ejpam-5560	299	17	of	of	ADP
ejpam-5560	299	18	15	15	NUM
ejpam-5560	299	19	4	4	NUM
ejpam-5560	299	20	.	.	PUNCT
ejpam-5560	299	21	conclusion	conclusion	NOUN
ejpam-5560	299	22	among	among	ADP
ejpam-5560	299	23	the	the	DET
ejpam-5560	299	24	things	thing	NOUN
ejpam-5560	299	25	that	that	PRON
ejpam-5560	299	26	math	math	NOUN
ejpam-5560	299	27	people	people	NOUN
ejpam-5560	299	28	like	like	VERB
ejpam-5560	299	29	is	be	AUX
ejpam-5560	299	30	finding	find	VERB
ejpam-5560	299	31	necessary	necessary	ADJ
ejpam-5560	299	32	an	an	DET
ejpam-5560	299	33	sufficient	sufficient	ADJ
ejpam-5560	299	34	conditions	condition	NOUN
ejpam-5560	299	35	so	so	SCONJ
ejpam-5560	299	36	that	that	SCONJ
ejpam-5560	299	37	the	the	DET
ejpam-5560	299	38	limit	limit	NOUN
ejpam-5560	299	39	of	of	ADP
ejpam-5560	299	40	a	a	DET
ejpam-5560	299	41	sequence	sequence	NOUN
ejpam-5560	299	42	of	of	ADP
ejpam-5560	299	43	mathematical	mathematical	ADJ
ejpam-5560	299	44	objects	object	NOUN
ejpam-5560	299	45	having	have	VERB
ejpam-5560	299	46	specific	specific	ADJ
ejpam-5560	299	47	properties	property	NOUN
ejpam-5560	299	48	has	have	VERB
ejpam-5560	299	49	same	same	ADJ
ejpam-5560	299	50	properties	property	NOUN
ejpam-5560	299	51	.	.	PUNCT
ejpam-5560	300	1	thi	thi	AUX
ejpam-5560	300	2	is	be	AUX
ejpam-5560	300	3	exactly	exactly	ADV
ejpam-5560	300	4	what	what	PRON
ejpam-5560	300	5	we	we	PRON
ejpam-5560	300	6	did	do	VERB
ejpam-5560	300	7	in	in	ADP
ejpam-5560	300	8	this	this	DET
ejpam-5560	300	9	article	article	NOUN
ejpam-5560	300	10	,	,	PUNCT
ejpam-5560	300	11	it	it	PRON
ejpam-5560	300	12	is	be	AUX
ejpam-5560	300	13	to	to	PART
ejpam-5560	300	14	find	find	VERB
ejpam-5560	300	15	necessary	necessary	ADJ
ejpam-5560	300	16	and	and	CCONJ
ejpam-5560	300	17	sufficient	sufficient	ADJ
ejpam-5560	300	18	conditions	condition	NOUN
ejpam-5560	300	19	so	so	SCONJ
ejpam-5560	300	20	that	that	SCONJ
ejpam-5560	300	21	the	the	DET
ejpam-5560	300	22	limit	limit	NOUN
ejpam-5560	300	23	of	of	ADP
ejpam-5560	300	24	equicontinuous	equicontinuous	ADJ
ejpam-5560	300	25	sequence	sequence	NOUN
ejpam-5560	300	26	k	k	NOUN
ejpam-5560	300	27	-	-	ADJ
ejpam-5560	300	28	convoluted	convoluted	ADJ
ejpam-5560	300	29	c	c	NOUN
ejpam-5560	300	30	-	-	PUNCT
ejpam-5560	300	31	cosine	cosine	NOUN
ejpam-5560	300	32	functions	function	NOUN
ejpam-5560	300	33	(	(	PUNCT
ejpam-5560	300	34	respectively	respectively	ADV
ejpam-5560	300	35	the	the	DET
ejpam-5560	300	36	c	c	NOUN
ejpam-5560	300	37	-	-	PUNCT
ejpam-5560	300	38	resolvent	resolvent	ADJ
ejpam-5560	300	39	operators	operator	NOUN
ejpam-5560	300	40	)	)	PUNCT
ejpam-5560	300	41	is	be	AUX
ejpam-5560	300	42	also	also	ADV
ejpam-5560	300	43	equicontinuous	equicontinuous	ADJ
ejpam-5560	300	44	k	k	ADV
ejpam-5560	300	45	-	-	ADJ
ejpam-5560	300	46	convoluted	convoluted	ADJ
ejpam-5560	300	47	c	c	NOUN
ejpam-5560	300	48	-	-	PUNCT
ejpam-5560	300	49	cosine	cosine	NOUN
ejpam-5560	300	50	functions	function	NOUN
ejpam-5560	300	51	(	(	PUNCT
ejpam-5560	300	52	respectively	respectively	ADV
ejpam-5560	300	53	c	c	NOUN
ejpam-5560	300	54	-	-	PUNCT
ejpam-5560	300	55	resolvent	resolvent	ADJ
ejpam-5560	300	56	operators	operator	NOUN
ejpam-5560	300	57	)	)	PUNCT
ejpam-5560	300	58	and	and	CCONJ
ejpam-5560	300	59	treated	treat	VERB
ejpam-5560	300	60	the	the	DET
ejpam-5560	300	61	equivalence	equivalence	NOUN
ejpam-5560	300	62	between	between	ADP
ejpam-5560	300	63	the	the	DET
ejpam-5560	300	64	convergence	convergence	NOUN
ejpam-5560	300	65	of	of	ADP
ejpam-5560	300	66	equicontinuous	equicontinuous	ADJ
ejpam-5560	300	67	sequence	sequence	NOUN
ejpam-5560	300	68	k	k	NOUN
ejpam-5560	300	69	-	-	ADJ
ejpam-5560	300	70	convoluted	convoluted	ADJ
ejpam-5560	300	71	c	c	NOUN
ejpam-5560	300	72	-	-	PUNCT
ejpam-5560	300	73	cosine	cosine	NOUN
ejpam-5560	300	74	functions	function	NOUN
ejpam-5560	300	75	and	and	CCONJ
ejpam-5560	300	76	the	the	DET
ejpam-5560	300	77	convergence	convergence	NOUN
ejpam-5560	300	78	of	of	ADP
ejpam-5560	300	79	the	the	DET
ejpam-5560	300	80	associated	associated	ADJ
ejpam-5560	300	81	c−resolvent	c−resolvent	NOUN
ejpam-5560	300	82	sequence	sequence	NOUN
ejpam-5560	300	83	.	.	PUNCT
ejpam-5560	301	1	references	reference	NOUN
ejpam-5560	301	2	[	[	X
ejpam-5560	301	3	1	1	NUM
ejpam-5560	301	4	]	]	PUNCT
ejpam-5560	301	5	w.	w.	PROPN
ejpam-5560	301	6	arendt	arendt	PROPN
ejpam-5560	301	7	,	,	PUNCT
ejpam-5560	301	8	c.	c.	PROPN
ejpam-5560	301	9	j.	j.	PROPN
ejpam-5560	301	10	k.	k.	PROPN
ejpam-5560	301	11	batty	batty	PROPN
ejpam-5560	301	12	,	,	PUNCT
ejpam-5560	301	13	m.	m.	NOUN
ejpam-5560	301	14	hieber	hieber	PROPN
ejpam-5560	301	15	,	,	PUNCT
ejpam-5560	301	16	and	and	CCONJ
ejpam-5560	301	17	f.	f.	PROPN
ejpam-5560	301	18	neubrander	neubrander	PROPN
ejpam-5560	301	19	.	.	PUNCT
ejpam-5560	302	1	vector	vector	NOUN
ejpam-5560	302	2	-	-	PUNCT
ejpam-5560	302	3	valued	value	VERB
ejpam-5560	302	4	laplace	laplace	NOUN
ejpam-5560	302	5	transforms	transform	VERB
ejpam-5560	302	6	and	and	CCONJ
ejpam-5560	302	7	cauchy	cauchy	NOUN
ejpam-5560	302	8	problems	problem	NOUN
ejpam-5560	302	9	,	,	PUNCT
ejpam-5560	302	10	volume	volume	NOUN
ejpam-5560	302	11	monographs	monograph	NOUN
ejpam-5560	302	12	in	in	ADP
ejpam-5560	302	13	mathematics	mathematics	PROPN
ejpam-5560	302	14	96	96	NUM
ejpam-5560	302	15	.	.	PUNCT
ejpam-5560	303	1	springer	springer	PROPN
ejpam-5560	303	2	basel	basel	PROPN
ejpam-5560	303	3	ag	ag	PROPN
ejpam-5560	303	4	,	,	PUNCT
ejpam-5560	303	5	2001	2001	NUM
ejpam-5560	303	6	.	.	PUNCT
ejpam-5560	304	1	[	[	X
ejpam-5560	304	2	2	2	X
ejpam-5560	304	3	]	]	PUNCT
ejpam-5560	304	4	v.	v.	ADP
ejpam-5560	304	5	keyantuo	keyantuo	PROPN
ejpam-5560	304	6	,	,	PUNCT
ejpam-5560	304	7	c.	c.	PROPN
ejpam-5560	304	8	lizama	lizama	NOUN
ejpam-5560	304	9	,	,	PUNCT
ejpam-5560	304	10	and	and	CCONJ
ejpam-5560	304	11	p.	p.	PROPN
ejpam-5560	304	12	j.	j.	PROPN
ejpam-5560	304	13	miana	miana	PROPN
ejpam-5560	304	14	.	.	PUNCT
ejpam-5560	305	1	algebra	algebra	NOUN
ejpam-5560	305	2	homomorphisms	homomorphism	NOUN
ejpam-5560	305	3	defined	define	VERB
ejpam-5560	305	4	via	via	ADP
ejpam-5560	305	5	convoluted	convoluted	ADJ
ejpam-5560	305	6	semigroups	semigroup	NOUN
ejpam-5560	305	7	and	and	CCONJ
ejpam-5560	305	8	cosine	cosine	NOUN
ejpam-5560	305	9	functions	function	NOUN
ejpam-5560	305	10	.	.	PUNCT
ejpam-5560	306	1	journal	journal	NOUN
ejpam-5560	306	2	of	of	ADP
ejpam-5560	306	3	functional	functional	ADJ
ejpam-5560	306	4	analysis	analysis	NOUN
ejpam-5560	306	5	,	,	PUNCT
ejpam-5560	306	6	257:3454	257:3454	NUM
ejpam-5560	306	7	–	–	PUNCT
ejpam-5560	306	8	3487	3487	NUM
ejpam-5560	306	9	,	,	PUNCT
ejpam-5560	306	10	2009	2009	NUM
ejpam-5560	306	11	.	.	PUNCT
ejpam-5560	307	1	[	[	X
ejpam-5560	307	2	3	3	NUM
ejpam-5560	307	3	]	]	PUNCT
ejpam-5560	307	4	m.	m.	NOUN
ejpam-5560	307	5	kostić.	kostić.	PROPN
ejpam-5560	307	6	convoluted	convolute	VERB
ejpam-5560	307	7	c	c	NOUN
ejpam-5560	307	8	-	-	PUNCT
ejpam-5560	307	9	cosine	cosine	NOUN
ejpam-5560	307	10	functions	function	NOUN
ejpam-5560	307	11	and	and	CCONJ
ejpam-5560	307	12	convoluted	convoluted	ADJ
ejpam-5560	307	13	c	c	NOUN
ejpam-5560	307	14	-	-	PUNCT
ejpam-5560	307	15	semigroups	semigroup	NOUN
ejpam-5560	307	16	.	.	PUNCT
ejpam-5560	308	1	bulletin	bulletin	NOUN
ejpam-5560	308	2	t.	t.	PROPN
ejpam-5560	308	3	cxxvii	cxxvii	PROPN
ejpam-5560	308	4	de	de	X
ejpam-5560	308	5	l’academie	l’academie	VERB
ejpam-5560	308	6	serbe	serbe	PROPN
ejpam-5560	308	7	des	des	PROPN
ejpam-5560	308	8	sciences	sciences	PROPN
ejpam-5560	308	9	et	et	PROPN
ejpam-5560	308	10	des	des	PROPN
ejpam-5560	308	11	arts	arts	PROPN
ejpam-5560	308	12	,	,	PUNCT
ejpam-5560	308	13	no	no	DET
ejpam-5560	308	14	28:75–92	28:75–92	PROPN
ejpam-5560	308	15	,	,	PUNCT
ejpam-5560	308	16	2003	2003	NUM
ejpam-5560	308	17	.	.	PUNCT
ejpam-5560	309	1	[	[	X
ejpam-5560	309	2	4	4	X
ejpam-5560	309	3	]	]	PUNCT
ejpam-5560	309	4	m.	m.	NOUN
ejpam-5560	309	5	kostić.	kostić.	PROPN
ejpam-5560	309	6	notes	note	VERB
ejpam-5560	309	7	on	on	ADP
ejpam-5560	309	8	analytic	analytic	ADJ
ejpam-5560	309	9	convoluted	convoluted	ADJ
ejpam-5560	309	10	c	c	NOUN
ejpam-5560	309	11	-	-	PUNCT
ejpam-5560	309	12	semigroups	semigroup	NOUN
ejpam-5560	309	13	.	.	PUNCT
ejpam-5560	310	1	publications	publication	NOUN
ejpam-5560	310	2	de	de	X
ejpam-5560	310	3	l’institut	l’institut	PROPN
ejpam-5560	310	4	mathematique	mathematique	NOUN
ejpam-5560	310	5	nouvelle	nouvelle	PROPN
ejpam-5560	310	6	serie	serie	X
ejpam-5560	310	7	,	,	PUNCT
ejpam-5560	310	8	88(102):67–76	88(102):67–76	NUM
ejpam-5560	310	9	,	,	PUNCT
ejpam-5560	310	10	2010	2010	NUM
ejpam-5560	310	11	.	.	PUNCT
ejpam-5560	311	1	[	[	X
ejpam-5560	311	2	5	5	NUM
ejpam-5560	311	3	]	]	PUNCT
ejpam-5560	311	4	m.	m.	NOUN
ejpam-5560	311	5	kostić.	kostić.	PROPN
ejpam-5560	311	6	generalized	generalize	VERB
ejpam-5560	311	7	semigroups	semigroup	NOUN
ejpam-5560	311	8	and	and	CCONJ
ejpam-5560	311	9	cosine	cosine	NOUN
ejpam-5560	311	10	functions	function	NOUN
ejpam-5560	311	11	.	.	PUNCT
ejpam-5560	312	1	mathematical	mathematical	PROPN
ejpam-5560	312	2	institute	institute	PROPN
ejpam-5560	312	3	belgrade	belgrade	PROPN
ejpam-5560	312	4	,	,	PUNCT
ejpam-5560	312	5	no	no	DET
ejpam-5560	312	6	28	28	NUM
ejpam-5560	312	7	,	,	PUNCT
ejpam-5560	312	8	2011	2011	NUM
ejpam-5560	312	9	.	.	PUNCT
ejpam-5560	313	1	[	[	X
ejpam-5560	313	2	6	6	NUM
ejpam-5560	313	3	]	]	PUNCT
ejpam-5560	313	4	m.	m.	NOUN
ejpam-5560	313	5	kostić.	kostić.	PROPN
ejpam-5560	313	6	hille	hille	PROPN
ejpam-5560	313	7	-	-	PUNCT
ejpam-5560	313	8	yosida	yosida	PROPN
ejpam-5560	313	9	theorems	theorem	VERB
ejpam-5560	313	10	for	for	ADP
ejpam-5560	313	11	local	local	ADJ
ejpam-5560	313	12	convoluted	convoluted	ADJ
ejpam-5560	313	13	c	c	NOUN
ejpam-5560	313	14	-	-	PUNCT
ejpam-5560	313	15	semigroups	semigroup	NOUN
ejpam-5560	313	16	and	and	CCONJ
ejpam-5560	313	17	cosine	cosine	NOUN
ejpam-5560	313	18	functions	function	NOUN
ejpam-5560	313	19	.	.	PUNCT
ejpam-5560	314	1	filomat	filomat	NOUN
ejpam-5560	314	2	,	,	PUNCT
ejpam-5560	314	3	25:4:177–190	25:4:177–190	NUM
ejpam-5560	314	4	,	,	PUNCT
ejpam-5560	314	5	2011	2011	NUM
ejpam-5560	314	6	.	.	PUNCT
ejpam-5560	315	1	[	[	X
ejpam-5560	315	2	7	7	X
ejpam-5560	315	3	]	]	X
ejpam-5560	315	4	m.	m.	NOUN
ejpam-5560	315	5	kostić.	kostić.	PROPN
ejpam-5560	315	6	degenerate	degenerate	VERB
ejpam-5560	315	7	k	k	ADV
ejpam-5560	315	8	-	-	ADJ
ejpam-5560	315	9	convoluted	convoluted	ADJ
ejpam-5560	315	10	c	c	NOUN
ejpam-5560	315	11	-	-	PUNCT
ejpam-5560	315	12	semigroups	semigroup	NOUN
ejpam-5560	315	13	and	and	CCONJ
ejpam-5560	315	14	degenerate	degenerate	ADJ
ejpam-5560	315	15	k	k	ADJ
ejpam-5560	315	16	-	-	ADJ
ejpam-5560	315	17	convoluted	convoluted	ADJ
ejpam-5560	315	18	ccosine	ccosine	NOUN
ejpam-5560	315	19	functions	function	NOUN
ejpam-5560	315	20	in	in	ADP
ejpam-5560	315	21	locally	locally	ADV
ejpam-5560	315	22	convex	convex	ADJ
ejpam-5560	315	23	spaces	space	NOUN
ejpam-5560	315	24	.	.	PUNCT
ejpam-5560	316	1	chelyab	chelyab	PROPN
ejpam-5560	316	2	.	.	PUNCT
ejpam-5560	317	1	fiz	fiz	PROPN
ejpam-5560	317	2	.	.	PUNCT
ejpam-5560	318	1	mat	mat	PROPN
ejpam-5560	318	2	.	.	PUNCT
ejpam-5560	318	3	zh	zh	PROPN
ejpam-5560	318	4	,	,	PUNCT
ejpam-5560	318	5	3:90–110	3:90–110	NUM
ejpam-5560	318	6	,	,	PUNCT
ejpam-5560	318	7	2018	2018	NUM
ejpam-5560	318	8	.	.	PUNCT
ejpam-5560	319	1	[	[	X
ejpam-5560	319	2	8	8	NUM
ejpam-5560	319	3	]	]	X
ejpam-5560	319	4	m.	m.	NOUN
ejpam-5560	319	5	kostić	kostić	PROPN
ejpam-5560	319	6	and	and	CCONJ
ejpam-5560	319	7	s.	s.	PROPN
ejpam-5560	319	8	pilipović.	pilipović.	PROPN
ejpam-5560	319	9	convoluted	convolute	VERB
ejpam-5560	319	10	c	c	NOUN
ejpam-5560	319	11	-	-	PUNCT
ejpam-5560	319	12	operator	operator	NOUN
ejpam-5560	319	13	families	family	NOUN
ejpam-5560	319	14	and	and	CCONJ
ejpam-5560	319	15	abstract	abstract	ADJ
ejpam-5560	319	16	cauchy	cauchy	ADJ
ejpam-5560	319	17	problems	problem	NOUN
ejpam-5560	319	18	.	.	PUNCT
ejpam-5560	320	1	kragujevac	kragujevac	PROPN
ejpam-5560	320	2	journal	journal	PROPN
ejpam-5560	320	3	of	of	ADP
ejpam-5560	320	4	mathematics	mathematic	NOUN
ejpam-5560	320	5	,	,	PUNCT
ejpam-5560	320	6	30:201–210	30:201–210	PROPN
ejpam-5560	320	7	,	,	PUNCT
ejpam-5560	320	8	2007	2007	NUM
ejpam-5560	320	9	.	.	PUNCT
ejpam-5560	321	1	[	[	X
ejpam-5560	321	2	9	9	NUM
ejpam-5560	321	3	]	]	PUNCT
ejpam-5560	321	4	m.	m.	NOUN
ejpam-5560	321	5	kostić	kostić	PROPN
ejpam-5560	321	6	and	and	CCONJ
ejpam-5560	321	7	s.	s.	PROPN
ejpam-5560	321	8	pilipović.	pilipović.	PROPN
ejpam-5560	321	9	convoluted	convolute	VERB
ejpam-5560	321	10	c	c	NOUN
ejpam-5560	321	11	-	-	PUNCT
ejpam-5560	321	12	cosine	cosine	NOUN
ejpam-5560	321	13	functions	function	NOUN
ejpam-5560	321	14	and	and	CCONJ
ejpam-5560	321	15	semigroups	semigroup	VERB
ejpam-5560	321	16	relations	relation	NOUN
ejpam-5560	321	17	with	with	ADP
ejpam-5560	321	18	ultradistribution	ultradistribution	NOUN
ejpam-5560	321	19	and	and	CCONJ
ejpam-5560	321	20	hyperfunction	hyperfunction	NOUN
ejpam-5560	321	21	sines	sine	NOUN
ejpam-5560	321	22	.	.	PUNCT
ejpam-5560	322	1	university	university	NOUN
ejpam-5560	322	2	of	of	ADP
ejpam-5560	322	3	novi	novi	PROPN
ejpam-5560	322	4	sad	sad	PROPN
ejpam-5560	322	5	,	,	PUNCT
ejpam-5560	322	6	serbia	serbia	PROPN
ejpam-5560	322	7	,	,	PUNCT
ejpam-5560	322	8	2008	2008	NUM
ejpam-5560	322	9	.	.	PUNCT
ejpam-5560	323	1	[	[	X
ejpam-5560	323	2	10	10	NUM
ejpam-5560	323	3	]	]	X
ejpam-5560	323	4	c.-c	c.-c	NOUN
ejpam-5560	323	5	.	.	PUNCT
ejpam-5560	324	1	kuo	kuo	PROPN
ejpam-5560	324	2	.	.	PUNCT
ejpam-5560	325	1	on	on	ADP
ejpam-5560	325	2	α	α	NUM
ejpam-5560	325	3	-	-	PUNCT
ejpam-5560	325	4	times	time	NOUN
ejpam-5560	325	5	integrated	integrated	ADJ
ejpam-5560	325	6	c	c	NOUN
ejpam-5560	325	7	-	-	PUNCT
ejpam-5560	325	8	cosine	cosine	NOUN
ejpam-5560	325	9	functions	function	NOUN
ejpam-5560	325	10	and	and	CCONJ
ejpam-5560	325	11	abstract	abstract	ADJ
ejpam-5560	325	12	cauchy	cauchy	PROPN
ejpam-5560	325	13	problem	problem	PROPN
ejpam-5560	325	14	i.	i.	PROPN
ejpam-5560	325	15	journal	journal	PROPN
ejpam-5560	325	16	of	of	ADP
ejpam-5560	325	17	mathematical	mathematical	ADJ
ejpam-5560	325	18	analysis	analysis	NOUN
ejpam-5560	325	19	and	and	CCONJ
ejpam-5560	325	20	applications	application	NOUN
ejpam-5560	325	21	,	,	PUNCT
ejpam-5560	325	22	313:142–162	313:142–162	NUM
ejpam-5560	325	23	,	,	PUNCT
ejpam-5560	325	24	2006	2006	NUM
ejpam-5560	325	25	.	.	PUNCT
ejpam-5560	326	1	[	[	X
ejpam-5560	326	2	11	11	NUM
ejpam-5560	326	3	]	]	X
ejpam-5560	326	4	c.-c	c.-c	NOUN
ejpam-5560	326	5	.	.	PUNCT
ejpam-5560	327	1	kuo	kuo	PROPN
ejpam-5560	327	2	.	.	PUNCT
ejpam-5560	328	1	local	local	ADJ
ejpam-5560	328	2	k	k	ADV
ejpam-5560	328	3	-	-	ADJ
ejpam-5560	328	4	convoluted	convoluted	ADJ
ejpam-5560	328	5	c	c	NOUN
ejpam-5560	328	6	-	-	PUNCT
ejpam-5560	328	7	semigroups	semigroup	NOUN
ejpam-5560	328	8	and	and	CCONJ
ejpam-5560	328	9	abstract	abstract	ADJ
ejpam-5560	328	10	cauchy	cauchy	ADJ
ejpam-5560	328	11	problems	problem	NOUN
ejpam-5560	328	12	.	.	PUNCT
ejpam-5560	329	1	taiwanese	taiwanese	ADJ
ejpam-5560	329	2	journal	journal	NOUN
ejpam-5560	329	3	of	of	ADP
ejpam-5560	329	4	mathematics	mathematic	NOUN
ejpam-5560	329	5	,	,	PUNCT
ejpam-5560	329	6	19:1227–1245	19:1227–1245	NUM
ejpam-5560	329	7	,	,	PUNCT
ejpam-5560	329	8	2015	2015	NUM
ejpam-5560	329	9	.	.	PUNCT
ejpam-5560	330	1	[	[	X
ejpam-5560	330	2	12	12	NUM
ejpam-5560	330	3	]	]	X
ejpam-5560	330	4	c.-c	c.-c	NOUN
ejpam-5560	330	5	.	.	PUNCT
ejpam-5560	331	1	kuo	kuo	PROPN
ejpam-5560	331	2	.	.	PUNCT
ejpam-5560	332	1	local	local	ADJ
ejpam-5560	332	2	k	k	ADV
ejpam-5560	332	3	-	-	ADJ
ejpam-5560	332	4	convoluted	convoluted	ADJ
ejpam-5560	332	5	c	c	NOUN
ejpam-5560	332	6	-	-	PUNCT
ejpam-5560	332	7	semigroups	semigroup	NOUN
ejpam-5560	332	8	and	and	CCONJ
ejpam-5560	332	9	complete	complete	ADJ
ejpam-5560	332	10	second	second	ADJ
ejpam-5560	332	11	order	order	NOUN
ejpam-5560	332	12	abstract	abstract	ADJ
ejpam-5560	332	13	cauchy	cauchy	PROPN
ejpam-5560	332	14	problems	problem	NOUN
ejpam-5560	332	15	.	.	PUNCT
ejpam-5560	333	1	filomat	filomat	NOUN
ejpam-5560	333	2	,	,	PUNCT
ejpam-5560	333	3	32:19:6789–6797	32:19:6789–6797	NUM
ejpam-5560	333	4	,	,	PUNCT
ejpam-5560	333	5	2018	2018	NUM
ejpam-5560	333	6	.	.	PUNCT
ejpam-5560	334	1	[	[	X
ejpam-5560	334	2	13	13	NUM
ejpam-5560	334	3	]	]	X
ejpam-5560	334	4	c.-c	c.-c	NOUN
ejpam-5560	334	5	.	.	PUNCT
ejpam-5560	335	1	kuo	kuo	PROPN
ejpam-5560	335	2	and	and	CCONJ
ejpam-5560	335	3	s.	s.	PROPN
ejpam-5560	335	4	y.	y.	PROPN
ejpam-5560	335	5	shaw	shaw	PROPN
ejpam-5560	335	6	.	.	PUNCT
ejpam-5560	336	1	on	on	ADP
ejpam-5560	336	2	α	α	NUM
ejpam-5560	336	3	-	-	PUNCT
ejpam-5560	336	4	times	time	NOUN
ejpam-5560	336	5	integrated	integrated	ADJ
ejpam-5560	336	6	c	c	NOUN
ejpam-5560	336	7	-	-	PUNCT
ejpam-5560	336	8	semigroups	semigroup	NOUN
ejpam-5560	336	9	and	and	CCONJ
ejpam-5560	336	10	the	the	DET
ejpam-5560	336	11	abstract	abstract	ADJ
ejpam-5560	336	12	cauchy	cauchy	PROPN
ejpam-5560	336	13	problem	problem	NOUN
ejpam-5560	336	14	.	.	PUNCT
ejpam-5560	337	1	studia	studia	PROPN
ejpam-5560	337	2	mathematica	mathematica	PROPN
ejpam-5560	337	3	,	,	PUNCT
ejpam-5560	337	4	142:201–217	142:201–217	NUM
ejpam-5560	337	5	,	,	PUNCT
ejpam-5560	337	6	2000	2000	NUM
ejpam-5560	337	7	.	.	PUNCT