id	sid	tid	token	lemma	pos
ma-236	1	1	2024	2024	NUM
ma-236	1	2	ada	ada	PROPN
ma-236	1	3	academica	academica	PROPN
ma-236	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-236	1	5	.	.	PUNCT
ma-236	2	1	j.	j.	PROPN
ma-236	2	2	math	math	PROPN
ma-236	2	3	.	.	PUNCT
ma-236	3	1	anal	anal	ADJ
ma-236	3	2	.	.	PUNCT
ma-236	4	1	4	4	NUM
ma-236	4	2	(	(	PUNCT
ma-236	4	3	2024	2024	NUM
ma-236	4	4	)	)	PUNCT
ma-236	4	5	17doi	17doi	NUM
ma-236	4	6	:	:	PUNCT
ma-236	4	7	10.28924	10.28924	NUM
ma-236	4	8	/	/	SYM
ma-236	4	9	ada	ada	PROPN
ma-236	4	10	/	/	SYM
ma-236	4	11	ma.4.17	ma.4.17	PROPN
ma-236	4	12	tensorial	tensorial	PROPN
ma-236	4	13	simpson	simpson	PROPN
ma-236	4	14	18	18	NUM
ma-236	4	15	type	type	NOUN
ma-236	4	16	inequalities	inequality	NOUN
ma-236	4	17	for	for	ADP
ma-236	4	18	convex	convex	NOUN
ma-236	4	19	functions	function	NOUN
ma-236	4	20	of	of	ADP
ma-236	4	21	selfadjoint	selfadjoint	NOUN
ma-236	4	22	operators	operator	NOUN
ma-236	4	23	in	in	ADP
ma-236	4	24	hilbert	hilbert	PROPN
ma-236	4	25	space	space	PROPN
ma-236	4	26	vuk	vuk	PROPN
ma-236	4	27	stojiljković1,∗	stojiljković1,∗	PROPN
ma-236	4	28	,	,	PUNCT
ma-236	4	29	sever	sever	VERB
ma-236	4	30	silvestru	silvestru	NOUN
ma-236	4	31	dragomir2	dragomir2	PROPN
ma-236	5	1	1faculty	1faculty	NUM
ma-236	5	2	of	of	ADP
ma-236	5	3	science	science	NOUN
ma-236	5	4	,	,	PUNCT
ma-236	5	5	university	university	NOUN
ma-236	5	6	of	of	ADP
ma-236	5	7	novi	novi	PROPN
ma-236	5	8	sad	sad	PROPN
ma-236	5	9	,	,	PUNCT
ma-236	5	10	trg	trg	PROPN
ma-236	5	11	dositeja	dositeja	NOUN
ma-236	5	12	obradovića	obradovića	PROPN
ma-236	5	13	3	3	NUM
ma-236	5	14	,	,	PUNCT
ma-236	5	15	21000	21000	NUM
ma-236	5	16	novi	novi	NOUN
ma-236	5	17	sad	sad	PROPN
ma-236	5	18	,	,	PUNCT
ma-236	5	19	serbia	serbia	NOUN
ma-236	5	20	vuk.stojiljkovic999@gmail.com	vuk.stojiljkovic999@gmail.com	X
ma-236	6	1	2mathematics	2mathematics	NUM
ma-236	6	2	,	,	PUNCT
ma-236	6	3	college	college	NOUN
ma-236	6	4	of	of	ADP
ma-236	6	5	sport	sport	PROPN
ma-236	6	6	health	health	PROPN
ma-236	6	7	and	and	CCONJ
ma-236	6	8	engineering	engineering	NOUN
ma-236	6	9	,	,	PUNCT
ma-236	6	10	victoria	victoria	PROPN
ma-236	6	11	university	university	PROPN
ma-236	6	12	melbourne	melbourne	PROPN
ma-236	6	13	city	city	PROPN
ma-236	6	14	,	,	PUNCT
ma-236	6	15	vic	vic	PROPN
ma-236	6	16	8001	8001	NUM
ma-236	6	17	,	,	PUNCT
ma-236	6	18	australia	australia	PROPN
ma-236	6	19	sever.dragomir@vu.edu.au	sever.dragomir@vu.edu.au	PROPN
ma-236	6	20	∗correspondence	∗correspondence	NOUN
ma-236	6	21	:	:	PUNCT
ma-236	6	22	vuk.stojiljkovic999@gmail.com	vuk.stojiljkovic999@gmail.com	X
ma-236	6	23	abstract	abstract	NOUN
ma-236	6	24	.	.	PUNCT
ma-236	7	1	several	several	ADJ
ma-236	7	2	simpson	simpson	NOUN
ma-236	7	3	1	1	NUM
ma-236	7	4	8	8	NUM
ma-236	7	5	tensorial	tensorial	ADJ
ma-236	7	6	type	type	NOUN
ma-236	7	7	inequalities	inequality	NOUN
ma-236	7	8	for	for	ADP
ma-236	7	9	selfadjoint	selfadjoint	NOUN
ma-236	7	10	operators	operator	NOUN
ma-236	7	11	have	have	AUX
ma-236	7	12	been	be	AUX
ma-236	7	13	obtainedwith	obtainedwith	ADP
ma-236	7	14	variation	variation	NOUN
ma-236	7	15	depending	depend	VERB
ma-236	7	16	on	on	ADP
ma-236	7	17	the	the	DET
ma-236	7	18	conditions	condition	NOUN
ma-236	7	19	imposed	impose	VERB
ma-236	7	20	on	on	ADP
ma-236	7	21	the	the	DET
ma-236	7	22	function	function	NOUN
ma-236	7	23	f∣∣∣∣∣∣∣∣18	f∣∣∣∣∣∣∣∣18	NOUN
ma-236	7	24	[	[	PUNCT
ma-236	7	25	f	f	X
ma-236	7	26	(	(	PUNCT
ma-236	7	27	a)⊗	a)⊗	NOUN
ma-236	7	28	1	1	NUM
ma-236	7	29	+	+	NUM
ma-236	7	30	6f	6f	NUM
ma-236	7	31	(	(	PUNCT
ma-236	7	32	a⊗	a⊗	NOUN
ma-236	7	33	1	1	NUM
ma-236	7	34	+	+	CCONJ
ma-236	7	35	1⊗b	1⊗b	NUM
ma-236	7	36	2	2	NUM
ma-236	7	37	)	)	PUNCT
ma-236	8	1	+	+	CCONJ
ma-236	9	1	1⊗	1⊗	NUM
ma-236	9	2	f	f	X
ma-236	9	3	(	(	PUNCT
ma-236	9	4	b	b	NOUN
ma-236	9	5	)	)	PUNCT
ma-236	9	6	]	]	PUNCT
ma-236	10	1	−	−	PROPN
ma-236	10	2	∫	∫	PROPN
ma-236	10	3	1	1	NUM
ma-236	10	4	0	0	NUM
ma-236	10	5	f	f	NOUN
ma-236	10	6	(	(	PUNCT
ma-236	10	7	λ1⊗b+	λ1⊗b+	NOUN
ma-236	10	8	(	(	PUNCT
ma-236	10	9	1−	1−	NUM
ma-236	10	10	λ)a⊗	λ)a⊗	X
ma-236	10	11	1)dλ	1)dλ	NUM
ma-236	10	12	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	10	13	≤	≤	ADV
ma-236	10	14	5	5	NUM
ma-236	10	15	‖1⊗b−	‖1⊗b−	NOUN
ma-236	10	16	a⊗	a⊗	NOUN
ma-236	10	17	1‖	1‖	NUM
ma-236	10	18	32	32	NUM
ma-236	10	19	∥∥f	∥∥f	NOUN
ma-236	10	20	′∥∥	′∥∥	VERB
ma-236	10	21	i,+∞	i,+∞	ADV
ma-236	10	22	.	.	PUNCT
ma-236	11	1	1	1	X
ma-236	11	2	.	.	X
ma-236	11	3	introduction	introduction	NOUN
ma-236	11	4	and	and	CCONJ
ma-236	11	5	preliminaries	preliminary	NOUN
ma-236	11	6	the	the	DET
ma-236	11	7	concept	concept	NOUN
ma-236	11	8	we	we	PRON
ma-236	11	9	now	now	ADV
ma-236	11	10	call	call	VERB
ma-236	11	11	a	a	DET
ma-236	11	12	"	"	PUNCT
ma-236	11	13	tensor	tensor	NOUN
ma-236	11	14	"	"	PUNCT
ma-236	11	15	was	be	AUX
ma-236	11	16	n’t	not	PART
ma-236	11	17	originally	originally	ADV
ma-236	11	18	named	name	VERB
ma-236	11	19	that	that	DET
ma-236	11	20	way	way	NOUN
ma-236	11	21	.	.	PUNCT
ma-236	12	1	when	when	SCONJ
ma-236	12	2	josiah	josiah	PROPN
ma-236	12	3	willard	willard	PROPN
ma-236	12	4	gibbsfirst	gibbsfirst	PROPN
ma-236	12	5	described	describe	VERB
ma-236	12	6	the	the	DET
ma-236	12	7	idea	idea	NOUN
ma-236	12	8	in	in	ADP
ma-236	12	9	the	the	DET
ma-236	12	10	late	late	ADJ
ma-236	12	11	19th	19th	ADJ
ma-236	12	12	century	century	NOUN
ma-236	12	13	,	,	PUNCT
ma-236	12	14	he	he	PRON
ma-236	12	15	used	use	VERB
ma-236	12	16	the	the	DET
ma-236	12	17	term	term	NOUN
ma-236	12	18	"	"	PUNCT
ma-236	12	19	dyadic	dyadic	ADJ
ma-236	12	20	.	.	PUNCT
ma-236	12	21	"	"	PUNCT
ma-236	13	1	today	today	NOUN
ma-236	13	2	,	,	PUNCT
ma-236	13	3	mathematiciansdefine	mathematiciansdefine	VERB
ma-236	13	4	a	a	DET
ma-236	13	5	tensor	tensor	NOUN
ma-236	13	6	as	as	ADP
ma-236	13	7	the	the	DET
ma-236	13	8	mathematical	mathematical	ADJ
ma-236	13	9	embodiment	embodiment	NOUN
ma-236	13	10	of	of	ADP
ma-236	13	11	gibbs	gibbs	PROPN
ma-236	13	12	’	'	PUNCT
ma-236	13	13	initial	initial	ADJ
ma-236	13	14	concept	concept	NOUN
ma-236	13	15	.	.	PUNCT
ma-236	14	1	tensors	tensor	NOUN
ma-236	14	2	and	and	CCONJ
ma-236	14	3	inequalitiesare	inequalitiesare	VERB
ma-236	14	4	natural	natural	ADJ
ma-236	14	5	partners	partner	NOUN
ma-236	14	6	,	,	PUNCT
ma-236	14	7	thanks	thank	NOUN
ma-236	14	8	to	to	ADP
ma-236	14	9	the	the	DET
ma-236	14	10	widespread	widespread	ADJ
ma-236	14	11	use	use	NOUN
ma-236	14	12	of	of	ADP
ma-236	14	13	inequalities	inequality	NOUN
ma-236	14	14	in	in	ADP
ma-236	14	15	mathematics	mathematic	NOUN
ma-236	14	16	.	.	PUNCT
ma-236	15	1	these	these	DET
ma-236	15	2	mathemat	mathemat	ADJ
ma-236	15	3	-	-	PUNCT
ma-236	15	4	ical	ical	ADJ
ma-236	15	5	statements	statement	NOUN
ma-236	15	6	about	about	ADP
ma-236	15	7	comparisons	comparison	NOUN
ma-236	15	8	have	have	VERB
ma-236	15	9	a	a	DET
ma-236	15	10	profound	profound	ADJ
ma-236	15	11	impact	impact	NOUN
ma-236	15	12	on	on	ADP
ma-236	15	13	various	various	ADJ
ma-236	15	14	scientific	scientific	ADJ
ma-236	15	15	disciplines	discipline	NOUN
ma-236	15	16	.	.	PUNCT
ma-236	16	1	whilemany	whilemany	NOUN
ma-236	16	2	types	type	NOUN
ma-236	16	3	of	of	ADP
ma-236	16	4	inequalities	inequality	NOUN
ma-236	16	5	exist	exist	VERB
ma-236	16	6	,	,	PUNCT
ma-236	16	7	some	some	PRON
ma-236	16	8	of	of	ADP
ma-236	16	9	the	the	DET
ma-236	16	10	most	most	ADV
ma-236	16	11	significant	significant	ADJ
ma-236	16	12	ones	one	NOUN
ma-236	16	13	include	include	VERB
ma-236	16	14	jensen	jensen	PROPN
ma-236	16	15	’s	’s	PROPN
ma-236	16	16	,	,	PUNCT
ma-236	16	17	ostrowski’s	ostrowski’s	ADJ
ma-236	16	18	,	,	PUNCT
ma-236	16	19	hermite	hermite	ADJ
ma-236	16	20	-	-	PUNCT
ma-236	16	21	hadamard	hadamard	NOUN
ma-236	16	22	’s	’s	ADV
ma-236	16	23	,	,	PUNCT
ma-236	16	24	and	and	CCONJ
ma-236	16	25	minkowski	minkowski	PROPN
ma-236	16	26	’s	’s	PART
ma-236	16	27	inequalities	inequality	NOUN
ma-236	16	28	.	.	PUNCT
ma-236	17	1	for	for	ADP
ma-236	17	2	those	those	PRON
ma-236	17	3	interested	interested	ADJ
ma-236	17	4	in	in	ADP
ma-236	17	5	delving	delve	VERB
ma-236	17	6	deeper	deep	ADJ
ma-236	17	7	,	,	PUNCT
ma-236	17	8	refer	refer	NOUN
ma-236	17	9	-	-	PUNCT
ma-236	17	10	ences	ence	NOUN
ma-236	17	11	[	[	X
ma-236	17	12	17	17	NUM
ma-236	17	13	]	]	PUNCT
ma-236	17	14	and	and	CCONJ
ma-236	17	15	[	[	X
ma-236	17	16	18	18	NUM
ma-236	17	17	]	]	PUNCT
ma-236	17	18	provide	provide	VERB
ma-236	17	19	more	more	ADJ
ma-236	17	20	details	detail	NOUN
ma-236	17	21	about	about	ADP
ma-236	17	22	inequalities	inequality	NOUN
ma-236	17	23	and	and	CCONJ
ma-236	17	24	their	their	PRON
ma-236	17	25	fascinating	fascinating	ADJ
ma-236	17	26	history	history	NOUN
ma-236	17	27	.	.	PUNCT
ma-236	18	1	regardingthe	regardingthe	DET
ma-236	18	2	generalizations	generalization	NOUN
ma-236	18	3	of	of	ADP
ma-236	18	4	the	the	DET
ma-236	18	5	aforementioned	aforementioned	ADJ
ma-236	18	6	inequalities	inequality	NOUN
ma-236	18	7	,	,	PUNCT
ma-236	18	8	numerous	numerous	ADJ
ma-236	18	9	studies	study	NOUN
ma-236	18	10	have	have	AUX
ma-236	18	11	been	be	AUX
ma-236	18	12	published	publish	VERB
ma-236	18	13	;	;	PUNCT
ma-236	18	14	foradditional	foradditional	ADJ
ma-236	18	15	information	information	NOUN
ma-236	18	16	,	,	PUNCT
ma-236	18	17	check	check	VERB
ma-236	18	18	the	the	DET
ma-236	18	19	following	following	NOUN
ma-236	18	20	and	and	CCONJ
ma-236	18	21	the	the	DET
ma-236	18	22	references	reference	NOUN
ma-236	18	23	therein	therein	ADV
ma-236	19	1	[	[	X
ma-236	19	2	1–5,7–9,21–23].classical	1–5,7–9,21–23].classical	ADJ
ma-236	19	3	inequalities	inequality	NOUN
ma-236	19	4	of	of	ADP
ma-236	19	5	simpson	simpson	PROPN
ma-236	19	6	type	type	PROPN
ma-236	19	7	have	have	AUX
ma-236	19	8	been	be	AUX
ma-236	19	9	given	give	VERB
ma-236	19	10	by	by	ADP
ma-236	19	11	hezenci	hezenci	PROPN
ma-236	19	12	et	et	PROPN
ma-236	19	13	al	al	PROPN
ma-236	19	14	.	.	PUNCT
ma-236	20	1	[	[	X
ma-236	20	2	15	15	NUM
ma-236	20	3	]	]	PUNCT
ma-236	20	4	and	and	CCONJ
ma-236	20	5	sarikaya	sarikaya	PROPN
ma-236	20	6	etal	etal	NOUN
ma-236	20	7	.	.	PUNCT
ma-236	21	1	[	[	X
ma-236	21	2	19	19	NUM
ma-236	21	3	]	]	PUNCT
ma-236	21	4	.	.	PUNCT
ma-236	22	1	to	to	PART
ma-236	22	2	enhance	enhance	VERB
ma-236	22	3	the	the	DET
ma-236	22	4	presentation	presentation	NOUN
ma-236	22	5	of	of	ADP
ma-236	22	6	this	this	DET
ma-236	22	7	work	work	NOUN
ma-236	22	8	,	,	PUNCT
ma-236	22	9	we	we	PRON
ma-236	22	10	will	will	AUX
ma-236	22	11	demonstrate	demonstrate	VERB
ma-236	22	12	new	new	ADJ
ma-236	22	13	developments	development	NOUN
ma-236	22	14	in	in	ADP
ma-236	22	15	the	the	DET
ma-236	22	16	received	received	NOUN
ma-236	22	17	:	:	PUNCT
ma-236	22	18	12	12	NUM
ma-236	22	19	apr	apr	NOUN
ma-236	22	20	2024	2024	NUM
ma-236	22	21	.	.	PUNCT
ma-236	23	1	key	key	ADJ
ma-236	23	2	words	word	NOUN
ma-236	23	3	and	and	CCONJ
ma-236	23	4	phrases	phrase	NOUN
ma-236	23	5	.	.	PUNCT
ma-236	24	1	tensorial	tensorial	ADJ
ma-236	24	2	product	product	NOUN
ma-236	24	3	,	,	PUNCT
ma-236	24	4	selfadjoint	selfadjoint	NOUN
ma-236	24	5	operators	operator	NOUN
ma-236	24	6	,	,	PUNCT
ma-236	24	7	convex	convex	VERB
ma-236	24	8	functions.1	functions.1	PROPN
ma-236	24	9	https://adac.ee	https://adac.ee	PROPN
ma-236	24	10	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	24	11	eur	eur	PROPN
ma-236	24	12	.	.	PUNCT
ma-236	25	1	j.	j.	PROPN
ma-236	25	2	math	math	PROPN
ma-236	25	3	.	.	PUNCT
ma-236	26	1	anal	anal	PROPN
ma-236	26	2	.	.	PUNCT
ma-236	27	1	10.28924	10.28924	NUM
ma-236	27	2	/	/	SYM
ma-236	27	3	ada	ada	PROPN
ma-236	27	4	/	/	SYM
ma-236	27	5	ma.4.17	ma.4.17	NOUN
ma-236	27	6	2theory	2theory	NUM
ma-236	27	7	of	of	ADP
ma-236	27	8	inequalities	inequality	NOUN
ma-236	27	9	in	in	ADP
ma-236	27	10	hilbert	hilbert	PROPN
ma-236	27	11	spaces	space	NOUN
ma-236	27	12	.	.	PUNCT
ma-236	28	1	one	one	NUM
ma-236	28	2	such	such	ADJ
ma-236	28	3	development	development	NOUN
ma-236	28	4	is	be	AUX
ma-236	28	5	the	the	DET
ma-236	28	6	dragomir	dragomir	NOUN
ma-236	28	7	’s	’s	PART
ma-236	28	8	inequality	inequality	PROPN
ma-236	28	9	fornormal	fornormal	ADJ
ma-236	28	10	operators	operator	NOUN
ma-236	28	11	given	give	VERB
ma-236	28	12	by	by	ADP
ma-236	28	13	the	the	DET
ma-236	28	14	following	following	NOUN
ma-236	28	15	[	[	X
ma-236	28	16	10	10	NUM
ma-236	28	17	]	]	NUM
ma-236	28	18	:	:	PUNCT
ma-236	28	19	theorem	theorem	NOUN
ma-236	28	20	1	1	X
ma-236	28	21	.	.	PUNCT
ma-236	29	1	let	let	VERB
ma-236	29	2	(	(	PUNCT
ma-236	29	3	h	h	NOUN
ma-236	29	4	;	;	PUNCT
ma-236	29	5	〈	〈	PROPN
ma-236	29	6	.	.	PROPN
ma-236	29	7	,	,	PUNCT
ma-236	29	8	.	.	PUNCT
ma-236	30	1	〉	〉	NOUN
ma-236	30	2	)	)	PUNCT
ma-236	30	3	be	be	VERB
ma-236	30	4	a	a	DET
ma-236	30	5	hilbert	hilbert	NOUN
ma-236	30	6	space	space	NOUN
ma-236	30	7	and	and	CCONJ
ma-236	30	8	t	t	NOUN
ma-236	30	9	:	:	PUNCT
ma-236	30	10	h	h	PROPN
ma-236	30	11	→	→	SYM
ma-236	30	12	h	h	NOUN
ma-236	30	13	a	a	DET
ma-236	30	14	normal	normal	ADJ
ma-236	30	15	linear	linear	NOUN
ma-236	30	16	operator	operator	NOUN
ma-236	30	17	on	on	ADP
ma-236	30	18	h	h	NOUN
ma-236	30	19	.	.	PUNCT
ma-236	31	1	then	then	ADV
ma-236	31	2	‖tx‖2	‖tx‖2	PROPN
ma-236	31	3	≥	≥	NUM
ma-236	31	4	1	1	NUM
ma-236	31	5	2	2	NUM
ma-236	31	6	(	(	PUNCT
ma-236	31	7	‖tx‖2	‖tx‖2	NOUN
ma-236	31	8	+	+	NUM
ma-236	31	9	|〈t2x	|〈t2x	NOUN
ma-236	31	10	,	,	PUNCT
ma-236	31	11	x〉|	x〉|	PROPN
ma-236	31	12	)	)	PUNCT
ma-236	31	13	≥	≥	NOUN
ma-236	32	1	|〈tx	|〈tx	ADJ
ma-236	32	2	,	,	PUNCT
ma-236	32	3	x〉|2	x〉|2	PROPN
ma-236	32	4	,	,	PUNCT
ma-236	32	5	for	for	ADP
ma-236	32	6	any	any	DET
ma-236	32	7	x	x	SYM
ma-236	32	8	∈	∈	PROPN
ma-236	32	9	h	h	NOUN
ma-236	32	10	,	,	PUNCT
ma-236	32	11	‖x‖	‖x‖	PROPN
ma-236	32	12	=	=	SYM
ma-236	33	1	1	1	X
ma-236	33	2	.	.	PUNCT
ma-236	34	1	the	the	DET
ma-236	34	2	constant	constant	ADJ
ma-236	34	3	12	12	NUM
ma-236	34	4	is	be	AUX
ma-236	34	5	the	the	DET
ma-236	34	6	best	good	ADJ
ma-236	34	7	possible	possible	ADJ
ma-236	34	8	.	.	PUNCT
ma-236	35	1	the	the	DET
ma-236	35	2	hermite	hermite	PROPN
ma-236	35	3	-	-	PUNCT
ma-236	35	4	hadamard	hadamard	ADJ
ma-236	35	5	inequality	inequality	NOUN
ma-236	35	6	in	in	ADP
ma-236	35	7	the	the	DET
ma-236	35	8	selfadjoint	selfadjoint	NOUN
ma-236	35	9	operator	operator	NOUN
ma-236	35	10	sense	sense	NOUN
ma-236	35	11	,	,	PUNCT
ma-236	35	12	as	as	SCONJ
ma-236	35	13	provided	provide	VERB
ma-236	35	14	by	by	ADP
ma-236	35	15	dragomir[11	dragomir[11	PROPN
ma-236	35	16	]	]	PUNCT
ma-236	35	17	,	,	PUNCT
ma-236	35	18	is	be	AUX
ma-236	35	19	another	another	DET
ma-236	35	20	intriguing	intriguing	ADJ
ma-236	35	21	conclusion	conclusion	NOUN
ma-236	35	22	.	.	PUNCT
ma-236	36	1	theorem	theorem	NOUN
ma-236	36	2	2	2	NUM
ma-236	36	3	.	.	PUNCT
ma-236	37	1	let	let	VERB
ma-236	37	2	f	f	NOUN
ma-236	37	3	:	:	PUNCT
ma-236	37	4	i	i	PRON
ma-236	37	5	→	→	PUNCT
ma-236	37	6	r	r	NOUN
ma-236	37	7	be	be	AUX
ma-236	37	8	an	an	DET
ma-236	37	9	operator	operator	NOUN
ma-236	37	10	convex	convex	NOUN
ma-236	37	11	function	function	NOUN
ma-236	37	12	on	on	ADP
ma-236	37	13	the	the	DET
ma-236	37	14	interval	interval	NOUN
ma-236	38	1	i	i	PRON
ma-236	38	2	.	.	PUNCT
ma-236	39	1	then	then	ADV
ma-236	39	2	for	for	ADP
ma-236	39	3	any	any	DET
ma-236	39	4	selfadjoint	selfadjoint	NOUN
ma-236	39	5	operators	operator	NOUN
ma-236	39	6	a	a	PRON
ma-236	39	7	and	and	CCONJ
ma-236	39	8	b	b	NOUN
ma-236	39	9	with	with	ADP
ma-236	39	10	spectra	spectra	NOUN
ma-236	39	11	in	in	ADP
ma-236	39	12	i	i	PRON
ma-236	39	13	we	we	PRON
ma-236	39	14	have	have	VERB
ma-236	39	15	the	the	DET
ma-236	39	16	inequality	inequality	NOUN
ma-236	39	17	f	f	PROPN
ma-236	39	18	(	(	PUNCT
ma-236	39	19	a+b	a+b	NUM
ma-236	39	20	2	2	NUM
ma-236	39	21	)	)	PUNCT
ma-236	39	22	≤	≤	NUM
ma-236	39	23	f	f	X
ma-236	39	24	(	(	PUNCT
ma-236	39	25	3a+b	3a+b	NUM
ma-236	39	26	4	4	NUM
ma-236	39	27	)	)	PUNCT
ma-236	40	1	+	+	CCONJ
ma-236	40	2	f	f	X
ma-236	40	3	(	(	PUNCT
ma-236	40	4	a+	a+	PUNCT
ma-236	40	5	3b	3b	NUM
ma-236	40	6	4	4	NUM
ma-236	40	7	)	)	PUNCT
ma-236	40	8	≤	≤	NUM
ma-236	40	9	∫	∫	PROPN
ma-236	40	10	1	1	NUM
ma-236	40	11	0	0	NUM
ma-236	40	12	f	f	NOUN
ma-236	40	13	(	(	PUNCT
ma-236	40	14	(	(	PUNCT
ma-236	40	15	1−	1−	NUM
ma-236	40	16	t)a+	t)a+	NOUN
ma-236	40	17	tb)dt	tb)dt	SYM
ma-236	40	18	≤	≤	NUM
ma-236	40	19	1	1	NUM
ma-236	40	20	2	2	NUM
ma-236	40	21	[	[	PUNCT
ma-236	40	22	f	f	X
ma-236	40	23	(	(	PUNCT
ma-236	40	24	a+b	a+b	NUM
ma-236	40	25	2	2	NUM
ma-236	40	26	)	)	PUNCT
ma-236	41	1	+	+	CCONJ
ma-236	41	2	f	f	X
ma-236	41	3	(	(	PUNCT
ma-236	41	4	a	a	NOUN
ma-236	41	5	)	)	PUNCT
ma-236	42	1	+	+	NOUN
ma-236	42	2	f	f	X
ma-236	42	3	(	(	PUNCT
ma-236	42	4	b	b	NOUN
ma-236	42	5	)	)	PUNCT
ma-236	42	6	2	2	NUM
ma-236	42	7	]	]	PUNCT
ma-236	42	8	≤	≤	NUM
ma-236	42	9	f	f	X
ma-236	42	10	(	(	PUNCT
ma-236	42	11	a	a	NOUN
ma-236	42	12	)	)	PUNCT
ma-236	42	13	+	+	NOUN
ma-236	42	14	f	f	X
ma-236	42	15	(	(	PUNCT
ma-236	42	16	b	b	NOUN
ma-236	42	17	)	)	PUNCT
ma-236	42	18	2	2	NUM
ma-236	42	19	.	.	PUNCT
ma-236	43	1	the	the	DET
ma-236	43	2	first	first	ADJ
ma-236	43	3	paper	paper	NOUN
ma-236	43	4	related	relate	VERB
ma-236	43	5	to	to	ADP
ma-236	43	6	tensorial	tensorial	ADJ
ma-236	43	7	inequalities	inequality	NOUN
ma-236	43	8	in	in	ADP
ma-236	43	9	hilbert	hilbert	NOUN
ma-236	43	10	space	space	NOUN
ma-236	43	11	was	be	AUX
ma-236	43	12	written	write	VERB
ma-236	43	13	by	by	ADP
ma-236	43	14	dragomir	dragomir	VERB
ma-236	43	15	[	[	PUNCT
ma-236	43	16	13].in	13].in	NUM
ma-236	43	17	the	the	DET
ma-236	43	18	paper	paper	NOUN
ma-236	43	19	,	,	PUNCT
ma-236	43	20	he	he	PRON
ma-236	43	21	proved	prove	VERB
ma-236	43	22	the	the	DET
ma-236	43	23	tensorial	tensorial	ADJ
ma-236	43	24	version	version	NOUN
ma-236	43	25	of	of	ADP
ma-236	43	26	the	the	DET
ma-236	43	27	ostrowski	ostrowski	ADJ
ma-236	43	28	type	type	NOUN
ma-236	43	29	inequality	inequality	NOUN
ma-236	43	30	given	give	VERB
ma-236	43	31	by	by	ADP
ma-236	43	32	the	the	DET
ma-236	43	33	following	following	NOUN
ma-236	43	34	.	.	PUNCT
ma-236	44	1	theorem	theorem	NOUN
ma-236	44	2	3	3	X
ma-236	44	3	.	.	PUNCT
ma-236	44	4	assume	assume	VERB
ma-236	44	5	that	that	SCONJ
ma-236	44	6	f	f	PROPN
ma-236	44	7	is	be	AUX
ma-236	44	8	continuously	continuously	ADV
ma-236	44	9	differentiable	differentiable	ADJ
ma-236	44	10	on	on	ADP
ma-236	44	11	i	i	PRON
ma-236	44	12	with	with	ADP
ma-236	44	13	‖f	‖f	PRON
ma-236	44	14	′‖i,+∞	′‖i,+∞	VERB
ma-236	44	15	:	:	PUNCT
ma-236	45	1	=	=	SYM
ma-236	45	2	supt∈i	supt∈i	PROPN
ma-236	45	3	|f	|f	PROPN
ma-236	45	4	′(t)|	′(t)|	X
ma-236	45	5	<	<	X
ma-236	46	1	+	+	NOUN
ma-236	46	2	∞	∞	PROPN
ma-236	46	3	and	and	CCONJ
ma-236	46	4	a	a	DET
ma-236	46	5	,	,	PUNCT
ma-236	46	6	b	b	NOUN
ma-236	46	7	are	be	AUX
ma-236	46	8	selfadjoint	selfadjoint	VERB
ma-236	46	9	operators	operator	NOUN
ma-236	46	10	with	with	ADP
ma-236	46	11	sp(a	sp(a	NOUN
ma-236	46	12	)	)	PUNCT
ma-236	46	13	,	,	PUNCT
ma-236	46	14	sp(b	sp(b	PROPN
ma-236	46	15	)	)	PUNCT
ma-236	47	1	⊂	⊂	PROPN
ma-236	48	1	i	i	INTJ
ma-236	48	2	.	.	PUNCT
ma-236	49	1	then	then	ADV
ma-236	49	2	the	the	DET
ma-236	49	3	following	follow	VERB
ma-236	49	4	inequality	inequality	NOUN
ma-236	49	5	holds:∥∥∥∥f	holds:∥∥∥∥f	NUM
ma-236	49	6	(	(	PUNCT
ma-236	49	7	(	(	PUNCT
ma-236	49	8	1−	1−	NUM
ma-236	49	9	λ)a⊗	λ)a⊗	NOUN
ma-236	49	10	1	1	NUM
ma-236	49	11	+	+	CCONJ
ma-236	49	12	λ1⊗b)−	λ1⊗b)−	PROPN
ma-236	49	13	∫	∫	PROPN
ma-236	49	14	1	1	NUM
ma-236	49	15	0	0	NUM
ma-236	49	16	f	f	NOUN
ma-236	49	17	(	(	PUNCT
ma-236	49	18	(	(	PUNCT
ma-236	49	19	1−	1−	NUM
ma-236	49	20	u)a⊗	u)a⊗	NOUN
ma-236	49	21	1	1	NUM
ma-236	49	22	+	+	CCONJ
ma-236	49	23	u1⊗b)du	u1⊗b)du	NUM
ma-236	49	24	∥∥∥∥	∥∥∥∥	NUM
ma-236	49	25	(	(	PUNCT
ma-236	49	26	1	1	X
ma-236	49	27	)	)	PUNCT
ma-236	49	28	≤	≤	NUM
ma-236	49	29	∥∥f	∥∥f	NOUN
ma-236	49	30	′∥∥	′∥∥	VERB
ma-236	49	31	i,+∞	i,+∞	ADV
ma-236	49	32	[	[	PUNCT
ma-236	49	33	1	1	NUM
ma-236	49	34	4	4	NUM
ma-236	49	35	+	+	CCONJ
ma-236	49	36	(	(	PUNCT
ma-236	49	37	λ−	λ−	PROPN
ma-236	49	38	1	1	NUM
ma-236	49	39	2	2	NUM
ma-236	49	40	)	)	PUNCT
ma-236	49	41	2	2	NUM
ma-236	49	42	]	]	PUNCT
ma-236	49	43	‖1⊗b−	‖1⊗b−	X
ma-236	49	44	a⊗	a⊗	PROPN
ma-236	49	45	1‖	1‖	NUM
ma-236	49	46	for	for	ADP
ma-236	49	47	λ	λ	PROPN
ma-236	49	48	∈	∈	PROPN
ma-236	50	1	[	[	X
ma-236	50	2	0	0	NUM
ma-236	50	3	,	,	PUNCT
ma-236	50	4	1	1	NUM
ma-236	50	5	]	]	PUNCT
ma-236	50	6	.	.	PUNCT
ma-236	51	1	recently	recently	ADV
ma-236	51	2	,	,	PUNCT
ma-236	51	3	various	various	ADJ
ma-236	51	4	inequalities	inequality	NOUN
ma-236	51	5	in	in	ADP
ma-236	51	6	the	the	DET
ma-236	51	7	same	same	ADJ
ma-236	51	8	tensorial	tensorial	NOUN
ma-236	51	9	surrounding	surrounding	NOUN
ma-236	51	10	have	have	AUX
ma-236	51	11	been	be	AUX
ma-236	51	12	obtained	obtain	VERB
ma-236	51	13	.	.	PUNCT
ma-236	52	1	the	the	DET
ma-236	52	2	fol	fol	NOUN
ma-236	52	3	-	-	PUNCT
ma-236	52	4	lowing	lowing	NOUN
ma-236	52	5	result	result	NOUN
ma-236	52	6	of	of	ADP
ma-236	52	7	simpson	simpson	PROPN
ma-236	52	8	type	type	PROPN
ma-236	52	9	was	be	AUX
ma-236	52	10	obtained	obtain	VERB
ma-236	52	11	by	by	ADP
ma-236	52	12	stojiljković	stojiljković	NOUN
ma-236	52	13	[	[	X
ma-236	52	14	24	24	NUM
ma-236	52	15	]	]	PUNCT
ma-236	52	16	.	.	PUNCT
ma-236	53	1	theorem	theorem	ADJ
ma-236	53	2	4	4	NUM
ma-236	53	3	.	.	PUNCT
ma-236	53	4	assume	assume	VERB
ma-236	53	5	that	that	SCONJ
ma-236	53	6	f	f	PROPN
ma-236	53	7	is	be	AUX
ma-236	53	8	continuously	continuously	ADV
ma-236	53	9	differentiable	differentiable	ADJ
ma-236	53	10	on	on	ADP
ma-236	53	11	i	i	PRON
ma-236	53	12	and	and	CCONJ
ma-236	53	13	|f	|f	PRON
ma-236	53	14	′′|	′′|	VERB
ma-236	53	15	is	be	AUX
ma-236	53	16	convex	convex	ADJ
ma-236	53	17	and	and	CCONJ
ma-236	53	18	a	a	DET
ma-236	53	19	,	,	PUNCT
ma-236	53	20	b	b	NOUN
ma-236	53	21	are	be	AUX
ma-236	53	22	selfadjoint	selfadjoint	VERB
ma-236	53	23	operators	operator	NOUN
ma-236	53	24	with	with	ADP
ma-236	53	25	sp(a	sp(a	NOUN
ma-236	53	26	)	)	PUNCT
ma-236	53	27	,	,	PUNCT
ma-236	53	28	sp(b	sp(b	PROPN
ma-236	53	29	)	)	PUNCT
ma-236	54	1	⊂	⊂	PROPN
ma-236	55	1	i	i	INTJ
ma-236	55	2	.	.	PUNCT
ma-236	56	1	then	then	ADV
ma-236	56	2	the	the	DET
ma-236	56	3	following	follow	VERB
ma-236	56	4	inequality	inequality	NOUN
ma-236	56	5	holds:∣∣∣∣∣∣∣∣16	holds:∣∣∣∣∣∣∣∣16	PROPN
ma-236	56	6	(	(	PUNCT
ma-236	56	7	f	f	X
ma-236	56	8	(	(	PUNCT
ma-236	56	9	a)⊗	a)⊗	NOUN
ma-236	56	10	1	1	NUM
ma-236	56	11	+	+	NUM
ma-236	56	12	4f	4f	NUM
ma-236	56	13	(	(	PUNCT
ma-236	56	14	a⊗	a⊗	NOUN
ma-236	56	15	1	1	NUM
ma-236	56	16	+	+	CCONJ
ma-236	56	17	1⊗b	1⊗b	NUM
ma-236	56	18	2	2	NUM
ma-236	56	19	)	)	PUNCT
ma-236	56	20	+	+	CCONJ
ma-236	57	1	1⊗	1⊗	NUM
ma-236	57	2	f	f	X
ma-236	57	3	(	(	PUNCT
ma-236	57	4	b	b	NOUN
ma-236	57	5	)	)	PUNCT
ma-236	57	6	)	)	PUNCT
ma-236	57	7	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	57	8	eur	eur	PROPN
ma-236	57	9	.	.	PUNCT
ma-236	58	1	j.	j.	PROPN
ma-236	58	2	math	math	PROPN
ma-236	58	3	.	.	PUNCT
ma-236	59	1	anal	anal	PROPN
ma-236	59	2	.	.	PUNCT
ma-236	60	1	10.28924	10.28924	NUM
ma-236	60	2	/	/	SYM
ma-236	60	3	ada	ada	PROPN
ma-236	60	4	/	/	SYM
ma-236	60	5	ma.4.17	ma.4.17	NOUN
ma-236	60	6	3	3	NUM
ma-236	60	7	−	−	NOUN
ma-236	60	8	1	1	NUM
ma-236	60	9	2	2	NUM
ma-236	60	10	α	α	NOUN
ma-236	60	11	(	(	PUNCT
ma-236	60	12	∫	∫	PROPN
ma-236	60	13	1	1	NUM
ma-236	60	14	0	0	NUM
ma-236	60	15	f	f	NOUN
ma-236	60	16	(	(	PUNCT
ma-236	60	17	(	(	PUNCT
ma-236	60	18	1−	1−	NUM
ma-236	60	19	k	k	NOUN
ma-236	60	20	2	2	X
ma-236	60	21	)	)	PUNCT
ma-236	60	22	a⊗	a⊗	NOUN
ma-236	60	23	1	1	NUM
ma-236	60	24	+	+	CCONJ
ma-236	60	25	(	(	PUNCT
ma-236	60	26	1	1	NUM
ma-236	60	27	+	+	CCONJ
ma-236	60	28	k	k	PROPN
ma-236	60	29	2	2	X
ma-236	60	30	)	)	PUNCT
ma-236	60	31	1⊗b	1⊗b	NUM
ma-236	60	32	)	)	PUNCT
ma-236	61	1	kα−1dk	kα−1dk	PROPN
ma-236	62	1	+	+	NUM
ma-236	62	2	∫	∫	PROPN
ma-236	62	3	1	1	NUM
ma-236	62	4	0	0	NUM
ma-236	62	5	f	f	NOUN
ma-236	62	6	(	(	PUNCT
ma-236	62	7	(	(	PUNCT
ma-236	62	8	1−	1−	NUM
ma-236	62	9	k	k	NOUN
ma-236	62	10	2	2	X
ma-236	62	11	)	)	PUNCT
ma-236	62	12	a⊗	a⊗	NOUN
ma-236	62	13	1	1	NUM
ma-236	62	14	+	+	CCONJ
ma-236	62	15	k	k	PROPN
ma-236	62	16	2	2	NUM
ma-236	62	17	1⊗b	1⊗b	NUM
ma-236	62	18	)	)	PUNCT
ma-236	62	19	(	(	PUNCT
ma-236	62	20	1−	1−	NUM
ma-236	62	21	k)α−1dk	k)α−1dk	PROPN
ma-236	62	22	)	)	PUNCT
ma-236	62	23	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	62	24	≤	≤	NUM
ma-236	62	25	‖1⊗b−	‖1⊗b−	NOUN
ma-236	62	26	a⊗	a⊗	NOUN
ma-236	62	27	1‖2	1‖2	NUM
ma-236	62	28	(	(	PUNCT
ma-236	62	29	‖f	‖f	ADP
ma-236	62	30	′′(a)‖+	′′(a)‖+	PROPN
ma-236	62	31	‖f	‖f	ADP
ma-236	62	32	′′(b)‖	′′(b)‖	PROPN
ma-236	62	33	)	)	PUNCT
ma-236	62	34	(	(	PUNCT
ma-236	62	35	3α2	3α2	NUM
ma-236	62	36	+	+	CCONJ
ma-236	62	37	8α+	8α+	NUM
ma-236	62	38	7	7	NUM
ma-236	62	39	)	)	PUNCT
ma-236	62	40	(	(	PUNCT
ma-236	62	41	α+	α+	PROPN
ma-236	62	42	2)(24α+	2)(24α+	NUM
ma-236	62	43	24	24	NUM
ma-236	62	44	)	)	PUNCT
ma-236	62	45	for	for	ADP
ma-236	62	46	α	α	DET
ma-236	62	47	≥	≥	NOUN
ma-236	62	48	0	0	NUM
ma-236	62	49	.	.	PUNCT
ma-236	63	1	the	the	DET
ma-236	63	2	following	follow	VERB
ma-236	63	3	inequality	inequality	NOUN
ma-236	63	4	has	have	AUX
ma-236	63	5	been	be	AUX
ma-236	63	6	recently	recently	ADV
ma-236	63	7	obtained	obtain	VERB
ma-236	63	8	by	by	ADP
ma-236	63	9	the	the	DET
ma-236	63	10	same	same	ADJ
ma-236	63	11	author	author	NOUN
ma-236	63	12	[	[	X
ma-236	63	13	25	25	NUM
ma-236	63	14	]	]	PUNCT
ma-236	63	15	.	.	PUNCT
ma-236	64	1	theorem	theorem	ADJ
ma-236	64	2	5	5	NUM
ma-236	64	3	.	.	PUNCT
ma-236	64	4	assume	assume	VERB
ma-236	64	5	that	that	SCONJ
ma-236	64	6	f	f	PROPN
ma-236	64	7	is	be	AUX
ma-236	64	8	continuously	continuously	ADV
ma-236	64	9	differentiable	differentiable	ADJ
ma-236	64	10	on	on	ADP
ma-236	64	11	i	i	PRON
ma-236	64	12	with	with	ADP
ma-236	64	13	‖f	‖f	PRON
ma-236	64	14	′‖i,+∞	′‖i,+∞	VERB
ma-236	64	15	:	:	PUNCT
ma-236	65	1	=	=	SYM
ma-236	65	2	supt∈i	supt∈i	PROPN
ma-236	65	3	|f	|f	PROPN
ma-236	65	4	′(t)|	′(t)|	X
ma-236	65	5	<	<	X
ma-236	66	1	+	+	NOUN
ma-236	66	2	∞	∞	PROPN
ma-236	66	3	and	and	CCONJ
ma-236	66	4	a	a	DET
ma-236	66	5	,	,	PUNCT
ma-236	66	6	b	b	NOUN
ma-236	66	7	are	be	AUX
ma-236	66	8	selfadjoint	selfadjoint	VERB
ma-236	66	9	operators	operator	NOUN
ma-236	66	10	with	with	ADP
ma-236	66	11	sp(a	sp(a	NOUN
ma-236	66	12	)	)	PUNCT
ma-236	66	13	,	,	PUNCT
ma-236	66	14	sp(b	sp(b	PROPN
ma-236	66	15	)	)	PUNCT
ma-236	67	1	⊂	⊂	PROPN
ma-236	68	1	i	i	INTJ
ma-236	68	2	.	.	PUNCT
ma-236	69	1	then	then	ADV
ma-236	69	2	the	the	DET
ma-236	69	3	following	follow	VERB
ma-236	69	4	inequality	inequality	NOUN
ma-236	69	5	holds:∥∥∥∥∫	holds:∥∥∥∥∫	ADJ
ma-236	69	6	1	1	NUM
ma-236	69	7	0	0	NUM
ma-236	69	8	f	f	NOUN
ma-236	69	9	(	(	PUNCT
ma-236	69	10	(	(	PUNCT
ma-236	69	11	1−	1−	NUM
ma-236	69	12	λ)a⊗	λ)a⊗	NOUN
ma-236	69	13	1	1	NUM
ma-236	69	14	+	+	CCONJ
ma-236	69	15	λ1⊗b)dλ−	λ1⊗b)dλ−	PROPN
ma-236	69	16	f	f	PROPN
ma-236	69	17	(	(	PUNCT
ma-236	69	18	a⊗	a⊗	NOUN
ma-236	69	19	1	1	NUM
ma-236	69	20	+	+	CCONJ
ma-236	69	21	1⊗b	1⊗b	NUM
ma-236	69	22	2	2	NUM
ma-236	69	23	)	)	PUNCT
ma-236	69	24	∥∥∥∥	∥∥∥∥	NUM
ma-236	69	25	6	6	NUM
ma-236	69	26	‖1⊗b−	‖1⊗b−	NOUN
ma-236	69	27	a⊗	a⊗	NOUN
ma-236	69	28	1‖2	1‖2	NUM
ma-236	69	29	‖f	‖f	ADP
ma-236	69	30	′′‖i,+∞	′′‖i,+∞	VERB
ma-236	69	31	24	24	NUM
ma-236	69	32	.	.	PUNCT
ma-236	70	1	recently	recently	ADV
ma-236	70	2	,	,	PUNCT
ma-236	70	3	the	the	DET
ma-236	70	4	following	follow	VERB
ma-236	70	5	inequality	inequality	NOUN
ma-236	70	6	of	of	ADP
ma-236	70	7	ostrowski	ostrowski	ADJ
ma-236	70	8	type	type	NOUN
ma-236	70	9	was	be	AUX
ma-236	70	10	obtained	obtain	VERB
ma-236	70	11	by	by	ADP
ma-236	70	12	stojiljković	stojiljković	PROPN
ma-236	70	13	et	et	PROPN
ma-236	70	14	al	al	PROPN
ma-236	70	15	.	.	PUNCT
ma-236	71	1	[	[	X
ma-236	71	2	26	26	NUM
ma-236	71	3	]	]	PUNCT
ma-236	71	4	whichgeneralized	whichgeneralize	VERB
ma-236	71	5	the	the	DET
ma-236	71	6	recently	recently	ADV
ma-236	71	7	obtained	obtain	VERB
ma-236	71	8	results	result	NOUN
ma-236	71	9	by	by	ADP
ma-236	71	10	dragomir	dragomir	VERB
ma-236	71	11	[	[	X
ma-236	71	12	13	13	NUM
ma-236	71	13	]	]	PUNCT
ma-236	71	14	.	.	PUNCT
ma-236	72	1	theorem	theorem	ADJ
ma-236	72	2	6	6	NUM
ma-236	72	3	.	.	PUNCT
ma-236	73	1	the	the	DET
ma-236	73	2	formulation	formulation	NOUN
ma-236	73	3	is	be	AUX
ma-236	73	4	the	the	DET
ma-236	73	5	same	same	ADJ
ma-236	73	6	as	as	ADP
ma-236	73	7	the	the	DET
ma-236	73	8	one	one	NOUN
ma-236	73	9	given	give	VERB
ma-236	73	10	by	by	ADP
ma-236	73	11	dragomir	dragomir	NOUN
ma-236	73	12	in	in	ADP
ma-236	73	13	his	his	PRON
ma-236	73	14	ostrowski	ostrowski	ADJ
ma-236	73	15	type	type	NOUN
ma-236	73	16	theorem	theorem	NOUN
ma-236	73	17	given	give	VERB
ma-236	73	18	above	above	ADV
ma-236	73	19	(	(	PUNCT
ma-236	73	20	1	1	NUM
ma-236	73	21	)	)	PUNCT
ma-236	73	22	with	with	ADP
ma-236	73	23	an	an	DET
ma-236	73	24	exception	exception	NOUN
ma-236	73	25	that	that	PRON
ma-236	73	26	α	α	PRON
ma-236	73	27	>	>	X
ma-236	73	28	0	0	NUM
ma-236	73	29	,	,	PUNCT
ma-236	73	30	then∣∣∣∣∣∣∣∣(λα	then∣∣∣∣∣∣∣∣(λα	NOUN
ma-236	73	31	+	+	CCONJ
ma-236	73	32	(	(	PUNCT
ma-236	73	33	1−	1−	NUM
ma-236	73	34	λ)α)f	λ)α)f	NOUN
ma-236	73	35	(	(	PUNCT
ma-236	73	36	(	(	PUNCT
ma-236	73	37	1−	1−	NUM
ma-236	73	38	λ)a⊗	λ)a⊗	NOUN
ma-236	73	39	1	1	NUM
ma-236	73	40	+	+	NUM
ma-236	73	41	λ1⊗b	λ1⊗b	NOUN
ma-236	73	42	)	)	PUNCT
ma-236	73	43	−α	−α	NOUN
ma-236	73	44	(	(	PUNCT
ma-236	73	45	(	(	PUNCT
ma-236	73	46	1−	1−	NUM
ma-236	73	47	λ)α	λ)α	NOUN
ma-236	73	48	∫	∫	PROPN
ma-236	73	49	1	1	NUM
ma-236	73	50	0	0	NUM
ma-236	73	51	f	f	NOUN
ma-236	73	52	(	(	PUNCT
ma-236	73	53	(	(	PUNCT
ma-236	73	54	1−	1−	NUM
ma-236	73	55	λ)(1−	λ)(1−	PROPN
ma-236	73	56	u)a⊗	u)a⊗	PROPN
ma-236	73	57	1	1	NUM
ma-236	73	58	+	+	CCONJ
ma-236	73	59	(	(	PUNCT
ma-236	73	60	u	u	NOUN
ma-236	73	61	+	+	X
ma-236	73	62	(	(	PUNCT
ma-236	73	63	1−	1−	NUM
ma-236	73	64	u)λ)1⊗b)(1−	u)λ)1⊗b)(1−	ADJ
ma-236	73	65	u)α−1du	u)α−1du	NOUN
ma-236	73	66	+	+	NOUN
ma-236	73	67	λα	λα	NOUN
ma-236	73	68	∫	∫	PROPN
ma-236	73	69	1	1	NUM
ma-236	73	70	0	0	NUM
ma-236	73	71	uα−1f	uα−1f	PROPN
ma-236	73	72	(	(	PUNCT
ma-236	73	73	(	(	PUNCT
ma-236	73	74	(	(	PUNCT
ma-236	73	75	1−	1−	NUM
ma-236	73	76	u	u	NOUN
ma-236	73	77	)	)	PUNCT
ma-236	73	78	+	+	CCONJ
ma-236	73	79	u(1−	u(1−	NOUN
ma-236	73	80	λ))a⊗	λ))a⊗	ADJ
ma-236	73	81	1	1	NUM
ma-236	73	82	+	+	CCONJ
ma-236	73	83	uλ1⊗b)du	uλ1⊗b)du	NOUN
ma-236	73	84	)	)	PUNCT
ma-236	73	85	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	73	86	6	6	NUM
ma-236	73	87	‖1⊗b−	‖1⊗b−	PROPN
ma-236	73	88	a⊗	a⊗	PROPN
ma-236	73	89	1‖	1‖	NUM
ma-236	74	1	(	(	PUNCT
ma-236	74	2	λα+1	λα+1	NOUN
ma-236	74	3	α+	α+	SYM
ma-236	74	4	1	1	NUM
ma-236	74	5	+	+	CCONJ
ma-236	74	6	(	(	PUNCT
ma-236	74	7	1−	1−	NUM
ma-236	74	8	λ)α+1	λ)α+1	NOUN
ma-236	74	9	α+	α+	PUNCT
ma-236	74	10	1	1	NUM
ma-236	74	11	)	)	PUNCT
ma-236	74	12	∥∥f	∥∥f	PROPN
ma-236	74	13	′∥∥	′∥∥	NOUN
ma-236	74	14	i,+∞	i,+∞	PROPN
ma-236	74	15	.	.	PUNCT
ma-236	75	1	stojiljković	stojiljković	PROPN
ma-236	75	2	et	et	PROPN
ma-236	75	3	al	al	PROPN
ma-236	75	4	.	.	PROPN
ma-236	75	5	,	,	PUNCT
ma-236	76	1	[	[	X
ma-236	76	2	27	27	NUM
ma-236	76	3	]	]	PUNCT
ma-236	76	4	recently	recently	ADV
ma-236	76	5	obtained	obtain	VERB
ma-236	76	6	a	a	DET
ma-236	76	7	trapezoid	trapezoid	ADJ
ma-236	76	8	type	type	NOUN
ma-236	76	9	tensorial	tensorial	ADJ
ma-236	76	10	inequality	inequality	NOUN
ma-236	76	11	which	which	PRON
ma-236	76	12	is	be	AUX
ma-236	76	13	given	give	VERB
ma-236	76	14	by	by	ADP
ma-236	76	15	theorem	theorem	NOUN
ma-236	76	16	7	7	NUM
ma-236	76	17	.	.	PUNCT
ma-236	76	18	assume	assume	VERB
ma-236	76	19	that	that	SCONJ
ma-236	76	20	f	f	PROPN
ma-236	76	21	is	be	AUX
ma-236	76	22	continuously	continuously	ADV
ma-236	76	23	differentiable	differentiable	ADJ
ma-236	76	24	on	on	ADP
ma-236	76	25	i	i	PRON
ma-236	76	26	with	with	ADP
ma-236	76	27	‖f	‖f	PRON
ma-236	76	28	′‖i,+∞	′‖i,+∞	VERB
ma-236	76	29	:	:	PUNCT
ma-236	77	1	=	=	SYM
ma-236	77	2	supt∈i	supt∈i	PROPN
ma-236	77	3	|f	|f	PROPN
ma-236	77	4	′(t)|	′(t)|	X
ma-236	77	5	<	<	X
ma-236	78	1	+	+	NOUN
ma-236	78	2	∞	∞	PROPN
ma-236	78	3	and	and	CCONJ
ma-236	78	4	a	a	DET
ma-236	78	5	,	,	PUNCT
ma-236	78	6	b	b	NOUN
ma-236	78	7	are	be	AUX
ma-236	78	8	selfadjoint	selfadjoint	VERB
ma-236	78	9	operators	operator	NOUN
ma-236	78	10	with	with	ADP
ma-236	78	11	sp(a	sp(a	NOUN
ma-236	78	12	)	)	PUNCT
ma-236	78	13	,	,	PUNCT
ma-236	78	14	sp(b	sp(b	PROPN
ma-236	78	15	)	)	PUNCT
ma-236	79	1	⊂	⊂	PROPN
ma-236	80	1	i	i	INTJ
ma-236	80	2	.	.	PUNCT
ma-236	81	1	then	then	ADV
ma-236	81	2	the	the	DET
ma-236	81	3	following	follow	VERB
ma-236	81	4	inequality	inequality	NOUN
ma-236	81	5	holds:∣∣∣∣∣∣∣∣	holds:∣∣∣∣∣∣∣∣	X
ma-236	81	6	(	(	PUNCT
ma-236	81	7	f	f	X
ma-236	81	8	(	(	PUNCT
ma-236	81	9	a)⊗	a)⊗	NOUN
ma-236	81	10	1	1	NUM
ma-236	81	11	+	+	SYM
ma-236	81	12	1⊗	1⊗	NUM
ma-236	81	13	f	f	X
ma-236	81	14	(	(	PUNCT
ma-236	81	15	b	b	NOUN
ma-236	81	16	)	)	PUNCT
ma-236	81	17	)	)	PUNCT
ma-236	81	18	(	(	PUNCT
ma-236	81	19	2	2	X
ma-236	81	20	)	)	PUNCT
ma-236	81	21	−α	−α	NOUN
ma-236	81	22	[	[	PUNCT
ma-236	81	23	∫	∫	PROPN
ma-236	81	24	1	1	NUM
ma-236	81	25	0	0	NUM
ma-236	81	26	(	(	PUNCT
ma-236	81	27	1−	1−	NUM
ma-236	81	28	λ)α−1f	λ)α−1f	NOUN
ma-236	81	29	(	(	PUNCT
ma-236	81	30	λ1⊗b+	λ1⊗b+	PROPN
ma-236	81	31	(	(	PUNCT
ma-236	81	32	1−	1−	NUM
ma-236	81	33	λ)a⊗	λ)a⊗	PROPN
ma-236	82	1	1)dλ	1)dλ	PROPN
ma-236	82	2	+	+	CCONJ
ma-236	82	3	∫	∫	PROPN
ma-236	82	4	1	1	NUM
ma-236	82	5	0	0	NUM
ma-236	82	6	λα−1f	λα−1f	X
ma-236	82	7	(	(	PUNCT
ma-236	82	8	λ1⊗b+	λ1⊗b+	NOUN
ma-236	82	9	(	(	PUNCT
ma-236	82	10	1−	1−	NUM
ma-236	83	1	λ)a⊗	λ)a⊗	X
ma-236	83	2	1)dλ	1)dλ	NUM
ma-236	83	3	]	]	PUNCT
ma-236	83	4	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ma-236	83	5	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	83	6	eur	eur	PROPN
ma-236	83	7	.	.	PUNCT
ma-236	84	1	j.	j.	PROPN
ma-236	84	2	math	math	PROPN
ma-236	84	3	.	.	PUNCT
ma-236	85	1	anal	anal	PROPN
ma-236	85	2	.	.	PUNCT
ma-236	86	1	10.28924	10.28924	NUM
ma-236	86	2	/	/	SYM
ma-236	86	3	ada	ada	PROPN
ma-236	86	4	/	/	SYM
ma-236	86	5	ma.4.17	ma.4.17	NOUN
ma-236	86	6	4	4	NUM
ma-236	86	7	≤	≤	PROPN
ma-236	86	8	‖1⊗b−	‖1⊗b−	NOUN
ma-236	86	9	a⊗	a⊗	NOUN
ma-236	87	1	1‖	1‖	NUM
ma-236	87	2	1	1	NUM
ma-236	87	3	1	1	NUM
ma-236	87	4	+	+	NUM
ma-236	87	5	α	α	PROPN
ma-236	87	6	(	(	PUNCT
ma-236	87	7	2−	2−	NUM
ma-236	87	8	21−α	21−α	NUM
ma-236	87	9	)	)	PUNCT
ma-236	87	10	∥∥f	∥∥f	PROPN
ma-236	87	11	′∥∥	′∥∥	VERB
ma-236	87	12	i,+∞	i,+∞	ADV
ma-236	87	13	.	.	PUNCT
ma-236	88	1	in	in	ADP
ma-236	88	2	order	order	NOUN
ma-236	88	3	to	to	PART
ma-236	88	4	derive	derive	VERB
ma-236	88	5	similar	similar	ADJ
ma-236	88	6	inequalities	inequality	NOUN
ma-236	88	7	of	of	ADP
ma-236	88	8	the	the	DET
ma-236	88	9	tensorial	tensorial	ADJ
ma-236	88	10	type	type	NOUN
ma-236	88	11	,	,	PUNCT
ma-236	88	12	we	we	PRON
ma-236	88	13	need	need	VERB
ma-236	88	14	the	the	DET
ma-236	88	15	following	follow	VERB
ma-236	88	16	introductionand	introductionand	NOUN
ma-236	88	17	preliminaries.let	preliminaries.let	PROPN
ma-236	88	18	i1	i1	PROPN
ma-236	88	19	,	,	PUNCT
ma-236	88	20	...	...	PUNCT
ma-236	88	21	,	,	PUNCT
ma-236	88	22	ik	ik	X
ma-236	88	23	be	be	VERB
ma-236	88	24	intervals	interval	NOUN
ma-236	88	25	from	from	ADP
ma-236	88	26	r	r	NOUN
ma-236	88	27	and	and	CCONJ
ma-236	88	28	let	let	VERB
ma-236	88	29	f	f	PROPN
ma-236	88	30	:	:	PUNCT
ma-236	89	1	i1	i1	PROPN
ma-236	89	2	×	×	PROPN
ma-236	89	3	...	...	PUNCT
ma-236	89	4	×	×	PROPN
ma-236	89	5	ik	ik	PROPN
ma-236	89	6	→	→	SYM
ma-236	89	7	r	r	NOUN
ma-236	89	8	be	be	AUX
ma-236	89	9	an	an	DET
ma-236	89	10	essentially	essentially	ADV
ma-236	89	11	bounded	bounded	ADJ
ma-236	89	12	realfunction	realfunction	NOUN
ma-236	89	13	defined	define	VERB
ma-236	89	14	on	on	ADP
ma-236	89	15	the	the	DET
ma-236	89	16	product	product	NOUN
ma-236	89	17	of	of	ADP
ma-236	89	18	the	the	DET
ma-236	89	19	intervals	interval	NOUN
ma-236	89	20	.	.	PUNCT
ma-236	90	1	let	let	VERB
ma-236	90	2	a	a	DET
ma-236	90	3	=	=	SYM
ma-236	90	4	(	(	PUNCT
ma-236	90	5	a1	a1	PROPN
ma-236	90	6	,	,	PUNCT
ma-236	90	7	...	...	PUNCT
ma-236	90	8	,	,	PUNCT
ma-236	90	9	ak	ak	PROPN
ma-236	90	10	)	)	PUNCT
ma-236	90	11	be	be	AUX
ma-236	90	12	a	a	DET
ma-236	90	13	k	k	NOUN
ma-236	90	14	-	-	NOUN
ma-236	90	15	tuple	tuple	NOUN
ma-236	90	16	of	of	ADP
ma-236	90	17	boundedselfadjoint	boundedselfadjoint	NOUN
ma-236	90	18	operators	operator	NOUN
ma-236	90	19	on	on	ADP
ma-236	90	20	hilbert	hilbert	PROPN
ma-236	90	21	spaces	space	NOUN
ma-236	90	22	h1	h1	PROPN
ma-236	90	23	,	,	PUNCT
ma-236	90	24	...	...	PUNCT
ma-236	90	25	,	,	PUNCT
ma-236	90	26	hk	hk	PROPN
ma-236	90	27	such	such	ADJ
ma-236	90	28	that	that	SCONJ
ma-236	90	29	the	the	DET
ma-236	90	30	spectrum	spectrum	NOUN
ma-236	90	31	of	of	ADP
ma-236	90	32	ai	ai	NOUN
ma-236	90	33	is	be	AUX
ma-236	90	34	contained	contain	VERB
ma-236	90	35	in	in	ADP
ma-236	90	36	iifor	iifor	ADP
ma-236	90	37	i	i	PROPN
ma-236	90	38	=	=	NOUN
ma-236	90	39	1	1	NUM
ma-236	90	40	,	,	PUNCT
ma-236	90	41	...	...	PUNCT
ma-236	90	42	,	,	PUNCT
ma-236	90	43	k	k	X
ma-236	90	44	.	.	PUNCT
ma-236	91	1	we	we	PRON
ma-236	91	2	say	say	VERB
ma-236	91	3	that	that	SCONJ
ma-236	91	4	such	such	DET
ma-236	91	5	a	a	DET
ma-236	91	6	k	k	NOUN
ma-236	91	7	-	-	NOUN
ma-236	91	8	tuple	tuple	NOUN
ma-236	91	9	is	be	AUX
ma-236	91	10	in	in	ADP
ma-236	91	11	the	the	DET
ma-236	91	12	domain	domain	NOUN
ma-236	91	13	of	of	ADP
ma-236	91	14	f	f	PROPN
ma-236	91	15	.	.	PUNCT
ma-236	92	1	if	if	SCONJ
ma-236	92	2	ai	ai	VERB
ma-236	92	3	=	=	PUNCT
ma-236	92	4	∫	∫	PROPN
ma-236	92	5	ii	ii	PROPN
ma-236	92	6	λidei(λi	λidei(λi	PROPN
ma-236	92	7	)	)	PUNCT
ma-236	92	8	is	be	AUX
ma-236	92	9	the	the	DET
ma-236	92	10	spectral	spectral	ADJ
ma-236	92	11	resolution	resolution	NOUN
ma-236	92	12	of	of	ADP
ma-236	92	13	ai	ai	VERB
ma-236	92	14	for	for	ADP
ma-236	92	15	i	i	PRON
ma-236	92	16	=	=	NOUN
ma-236	92	17	1	1	NUM
ma-236	92	18	,	,	PUNCT
ma-236	92	19	...	...	PUNCT
ma-236	92	20	,	,	PUNCT
ma-236	92	21	k	k	X
ma-236	92	22	by	by	ADP
ma-236	92	23	following	follow	VERB
ma-236	92	24	,	,	PUNCT
ma-236	92	25	we	we	PRON
ma-236	92	26	define	define	VERB
ma-236	92	27	f	f	PROPN
ma-236	92	28	(	(	PUNCT
ma-236	92	29	a1	a1	PROPN
ma-236	92	30	,	,	PUNCT
ma-236	92	31	...	...	PUNCT
ma-236	92	32	,	,	PUNCT
ma-236	92	33	ak	ak	PROPN
ma-236	92	34	)	)	PUNCT
ma-236	92	35	:	:	PUNCT
ma-236	93	1	=	=	PROPN
ma-236	93	2	∫	∫	PROPN
ma-236	93	3	i1	i1	PROPN
ma-236	93	4	...	...	PUNCT
ma-236	94	1	∫	∫	PROPN
ma-236	94	2	ik	ik	PROPN
ma-236	94	3	f	f	PROPN
ma-236	94	4	(	(	PUNCT
ma-236	94	5	λ1	λ1	PROPN
ma-236	94	6	,	,	PUNCT
ma-236	94	7	...	...	PUNCT
ma-236	94	8	,	,	PUNCT
ma-236	94	9	λk)de1(λ1)⊗	λk)de1(λ1)⊗	X
ma-236	94	10	...	...	PUNCT
ma-236	95	1	⊗	⊗	NUM
ma-236	95	2	dek(λk	dek(λk	NOUN
ma-236	95	3	)	)	PUNCT
ma-236	95	4	as	as	SCONJ
ma-236	95	5	bounded	bounded	ADJ
ma-236	95	6	selfadjoint	selfadjoint	NOUN
ma-236	95	7	operator	operator	NOUN
ma-236	95	8	on	on	ADP
ma-236	95	9	the	the	DET
ma-236	95	10	tensorial	tensorial	ADJ
ma-236	95	11	product	product	NOUN
ma-236	95	12	h1	h1	NOUN
ma-236	95	13	⊗	⊗	PROPN
ma-236	95	14	...	...	PUNCT
ma-236	96	1	⊗hk	⊗hk	NUM
ma-236	96	2	.if	.if	PUNCT
ma-236	97	1	the	the	DET
ma-236	97	2	hilbert	hilbert	PROPN
ma-236	97	3	spaces	space	NOUN
ma-236	97	4	are	be	AUX
ma-236	97	5	of	of	ADP
ma-236	97	6	finite	finite	ADJ
ma-236	97	7	dimension	dimension	NOUN
ma-236	97	8	,	,	PUNCT
ma-236	97	9	then	then	ADV
ma-236	97	10	the	the	DET
ma-236	97	11	above	above	ADJ
ma-236	97	12	integrals	integral	NOUN
ma-236	97	13	become	become	VERB
ma-236	97	14	finite	finite	ADJ
ma-236	97	15	sums	sum	NOUN
ma-236	97	16	,	,	PUNCT
ma-236	97	17	and	and	CCONJ
ma-236	97	18	wemay	wemay	ADV
ma-236	97	19	consider	consider	VERB
ma-236	97	20	the	the	DET
ma-236	97	21	functional	functional	ADJ
ma-236	97	22	calculus	calculus	NOUN
ma-236	97	23	for	for	ADP
ma-236	97	24	arbitrary	arbitrary	ADJ
ma-236	97	25	real	real	ADJ
ma-236	97	26	functions	function	NOUN
ma-236	97	27	.	.	PUNCT
ma-236	98	1	this	this	DET
ma-236	98	2	construction	construction	NOUN
ma-236	98	3	[	[	X
ma-236	98	4	6	6	NUM
ma-236	98	5	]	]	PUNCT
ma-236	98	6	extends	extend	VERB
ma-236	98	7	thedefinition	thedefinition	NOUN
ma-236	98	8	of	of	ADP
ma-236	98	9	koranyi	koranyi	PROPN
ma-236	99	1	[	[	X
ma-236	99	2	16	16	NUM
ma-236	99	3	]	]	PUNCT
ma-236	99	4	for	for	ADP
ma-236	99	5	functions	function	NOUN
ma-236	99	6	of	of	ADP
ma-236	99	7	two	two	NUM
ma-236	99	8	variables	variable	NOUN
ma-236	99	9	and	and	CCONJ
ma-236	99	10	have	have	VERB
ma-236	99	11	the	the	DET
ma-236	99	12	property	property	NOUN
ma-236	99	13	that	that	PRON
ma-236	99	14	f	f	PROPN
ma-236	99	15	(	(	PUNCT
ma-236	99	16	a1	a1	PROPN
ma-236	99	17	,	,	PUNCT
ma-236	99	18	...	...	PUNCT
ma-236	99	19	ak	ak	PROPN
ma-236	99	20	)	)	PUNCT
ma-236	99	21	=	=	NUM
ma-236	99	22	f1(a1)⊗	f1(a1)⊗	NOUN
ma-236	99	23	...	...	PUNCT
ma-236	100	1	⊗	⊗	PROPN
ma-236	100	2	fk(ak	fk(ak	PROPN
ma-236	100	3	)	)	PUNCT
ma-236	100	4	,	,	PUNCT
ma-236	100	5	whenever	whenever	SCONJ
ma-236	100	6	f	f	PROPN
ma-236	100	7	can	can	AUX
ma-236	100	8	be	be	AUX
ma-236	100	9	separated	separate	VERB
ma-236	100	10	as	as	ADP
ma-236	100	11	a	a	DET
ma-236	100	12	product	product	NOUN
ma-236	100	13	f	f	X
ma-236	100	14	(	(	PUNCT
ma-236	100	15	t1	t1	PROPN
ma-236	100	16	,	,	PUNCT
ma-236	100	17	...	...	PUNCT
ma-236	100	18	,	,	PUNCT
ma-236	100	19	tk	tk	PROPN
ma-236	100	20	)	)	PUNCT
ma-236	100	21	=	=	SYM
ma-236	100	22	f1(t1)	f1(t1)	NOUN
ma-236	100	23	...	...	PUNCT
ma-236	100	24	fk(tk	fk(tk	PROPN
ma-236	100	25	)	)	PUNCT
ma-236	100	26	of	of	ADP
ma-236	100	27	k	k	PROPN
ma-236	100	28	functions	function	NOUN
ma-236	100	29	each	each	PRON
ma-236	100	30	de	de	X
ma-236	100	31	-	-	VERB
ma-236	100	32	pending	pende	VERB
ma-236	100	33	on	on	ADP
ma-236	100	34	only	only	ADV
ma-236	100	35	one	one	NUM
ma-236	100	36	variable.recall	variable.recall	NOUN
ma-236	100	37	the	the	DET
ma-236	100	38	following	follow	VERB
ma-236	100	39	property	property	NOUN
ma-236	100	40	of	of	ADP
ma-236	100	41	the	the	DET
ma-236	100	42	tensorial	tensorial	ADJ
ma-236	100	43	product	product	NOUN
ma-236	100	44	(	(	PUNCT
ma-236	100	45	ac)⊗	ac)⊗	PROPN
ma-236	100	46	(	(	PUNCT
ma-236	100	47	b⊗d	b⊗d	NOUN
ma-236	100	48	)	)	PUNCT
ma-236	100	49	=	=	PRON
ma-236	100	50	(	(	PUNCT
ma-236	100	51	a⊗b)(c⊗d	a⊗b)(c⊗d	PROPN
ma-236	100	52	)	)	PUNCT
ma-236	100	53	that	that	PRON
ma-236	100	54	holds	hold	VERB
ma-236	100	55	for	for	ADP
ma-236	100	56	any	any	DET
ma-236	100	57	a	a	DET
ma-236	100	58	,	,	PUNCT
ma-236	100	59	b	b	NOUN
ma-236	100	60	,	,	PUNCT
ma-236	100	61	c	c	NOUN
ma-236	100	62	,	,	PUNCT
ma-236	100	63	d	d	PROPN
ma-236	100	64	∈	∈	PROPN
ma-236	100	65	b(h	b(h	PROPN
ma-236	100	66	)	)	PUNCT
ma-236	100	67	.from	.from	ADP
ma-236	100	68	the	the	DET
ma-236	100	69	property	property	NOUN
ma-236	100	70	we	we	PRON
ma-236	100	71	can	can	AUX
ma-236	100	72	deduce	deduce	VERB
ma-236	100	73	easily	easily	ADV
ma-236	100	74	the	the	DET
ma-236	100	75	following	follow	VERB
ma-236	100	76	consequences	consequence	NOUN
ma-236	100	77	an	an	DET
ma-236	100	78	⊗bn	⊗bn	ADJ
ma-236	100	79	=	=	SYM
ma-236	100	80	(	(	PUNCT
ma-236	100	81	a⊗b)n	a⊗b)n	PROPN
ma-236	100	82	,	,	PUNCT
ma-236	100	83	n	n	PROPN
ma-236	100	84	>	>	X
ma-236	100	85	0	0	NUM
ma-236	100	86	,	,	PUNCT
ma-236	100	87	(	(	PUNCT
ma-236	100	88	a⊗	a⊗	NOUN
ma-236	100	89	1)(1⊗b	1)(1⊗b	NUM
ma-236	100	90	)	)	PUNCT
ma-236	100	91	=	=	PUNCT
ma-236	100	92	(	(	PUNCT
ma-236	100	93	1⊗b)(a⊗	1⊗b)(a⊗	NUM
ma-236	100	94	1	1	NUM
ma-236	100	95	)	)	PUNCT
ma-236	100	96	=	=	NOUN
ma-236	100	97	a⊗	a⊗	NOUN
ma-236	100	98	b	b	NOUN
ma-236	100	99	,	,	PUNCT
ma-236	100	100	which	which	PRON
ma-236	100	101	can	can	AUX
ma-236	100	102	be	be	AUX
ma-236	100	103	extended	extend	VERB
ma-236	100	104	,	,	PUNCT
ma-236	100	105	for	for	ADP
ma-236	100	106	two	two	NUM
ma-236	100	107	natural	natural	ADJ
ma-236	100	108	numbers	number	NOUN
ma-236	100	109	m	m	PROPN
ma-236	100	110	,	,	PUNCT
ma-236	100	111	n	n	CCONJ
ma-236	100	112	we	we	PRON
ma-236	100	113	have	have	VERB
ma-236	100	114	(	(	PUNCT
ma-236	100	115	a⊗	a⊗	NOUN
ma-236	100	116	1)n(1⊗b)m	1)n(1⊗b)m	NUM
ma-236	101	1	=	=	SYM
ma-236	101	2	(	(	PUNCT
ma-236	101	3	1⊗b)m(a⊗	1⊗b)m(a⊗	NUM
ma-236	101	4	1)n	1)n	NUM
ma-236	101	5	=	=	PUNCT
ma-236	101	6	an	an	DET
ma-236	101	7	⊗bm	⊗bm	NOUN
ma-236	101	8	.	.	PUNCT
ma-236	102	1	for	for	ADP
ma-236	102	2	more	more	ADJ
ma-236	102	3	information	information	NOUN
ma-236	102	4	,	,	PUNCT
ma-236	102	5	consult	consult	VERB
ma-236	102	6	the	the	DET
ma-236	102	7	following	follow	VERB
ma-236	102	8	book	book	NOUN
ma-236	102	9	related	relate	VERB
ma-236	102	10	to	to	ADP
ma-236	102	11	tensors	tensor	NOUN
ma-236	102	12	[	[	X
ma-236	102	13	14	14	NUM
ma-236	102	14	]	]	PUNCT
ma-236	102	15	.	.	PUNCT
ma-236	103	1	the	the	DET
ma-236	103	2	following	follow	VERB
ma-236	103	3	lemmawhich	lemmawhich	NOUN
ma-236	103	4	we	we	PRON
ma-236	103	5	require	require	VERB
ma-236	103	6	can	can	AUX
ma-236	103	7	be	be	AUX
ma-236	103	8	found	find	VERB
ma-236	103	9	in	in	ADP
ma-236	103	10	a	a	DET
ma-236	103	11	paper	paper	NOUN
ma-236	103	12	of	of	ADP
ma-236	103	13	dragomir	dragomir	NOUN
ma-236	103	14	[	[	X
ma-236	103	15	12	12	NUM
ma-236	103	16	]	]	PUNCT
ma-236	103	17	.	.	PUNCT
ma-236	104	1	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	104	2	eur	eur	PROPN
ma-236	104	3	.	.	PUNCT
ma-236	105	1	j.	j.	PROPN
ma-236	105	2	math	math	PROPN
ma-236	105	3	.	.	PUNCT
ma-236	106	1	anal	anal	PROPN
ma-236	106	2	.	.	PUNCT
ma-236	107	1	10.28924	10.28924	NUM
ma-236	107	2	/	/	SYM
ma-236	107	3	ada	ada	PROPN
ma-236	107	4	/	/	SYM
ma-236	107	5	ma.4.17	ma.4.17	NOUN
ma-236	107	6	5	5	NUM
ma-236	107	7	lemma	lemma	PROPN
ma-236	107	8	1	1	X
ma-236	107	9	.	.	PUNCT
ma-236	107	10	assume	assume	VERB
ma-236	107	11	a	a	PRON
ma-236	107	12	and	and	CCONJ
ma-236	107	13	b	b	NOUN
ma-236	107	14	are	be	AUX
ma-236	107	15	selfadjoint	selfadjoint	VERB
ma-236	107	16	operators	operator	NOUN
ma-236	107	17	with	with	ADP
ma-236	107	18	sp(a	sp(a	NOUN
ma-236	107	19	)	)	PUNCT
ma-236	108	1	⊂	⊂	PROPN
ma-236	109	1	i	i	PRON
ma-236	109	2	,	,	PUNCT
ma-236	109	3	sp(b	sp(b	PROPN
ma-236	109	4	)	)	PUNCT
ma-236	110	1	⊂	⊂	PROPN
ma-236	110	2	j	j	PROPN
ma-236	110	3	and	and	CCONJ
ma-236	110	4	having	have	VERB
ma-236	110	5	the	the	DET
ma-236	110	6	spectral	spectral	ADJ
ma-236	110	7	resolutions	resolution	NOUN
ma-236	110	8	.	.	PUNCT
ma-236	111	1	let	let	VERB
ma-236	111	2	f	f	NOUN
ma-236	111	3	;	;	PUNCT
ma-236	111	4	h	h	PRON
ma-236	111	5	be	be	AUX
ma-236	111	6	continuous	continuous	ADJ
ma-236	111	7	on	on	ADP
ma-236	111	8	i	i	PRON
ma-236	111	9	,	,	PUNCT
ma-236	111	10	g	g	PROPN
ma-236	111	11	,	,	PUNCT
ma-236	111	12	k	k	X
ma-236	111	13	continuous	continuous	ADJ
ma-236	111	14	on	on	ADP
ma-236	111	15	j	j	PROPN
ma-236	111	16	and	and	CCONJ
ma-236	111	17	φ	φ	PROPN
ma-236	111	18	and	and	CCONJ
ma-236	111	19	ψ	ψ	X
ma-236	111	20	continuous	continuous	ADJ
ma-236	111	21	on	on	ADP
ma-236	111	22	an	an	DET
ma-236	111	23	interval	interval	NOUN
ma-236	111	24	k	k	PROPN
ma-236	112	1	that	that	PRON
ma-236	112	2	contains	contain	VERB
ma-236	112	3	the	the	DET
ma-236	112	4	sum	sum	NOUN
ma-236	112	5	of	of	ADP
ma-236	112	6	the	the	DET
ma-236	112	7	intervals	interval	NOUN
ma-236	112	8	f	f	X
ma-236	112	9	(	(	PUNCT
ma-236	112	10	i	i	NOUN
ma-236	112	11	)	)	PUNCT
ma-236	113	1	+	+	CCONJ
ma-236	113	2	g(j	g(j	PROPN
ma-236	113	3	)	)	PUNCT
ma-236	113	4	;	;	PUNCT
ma-236	114	1	h(i	h(i	X
ma-236	114	2	)	)	PUNCT
ma-236	115	1	+	+	CCONJ
ma-236	115	2	k(j),then	k(j),then	PROPN
ma-236	115	3	φ(f	φ(f	PROPN
ma-236	115	4	(	(	PUNCT
ma-236	115	5	a)⊗	a)⊗	NOUN
ma-236	115	6	1	1	NUM
ma-236	115	7	+	+	SYM
ma-236	115	8	1⊗	1⊗	NUM
ma-236	115	9	g(b))ψ(h(a)⊗	g(b))ψ(h(a)⊗	NOUN
ma-236	115	10	1	1	NUM
ma-236	115	11	+	+	SYM
ma-236	115	12	1⊗	1⊗	NUM
ma-236	115	13	k(b	k(b	PROPN
ma-236	115	14	)	)	PUNCT
ma-236	115	15	)	)	PUNCT
ma-236	116	1	=	=	SYM
ma-236	116	2	∫	∫	PROPN
ma-236	117	1	i	i	PRON
ma-236	117	2	∫	∫	PROPN
ma-236	117	3	j	j	PROPN
ma-236	117	4	φ(f	φ(f	PROPN
ma-236	117	5	(	(	PUNCT
ma-236	117	6	t	t	PROPN
ma-236	117	7	)	)	PUNCT
ma-236	117	8	+	+	CCONJ
ma-236	117	9	g(s))ψ(h(t	g(s))ψ(h(t	NUM
ma-236	117	10	)	)	PUNCT
ma-236	117	11	+	+	CCONJ
ma-236	117	12	k(s))det	k(s))det	PROPN
ma-236	117	13	⊗	⊗	PROPN
ma-236	117	14	dfs	dfs	INTJ
ma-236	117	15	.	.	PUNCT
ma-236	118	1	in	in	ADP
ma-236	118	2	[	[	X
ma-236	118	3	20	20	NUM
ma-236	118	4	]	]	PUNCT
ma-236	118	5	,	,	PUNCT
ma-236	118	6	shuang	shuang	PROPN
ma-236	118	7	,	,	PUNCT
ma-236	118	8	wang	wang	PROPN
ma-236	118	9	and	and	CCONJ
ma-236	118	10	qi	qi	PROPN
ma-236	118	11	used	use	VERB
ma-236	118	12	the	the	DET
ma-236	118	13	following	follow	VERB
ma-236	118	14	identity	identity	NOUN
ma-236	118	15	to	to	PART
ma-236	118	16	obtain	obtain	VERB
ma-236	118	17	simpson	simpson	PROPN
ma-236	118	18	type	type	PROPN
ma-236	118	19	inequalitiesand	inequalitiesand	NOUN
ma-236	118	20	some	some	DET
ma-236	118	21	applications	application	NOUN
ma-236	118	22	.	.	PUNCT
ma-236	119	1	lemma	lemma	PROPN
ma-236	119	2	2	2	X
ma-236	119	3	.	.	PUNCT
ma-236	120	1	let	let	VERB
ma-236	120	2	f	f	NOUN
ma-236	120	3	:	:	PUNCT
ma-236	121	1	i	i	PRON
ma-236	121	2	⊂	⊂	PROPN
ma-236	122	1	r→	r→	VERB
ma-236	122	2	r	r	NOUN
ma-236	122	3	be	be	AUX
ma-236	122	4	a	a	DET
ma-236	122	5	differentiable	differentiable	ADJ
ma-236	122	6	function	function	NOUN
ma-236	122	7	on	on	ADP
ma-236	122	8	i	i	PROPN
ma-236	122	9	◦	◦	NOUN
ma-236	122	10	,	,	PUNCT
ma-236	122	11	a	a	DET
ma-236	122	12	,	,	PUNCT
ma-236	122	13	b	b	X
ma-236	122	14	∈	∈	PROPN
ma-236	123	1	i	i	PRON
ma-236	123	2	◦	◦	VERB
ma-236	123	3	with	with	ADP
ma-236	123	4	a	a	DET
ma-236	123	5	<	<	X
ma-236	123	6	b.	b.	NOUN
ma-236	123	7	if	if	SCONJ
ma-236	123	8	f	f	PROPN
ma-236	123	9	′	′	NOUN
ma-236	123	10	∈	∈	PROPN
ma-236	123	11	l1[a	l1[a	NOUN
ma-236	123	12	,	,	PUNCT
ma-236	123	13	b	b	NOUN
ma-236	123	14	]	]	X
ma-236	123	15	,	,	PUNCT
ma-236	123	16	then	then	ADV
ma-236	123	17	the	the	DET
ma-236	123	18	following	follow	VERB
ma-236	123	19	equality	equality	NOUN
ma-236	123	20	holds	hold	VERB
ma-236	123	21	:	:	PUNCT
ma-236	123	22	1	1	NUM
ma-236	123	23	8	8	NUM
ma-236	123	24	[	[	PUNCT
ma-236	123	25	f	f	X
ma-236	123	26	(	(	PUNCT
ma-236	123	27	a	a	NOUN
ma-236	123	28	)	)	PUNCT
ma-236	124	1	+	+	NOUN
ma-236	124	2	6f	6f	NUM
ma-236	124	3	(	(	PUNCT
ma-236	124	4	a	a	DET
ma-236	124	5	+	+	NOUN
ma-236	124	6	b	b	SYM
ma-236	124	7	2	2	NUM
ma-236	124	8	)	)	PUNCT
ma-236	125	1	+	+	CCONJ
ma-236	125	2	f	f	X
ma-236	125	3	(	(	PUNCT
ma-236	125	4	b	b	NOUN
ma-236	125	5	)	)	PUNCT
ma-236	125	6	]	]	PUNCT
ma-236	125	7	−	−	PROPN
ma-236	125	8	1	1	NUM
ma-236	125	9	b	b	X
ma-236	125	10	−	−	PROPN
ma-236	125	11	a	a	DET
ma-236	125	12	∫	∫	PROPN
ma-236	125	13	b	b	PROPN
ma-236	125	14	a	a	DET
ma-236	125	15	f	f	X
ma-236	125	16	(	(	PUNCT
ma-236	125	17	x)dx	x)dx	PROPN
ma-236	125	18	(	(	PUNCT
ma-236	125	19	3	3	NUM
ma-236	125	20	)	)	PUNCT
ma-236	125	21	=	=	SYM
ma-236	126	1	b	b	X
ma-236	126	2	−	−	NOUN
ma-236	126	3	a	a	DET
ma-236	126	4	4	4	NUM
ma-236	126	5	(	(	PUNCT
ma-236	126	6	∫	∫	PROPN
ma-236	126	7	1	1	NUM
ma-236	126	8	0	0	NUM
ma-236	127	1	[	[	X
ma-236	127	2	(	(	PUNCT
ma-236	127	3	3	3	NUM
ma-236	127	4	4	4	NUM
ma-236	127	5	−	−	NOUN
ma-236	127	6	t	t	NOUN
ma-236	127	7	)	)	PUNCT
ma-236	128	1	f	f	PROPN
ma-236	129	1	′	′	NUM
ma-236	129	2	(	(	PUNCT
ma-236	129	3	ta	ta	PART
ma-236	129	4	+	+	CCONJ
ma-236	129	5	(	(	PUNCT
ma-236	129	6	1−	1−	NUM
ma-236	129	7	t	t	PROPN
ma-236	129	8	)	)	PUNCT
ma-236	129	9	a	a	PRON
ma-236	130	1	+	+	NOUN
ma-236	130	2	b	b	SYM
ma-236	130	3	2	2	NUM
ma-236	130	4	)	)	PUNCT
ma-236	131	1	+	+	CCONJ
ma-236	131	2	(	(	PUNCT
ma-236	131	3	1	1	NUM
ma-236	131	4	4	4	NUM
ma-236	131	5	−	−	NOUN
ma-236	131	6	t	t	NOUN
ma-236	131	7	)	)	PUNCT
ma-236	132	1	f	f	PROPN
ma-236	133	1	′	′	NUM
ma-236	133	2	(	(	PUNCT
ma-236	133	3	t	t	PROPN
ma-236	133	4	a	a	DET
ma-236	133	5	+	+	NOUN
ma-236	133	6	b	b	SYM
ma-236	133	7	2	2	NUM
ma-236	133	8	+	+	CCONJ
ma-236	133	9	(	(	PUNCT
ma-236	133	10	1−	1−	NUM
ma-236	133	11	t)b	t)b	NOUN
ma-236	133	12	)	)	PUNCT
ma-236	133	13	]	]	PUNCT
ma-236	134	1	dt	dt	PUNCT
ma-236	134	2	)	)	PUNCT
ma-236	134	3	.	.	PUNCT
ma-236	135	1	this	this	DET
ma-236	135	2	paper	paper	NOUN
ma-236	135	3	delves	delve	VERB
ma-236	135	4	into	into	ADP
ma-236	135	5	a	a	DET
ma-236	135	6	novel	novel	ADJ
ma-236	135	7	area	area	NOUN
ma-236	135	8	of	of	ADP
ma-236	135	9	mathematics	mathematic	NOUN
ma-236	135	10	:	:	PUNCT
ma-236	135	11	tensorial	tensorial	ADJ
ma-236	135	12	inequalities	inequality	NOUN
ma-236	135	13	of	of	ADP
ma-236	135	14	the	the	DET
ma-236	135	15	simpson	simpson	PROPN
ma-236	135	16	type	type	PROPN
ma-236	135	17	fordifferentiable	fordifferentiable	ADJ
ma-236	135	18	functions	function	NOUN
ma-236	135	19	within	within	ADP
ma-236	135	20	a	a	DET
ma-236	135	21	tensorial	tensorial	ADJ
ma-236	135	22	hilbert	hilbert	NOUN
ma-236	135	23	space	space	NOUN
ma-236	135	24	.	.	PUNCT
ma-236	136	1	this	this	DET
ma-236	136	2	field	field	NOUN
ma-236	136	3	is	be	AUX
ma-236	136	4	young	young	ADJ
ma-236	136	5	and	and	CCONJ
ma-236	136	6	ripe	ripe	ADJ
ma-236	136	7	for	for	ADP
ma-236	136	8	exploration	exploration	NOUN
ma-236	136	9	,	,	PUNCT
ma-236	136	10	and	and	CCONJ
ma-236	136	11	obtaining	obtain	VERB
ma-236	136	12	new	new	ADJ
ma-236	136	13	bounds	bound	NOUN
ma-236	136	14	for	for	ADP
ma-236	136	15	various	various	ADJ
ma-236	136	16	combinations	combination	NOUN
ma-236	136	17	of	of	ADP
ma-236	136	18	convex	convex	NOUN
ma-236	136	19	functions	function	NOUN
ma-236	136	20	is	be	AUX
ma-236	136	21	crucial	crucial	ADJ
ma-236	136	22	for	for	SCONJ
ma-236	136	23	its	its	PRON
ma-236	136	24	advancement.the	advancement.the	DET
ma-236	136	25	paper	paper	NOUN
ma-236	136	26	is	be	AUX
ma-236	136	27	structured	structure	VERB
ma-236	136	28	logically	logically	ADV
ma-236	136	29	.	.	PUNCT
ma-236	137	1	the	the	DET
ma-236	137	2	"	"	PUNCT
ma-236	137	3	main	main	ADJ
ma-236	137	4	results	result	NOUN
ma-236	137	5	"	"	PUNCT
ma-236	137	6	section	section	NOUN
ma-236	137	7	unveils	unveil	VERB
ma-236	137	8	the	the	DET
ma-236	137	9	key	key	ADJ
ma-236	137	10	findings	finding	NOUN
ma-236	137	11	that	that	PRON
ma-236	137	12	contributeto	contributeto	VERB
ma-236	137	13	the	the	DET
ma-236	137	14	novelty	novelty	NOUN
ma-236	137	15	of	of	ADP
ma-236	137	16	this	this	DET
ma-236	137	17	work	work	NOUN
ma-236	137	18	.	.	PUNCT
ma-236	138	1	subsequently	subsequently	ADV
ma-236	138	2	,	,	PUNCT
ma-236	138	3	the	the	DET
ma-236	138	4	"	"	PUNCT
ma-236	138	5	examples	example	NOUN
ma-236	138	6	and	and	CCONJ
ma-236	138	7	consequences	consequence	NOUN
ma-236	138	8	"	"	PUNCT
ma-236	138	9	section	section	NOUN
ma-236	138	10	showcasespractical	showcasespractical	ADJ
ma-236	138	11	applications	application	NOUN
ma-236	138	12	of	of	ADP
ma-236	138	13	the	the	DET
ma-236	138	14	obtained	obtain	VERB
ma-236	138	15	results	result	NOUN
ma-236	138	16	.	.	PUNCT
ma-236	139	1	by	by	ADP
ma-236	139	2	leveraging	leverage	VERB
ma-236	139	3	known	know	VERB
ma-236	139	4	properties	property	NOUN
ma-236	139	5	of	of	ADP
ma-236	139	6	the	the	DET
ma-236	139	7	exponentialoperator	exponentialoperator	NOUN
ma-236	139	8	and	and	CCONJ
ma-236	139	9	its	its	PRON
ma-236	139	10	integral	integral	ADJ
ma-236	139	11	,	,	PUNCT
ma-236	139	12	and	and	CCONJ
ma-236	139	13	by	by	ADP
ma-236	139	14	choosing	choose	VERB
ma-236	139	15	specific	specific	ADJ
ma-236	139	16	convex	convex	NOUN
ma-236	139	17	functions	function	NOUN
ma-236	139	18	,	,	PUNCT
ma-236	139	19	the	the	DET
ma-236	139	20	authors	author	NOUN
ma-236	139	21	generate	generate	VERB
ma-236	139	22	numeroustensorial	numeroustensorial	ADJ
ma-236	139	23	simpson	simpson	PROPN
ma-236	139	24	-	-	PUNCT
ma-236	139	25	type	type	NOUN
ma-236	139	26	inequalities	inequality	NOUN
ma-236	139	27	and	and	CCONJ
ma-236	139	28	bounds	bound	NOUN
ma-236	139	29	.	.	PUNCT
ma-236	140	1	finally	finally	ADV
ma-236	140	2	,	,	PUNCT
ma-236	140	3	the	the	DET
ma-236	140	4	"	"	PUNCT
ma-236	140	5	conclusion	conclusion	NOUN
ma-236	140	6	"	"	PUNCT
ma-236	140	7	section	section	NOUN
ma-236	140	8	summarizes	summarize	NOUN
ma-236	140	9	thepaper	thepaper	PROPN
ma-236	140	10	’s	’s	PART
ma-236	140	11	contributions	contribution	NOUN
ma-236	140	12	and	and	CCONJ
ma-236	140	13	highlights	highlight	NOUN
ma-236	140	14	its	its	PRON
ma-236	140	15	significance	significance	NOUN
ma-236	140	16	for	for	ADP
ma-236	140	17	the	the	DET
ma-236	140	18	development	development	NOUN
ma-236	140	19	of	of	ADP
ma-236	140	20	tensorial	tensorial	ADJ
ma-236	140	21	inequalities.in	inequalities.in	PROPN
ma-236	140	22	the	the	DET
ma-236	140	23	following	follow	VERB
ma-236	140	24	theorem	theorem	NOUN
ma-236	140	25	,	,	PUNCT
ma-236	140	26	you	you	PRON
ma-236	140	27	’ll	’ll	AUX
ma-236	140	28	find	find	VERB
ma-236	140	29	a	a	DET
ma-236	140	30	fundamental	fundamental	ADJ
ma-236	140	31	result	result	NOUN
ma-236	140	32	that	that	PRON
ma-236	140	33	serves	serve	VERB
ma-236	140	34	as	as	ADP
ma-236	140	35	the	the	DET
ma-236	140	36	foundation	foundation	NOUN
ma-236	140	37	for	for	ADP
ma-236	140	38	derivingfurther	derivingfurther	ADJ
ma-236	140	39	inequalities	inequality	NOUN
ma-236	140	40	throughout	throughout	ADP
ma-236	140	41	the	the	DET
ma-236	140	42	paper	paper	NOUN
ma-236	140	43	.	.	PUNCT
ma-236	141	1	2	2	X
ma-236	141	2	.	.	X
ma-236	141	3	main	main	ADJ
ma-236	141	4	results	result	NOUN
ma-236	141	5	the	the	DET
ma-236	141	6	following	follow	VERB
ma-236	141	7	lemma	lemma	PROPN
ma-236	141	8	will	will	AUX
ma-236	141	9	be	be	AUX
ma-236	141	10	used	use	VERB
ma-236	141	11	crucial	crucial	ADJ
ma-236	141	12	in	in	ADP
ma-236	141	13	obtaining	obtain	VERB
ma-236	141	14	the	the	DET
ma-236	141	15	inequalities	inequality	NOUN
ma-236	141	16	which	which	PRON
ma-236	141	17	follow	follow	VERB
ma-236	141	18	.	.	PUNCT
ma-236	142	1	lemma	lemma	PROPN
ma-236	143	1	3	3	X
ma-236	143	2	.	.	PROPN
ma-236	143	3	assume	assume	VERB
ma-236	143	4	that	that	SCONJ
ma-236	143	5	f	f	PROPN
ma-236	143	6	is	be	AUX
ma-236	143	7	continuously	continuously	ADV
ma-236	143	8	differentiable	differentiable	ADJ
ma-236	143	9	on	on	ADP
ma-236	143	10	i	i	PRON
ma-236	143	11	,	,	PUNCT
ma-236	143	12	a	a	PRON
ma-236	143	13	and	and	CCONJ
ma-236	143	14	b	b	NOUN
ma-236	143	15	are	be	AUX
ma-236	143	16	selfadjoint	selfadjoint	VERB
ma-236	143	17	operators	operator	NOUN
ma-236	143	18	with	with	ADP
ma-236	143	19	sp(a	sp(a	NOUN
ma-236	143	20	)	)	PUNCT
ma-236	143	21	,	,	PUNCT
ma-236	143	22	sp(b	sp(b	PROPN
ma-236	143	23	)	)	PUNCT
ma-236	144	1	⊂	⊂	PROPN
ma-236	145	1	i	i	PRON
ma-236	145	2	,	,	PUNCT
ma-236	145	3	then	then	ADV
ma-236	145	4	1	1	NUM
ma-236	145	5	8	8	NUM
ma-236	145	6	[	[	PUNCT
ma-236	145	7	f	f	X
ma-236	145	8	(	(	PUNCT
ma-236	145	9	a)⊗	a)⊗	NOUN
ma-236	145	10	1	1	NUM
ma-236	145	11	+	+	NUM
ma-236	145	12	6f	6f	NUM
ma-236	145	13	(	(	PUNCT
ma-236	145	14	a⊗	a⊗	NOUN
ma-236	145	15	1	1	NUM
ma-236	145	16	+	+	CCONJ
ma-236	145	17	1⊗b	1⊗b	NUM
ma-236	145	18	2	2	NUM
ma-236	145	19	)	)	PUNCT
ma-236	145	20	+	+	CCONJ
ma-236	145	21	1⊗	1⊗	NUM
ma-236	145	22	f	f	X
ma-236	145	23	(	(	PUNCT
ma-236	145	24	b	b	NOUN
ma-236	145	25	)	)	PUNCT
ma-236	145	26	]	]	PUNCT
ma-236	145	27	−	−	PROPN
ma-236	145	28	∫	∫	PROPN
ma-236	145	29	1	1	NUM
ma-236	145	30	0	0	NUM
ma-236	145	31	f	f	NOUN
ma-236	145	32	(	(	PUNCT
ma-236	145	33	λ1⊗b+	λ1⊗b+	NOUN
ma-236	145	34	(	(	PUNCT
ma-236	145	35	1−	1−	NUM
ma-236	145	36	λ)a⊗	λ)a⊗	X
ma-236	145	37	1)dλ	1)dλ	NUM
ma-236	145	38	(	(	PUNCT
ma-236	145	39	4	4	NUM
ma-236	145	40	)	)	PUNCT
ma-236	145	41	=	=	NOUN
ma-236	145	42	1⊗b−	1⊗b−	NUM
ma-236	145	43	a⊗	a⊗	NOUN
ma-236	145	44	1	1	NUM
ma-236	145	45	4	4	NUM
ma-236	145	46	∫	∫	NOUN
ma-236	145	47	1	1	NUM
ma-236	145	48	0	0	NUM
ma-236	146	1	[	[	X
ma-236	146	2	(	(	PUNCT
ma-236	146	3	3	3	NUM
ma-236	146	4	4	4	NUM
ma-236	146	5	−	−	NOUN
ma-236	146	6	k	k	NOUN
ma-236	146	7	)	)	PUNCT
ma-236	146	8	f	f	PROPN
ma-236	147	1	′	′	NUM
ma-236	148	1	(	(	PUNCT
ma-236	148	2	a⊗	a⊗	NOUN
ma-236	148	3	1	1	NUM
ma-236	148	4	(	(	PUNCT
ma-236	148	5	1	1	NUM
ma-236	148	6	+	+	CCONJ
ma-236	148	7	k	k	PROPN
ma-236	148	8	2	2	NUM
ma-236	148	9	)	)	PUNCT
ma-236	149	1	+	+	CCONJ
ma-236	150	1	1⊗b	1⊗b	NUM
ma-236	150	2	(	(	PUNCT
ma-236	150	3	1−	1−	NUM
ma-236	150	4	k	k	NOUN
ma-236	150	5	2	2	NUM
ma-236	150	6	)	)	PUNCT
ma-236	150	7	)	)	PUNCT
ma-236	150	8	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	150	9	eur	eur	PROPN
ma-236	150	10	.	.	PUNCT
ma-236	151	1	j.	j.	PROPN
ma-236	151	2	math	math	PROPN
ma-236	151	3	.	.	PUNCT
ma-236	152	1	anal	anal	PROPN
ma-236	152	2	.	.	PUNCT
ma-236	153	1	10.28924	10.28924	NUM
ma-236	153	2	/	/	SYM
ma-236	153	3	ada	ada	PROPN
ma-236	153	4	/	/	SYM
ma-236	153	5	ma.4.17	ma.4.17	NOUN
ma-236	153	6	6	6	NUM
ma-236	153	7	+	+	CCONJ
ma-236	153	8	(	(	PUNCT
ma-236	153	9	1	1	NUM
ma-236	153	10	4	4	NUM
ma-236	153	11	−	−	NOUN
ma-236	153	12	k	k	NOUN
ma-236	153	13	)	)	PUNCT
ma-236	153	14	f	f	PROPN
ma-236	154	1	′	′	NUM
ma-236	154	2	(	(	PUNCT
ma-236	154	3	k	k	PROPN
ma-236	154	4	2	2	NUM
ma-236	154	5	a⊗	a⊗	NOUN
ma-236	154	6	1	1	NUM
ma-236	154	7	+	+	CCONJ
ma-236	154	8	1⊗b	1⊗b	NUM
ma-236	154	9	(	(	PUNCT
ma-236	154	10	2−	2−	NUM
ma-236	154	11	k	k	NOUN
ma-236	154	12	2	2	NUM
ma-236	154	13	)	)	PUNCT
ma-236	154	14	)	)	PUNCT
ma-236	154	15	]	]	PUNCT
ma-236	155	1	dk	dk	X
ma-236	155	2	.	.	PUNCT
ma-236	155	3	proof	proof	NOUN
ma-236	155	4	.	.	PUNCT
ma-236	156	1	we	we	PRON
ma-236	156	2	will	will	AUX
ma-236	156	3	start	start	VERB
ma-236	156	4	the	the	DET
ma-236	156	5	proof	proof	NOUN
ma-236	156	6	with	with	ADP
ma-236	156	7	lemma	lemma	PROPN
ma-236	156	8	(	(	PUNCT
ma-236	156	9	3	3	NUM
ma-236	156	10	)	)	PUNCT
ma-236	156	11	.	.	PUNCT
ma-236	157	1	introducing	introduce	VERB
ma-236	157	2	the	the	DET
ma-236	157	3	substitutions	substitution	NOUN
ma-236	157	4	on	on	ADP
ma-236	157	5	the	the	DET
ma-236	157	6	left	left	ADJ
ma-236	157	7	hand	hand	NOUN
ma-236	157	8	sideand	sideand	NOUN
ma-236	157	9	simplifying	simplify	VERB
ma-236	157	10	the	the	DET
ma-236	157	11	fractional	fractional	ADJ
ma-236	157	12	integral	integral	ADJ
ma-236	157	13	,	,	PUNCT
ma-236	157	14	then	then	ADV
ma-236	157	15	assuming	assume	VERB
ma-236	157	16	that	that	SCONJ
ma-236	157	17	a	a	PRON
ma-236	157	18	and	and	CCONJ
ma-236	157	19	b	b	NOUN
ma-236	157	20	have	have	VERB
ma-236	157	21	the	the	DET
ma-236	157	22	spectral	spectral	ADJ
ma-236	157	23	resolutions	resolution	NOUN
ma-236	157	24	a	a	DET
ma-236	157	25	=	=	SYM
ma-236	157	26	∫	∫	PROPN
ma-236	157	27	tde(t	tde(t	PROPN
ma-236	157	28	)	)	PUNCT
ma-236	157	29	and	and	CCONJ
ma-236	157	30	b	b	X
ma-236	157	31	=	=	SYM
ma-236	157	32	∫	∫	PROPN
ma-236	157	33	sdf	sdf	PROPN
ma-236	157	34	(	(	PUNCT
ma-236	157	35	s	s	PROPN
ma-236	157	36	)	)	PUNCT
ma-236	157	37	.	.	PUNCT
ma-236	158	1	if	if	SCONJ
ma-236	158	2	we	we	PRON
ma-236	158	3	take	take	VERB
ma-236	158	4	the	the	DET
ma-236	158	5	integral	integral	ADJ
ma-236	158	6	∫i	∫i	VERB
ma-236	158	7	∫i	∫i	VERB
ma-236	158	8	over	over	ADP
ma-236	158	9	det	det	PROPN
ma-236	158	10	⊗	⊗	PROPN
ma-236	158	11	dfs	dfs	PROPN
ma-236	158	12	,	,	PUNCT
ma-236	158	13	then	then	ADV
ma-236	158	14	we	we	PRON
ma-236	158	15	get∫	get∫	VERB
ma-236	159	1	i	i	PRON
ma-236	159	2	∫	∫	VERB
ma-236	160	1	i	i	PRON
ma-236	160	2	(	(	PUNCT
ma-236	160	3	1	1	NUM
ma-236	160	4	8	8	NUM
ma-236	160	5	[	[	PUNCT
ma-236	160	6	f	f	X
ma-236	160	7	(	(	PUNCT
ma-236	160	8	t	t	PROPN
ma-236	160	9	)	)	PUNCT
ma-236	160	10	+	+	NUM
ma-236	160	11	6f	6f	NUM
ma-236	160	12	(	(	PUNCT
ma-236	160	13	t	t	PROPN
ma-236	160	14	+	+	SYM
ma-236	160	15	s	s	X
ma-236	160	16	2	2	NUM
ma-236	160	17	)	)	PUNCT
ma-236	161	1	+	+	CCONJ
ma-236	161	2	f	f	X
ma-236	161	3	(	(	PUNCT
ma-236	161	4	s	s	NOUN
ma-236	161	5	)	)	PUNCT
ma-236	161	6	]	]	PUNCT
ma-236	162	1	−	−	PROPN
ma-236	162	2	∫	∫	PROPN
ma-236	162	3	1	1	NUM
ma-236	162	4	0	0	NUM
ma-236	162	5	f	f	NOUN
ma-236	162	6	(	(	PUNCT
ma-236	162	7	λs	λs	X
ma-236	162	8	+	+	CCONJ
ma-236	162	9	(	(	PUNCT
ma-236	162	10	1−	1−	NUM
ma-236	162	11	λ)t)dλ	λ)t)dλ	NOUN
ma-236	162	12	)	)	PUNCT
ma-236	162	13	det	det	PROPN
ma-236	162	14	⊗	⊗	PROPN
ma-236	163	1	dfs	dfs	PROPN
ma-236	164	1	=	=	SYM
ma-236	164	2	∫	∫	PROPN
ma-236	165	1	i	i	PRON
ma-236	165	2	∫	∫	VERB
ma-236	166	1	i	i	PRON
ma-236	166	2	(	(	PUNCT
ma-236	166	3	s	s	VERB
ma-236	166	4	−	−	PROPN
ma-236	166	5	t	t	NOUN
ma-236	166	6	2	2	NUM
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ma-236	167	1	[	[	X
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ma-236	167	5	−	−	NOUN
ma-236	167	6	k	k	NOUN
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ma-236	167	8	f	f	PROPN
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ma-236	168	2	(	(	PUNCT
ma-236	168	3	t	t	PROPN
ma-236	168	4	(	(	PUNCT
ma-236	168	5	1	1	NUM
ma-236	168	6	+	+	CCONJ
ma-236	168	7	k	k	PROPN
ma-236	168	8	2	2	NUM
ma-236	168	9	)	)	PUNCT
ma-236	169	1	+	+	SYM
ma-236	169	2	s	s	X
ma-236	169	3	(	(	PUNCT
ma-236	169	4	1−	1−	NUM
ma-236	169	5	k	k	NOUN
ma-236	169	6	2	2	NUM
ma-236	169	7	)	)	PUNCT
ma-236	169	8	)	)	PUNCT
ma-236	170	1	+	+	CCONJ
ma-236	170	2	(	(	PUNCT
ma-236	170	3	1	1	NUM
ma-236	170	4	4	4	NUM
ma-236	170	5	−	−	NOUN
ma-236	170	6	k	k	NOUN
ma-236	170	7	)	)	PUNCT
ma-236	170	8	f	f	PROPN
ma-236	171	1	′	′	NUM
ma-236	171	2	(	(	PUNCT
ma-236	171	3	k	k	PROPN
ma-236	171	4	2	2	NUM
ma-236	171	5	t	t	NOUN
ma-236	171	6	+	+	SYM
ma-236	171	7	s	s	X
ma-236	171	8	(	(	PUNCT
ma-236	171	9	2−	2−	NUM
ma-236	171	10	k	k	NOUN
ma-236	171	11	2	2	NUM
ma-236	171	12	)	)	PUNCT
ma-236	171	13	)	)	PUNCT
ma-236	171	14	]	]	PUNCT
ma-236	172	1	dk	dk	PROPN
ma-236	172	2	)	)	PUNCT
ma-236	172	3	det	det	PROPN
ma-236	172	4	⊗	⊗	PROPN
ma-236	172	5	dfs	dfs	PROPN
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ma-236	172	7	utilizing	utilize	VERB
ma-236	172	8	the	the	DET
ma-236	172	9	fubinis	fubini	NOUN
ma-236	172	10	theorem	theorem	VERB
ma-236	172	11	and	and	CCONJ
ma-236	172	12	lemma	lemma	PROPN
ma-236	172	13	1	1	NUM
ma-236	172	14	for	for	ADP
ma-236	172	15	appropriate	appropriate	ADJ
ma-236	172	16	choices	choice	NOUN
ma-236	172	17	of	of	ADP
ma-236	172	18	the	the	DET
ma-236	172	19	functions	function	NOUN
ma-236	172	20	involved	involve	VERB
ma-236	172	21	,	,	PUNCT
ma-236	172	22	we	we	PRON
ma-236	172	23	have	have	VERB
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ma-236	172	25	∫	∫	PROPN
ma-236	173	1	i	i	PRON
ma-236	173	2	∫	∫	VERB
ma-236	174	1	i	i	PRON
ma-236	174	2	f	f	PROPN
ma-236	175	1	(	(	PUNCT
ma-236	175	2	t	t	PROPN
ma-236	175	3	+	+	SYM
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ma-236	175	5	2	2	NUM
ma-236	175	6	)	)	PUNCT
ma-236	175	7	det	det	NOUN
ma-236	175	8	⊗	⊗	PROPN
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ma-236	175	10	=	=	SYM
ma-236	175	11	f	f	PROPN
ma-236	175	12	(	(	PUNCT
ma-236	175	13	a⊗	a⊗	NOUN
ma-236	175	14	1	1	NUM
ma-236	175	15	+	+	CCONJ
ma-236	175	16	1⊗b	1⊗b	NUM
ma-236	175	17	2	2	NUM
ma-236	175	18	)	)	PUNCT
ma-236	175	19	,	,	PUNCT
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ma-236	176	2	∫	∫	VERB
ma-236	177	1	i	i	PRON
ma-236	177	2	∫	∫	PROPN
ma-236	177	3	1	1	NUM
ma-236	177	4	0	0	NUM
ma-236	177	5	f	f	NOUN
ma-236	177	6	(	(	PUNCT
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ma-236	177	8	+	+	CCONJ
ma-236	177	9	(	(	PUNCT
ma-236	177	10	1−	1−	NUM
ma-236	177	11	λ)t)dλdet	λ)t)dλdet	NOUN
ma-236	177	12	⊗	⊗	NUM
ma-236	177	13	dfs	dfs	NOUN
ma-236	177	14	=	=	SYM
ma-236	177	15	∫	∫	PROPN
ma-236	177	16	1	1	NUM
ma-236	177	17	0	0	NUM
ma-236	177	18	∫	∫	PROPN
ma-236	178	1	i	i	PRON
ma-236	178	2	∫	∫	VERB
ma-236	179	1	i	i	PRON
ma-236	179	2	f	f	X
ma-236	180	1	(	(	PUNCT
ma-236	180	2	λs	λs	X
ma-236	180	3	+	+	CCONJ
ma-236	180	4	(	(	PUNCT
ma-236	180	5	1−	1−	NUM
ma-236	180	6	λ)t)dλ	λ)t)dλ	NOUN
ma-236	180	7	)	)	PUNCT
ma-236	180	8	det	det	PROPN
ma-236	180	9	⊗	⊗	PROPN
ma-236	180	10	dfsdλ	dfsdλ	PROPN
ma-236	181	1	=	=	SYM
ma-236	182	1	∫	∫	PROPN
ma-236	183	1	1	1	NUM
ma-236	183	2	0	0	NUM
ma-236	183	3	f	f	X
ma-236	183	4	(	(	PUNCT
ma-236	183	5	λ1⊗b+	λ1⊗b+	NOUN
ma-236	183	6	(	(	PUNCT
ma-236	183	7	1−	1−	NUM
ma-236	183	8	λ)a⊗	λ)a⊗	X
ma-236	183	9	1)dλ	1)dλ	NUM
ma-236	183	10	,	,	PUNCT
ma-236	183	11	∫	∫	PROPN
ma-236	184	1	i	i	PRON
ma-236	184	2	∫	∫	VERB
ma-236	185	1	i	i	PRON
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ma-236	185	3	−	−	PROPN
ma-236	185	4	t	t	NOUN
ma-236	185	5	2	2	NUM
ma-236	185	6	∫	∫	NOUN
ma-236	185	7	1	1	NUM
ma-236	185	8	0	0	NUM
ma-236	185	9	(	(	PUNCT
ma-236	185	10	3	3	NUM
ma-236	185	11	4	4	NUM
ma-236	185	12	−	−	NOUN
ma-236	185	13	k	k	NOUN
ma-236	186	1	)	)	PUNCT
ma-236	186	2	f	f	PROPN
ma-236	187	1	′	′	NUM
ma-236	187	2	(	(	PUNCT
ma-236	187	3	t	t	PROPN
ma-236	187	4	(	(	PUNCT
ma-236	187	5	1	1	NUM
ma-236	187	6	+	+	CCONJ
ma-236	187	7	k	k	PROPN
ma-236	187	8	2	2	NUM
ma-236	187	9	)	)	PUNCT
ma-236	188	1	+	+	SYM
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ma-236	188	3	(	(	PUNCT
ma-236	188	4	1−	1−	NUM
ma-236	188	5	k	k	NOUN
ma-236	188	6	2	2	NUM
ma-236	188	7	)	)	PUNCT
ma-236	188	8	)	)	PUNCT
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ma-236	189	1	⊗	⊗	NOUN
ma-236	189	2	dfs	dfs	PROPN
ma-236	189	3	=	=	SYM
ma-236	189	4	∫	∫	PROPN
ma-236	189	5	1	1	NUM
ma-236	189	6	0	0	NUM
ma-236	189	7	(	(	PUNCT
ma-236	189	8	3	3	NUM
ma-236	189	9	4	4	NUM
ma-236	189	10	−	−	NOUN
ma-236	189	11	k	k	X
ma-236	189	12	)	)	PUNCT
ma-236	189	13	∫	∫	PROPN
ma-236	190	1	i	i	PRON
ma-236	190	2	∫	∫	VERB
ma-236	191	1	i	i	PRON
ma-236	191	2	s	s	VERB
ma-236	191	3	−	−	PROPN
ma-236	191	4	t	t	NOUN
ma-236	191	5	2	2	NUM
ma-236	191	6	f	f	NOUN
ma-236	192	1	′	′	NUM
ma-236	193	1	(	(	PUNCT
ma-236	193	2	t	t	PROPN
ma-236	193	3	(	(	PUNCT
ma-236	193	4	1	1	NUM
ma-236	193	5	+	+	CCONJ
ma-236	193	6	k	k	PROPN
ma-236	193	7	2	2	NUM
ma-236	193	8	)	)	PUNCT
ma-236	194	1	+	+	SYM
ma-236	194	2	s	s	X
ma-236	194	3	(	(	PUNCT
ma-236	194	4	1−	1−	NUM
ma-236	194	5	k	k	NOUN
ma-236	194	6	2	2	NUM
ma-236	194	7	)	)	PUNCT
ma-236	194	8	)	)	PUNCT
ma-236	194	9	det	det	PROPN
ma-236	194	10	⊗	⊗	PROPN
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ma-236	194	12	=	=	SYM
ma-236	194	13	(	(	PUNCT
ma-236	194	14	1⊗b−	1⊗b−	NUM
ma-236	194	15	a⊗	a⊗	NOUN
ma-236	194	16	1	1	NUM
ma-236	194	17	)	)	PUNCT
ma-236	194	18	4	4	NUM
ma-236	194	19	∫	∫	NOUN
ma-236	194	20	1	1	NUM
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ma-236	194	22	(	(	PUNCT
ma-236	194	23	3	3	NUM
ma-236	194	24	4	4	NUM
ma-236	194	25	−	−	NOUN
ma-236	194	26	k	k	NOUN
ma-236	194	27	)	)	PUNCT
ma-236	194	28	f	f	PROPN
ma-236	195	1	′	′	NUM
ma-236	195	2	(	(	PUNCT
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ma-236	195	4	1	1	NUM
ma-236	195	5	(	(	PUNCT
ma-236	195	6	1	1	NUM
ma-236	195	7	+	+	CCONJ
ma-236	195	8	k	k	PROPN
ma-236	195	9	2	2	NUM
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ma-236	196	1	+	+	CCONJ
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ma-236	196	3	(	(	PUNCT
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ma-236	196	5	k	k	NOUN
ma-236	196	6	2	2	NUM
ma-236	196	7	)	)	PUNCT
ma-236	196	8	)	)	PUNCT
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ma-236	198	2	the	the	DET
ma-236	198	3	same	same	ADJ
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ma-236	198	5	for	for	ADP
ma-236	198	6	other	other	ADJ
ma-236	198	7	terms	term	NOUN
ma-236	198	8	,	,	PUNCT
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ma-236	198	11	follows	follow	VERB
ma-236	198	12	.	.	PUNCT
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ma-236	199	3	8	8	NUM
ma-236	199	4	.	.	PUNCT
ma-236	199	5	assume	assume	VERB
ma-236	199	6	that	that	SCONJ
ma-236	199	7	f	f	PROPN
ma-236	199	8	is	be	AUX
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ma-236	199	11	on	on	ADP
ma-236	199	12	i	i	PRON
ma-236	199	13	with	with	ADP
ma-236	199	14	‖f	‖f	PRON
ma-236	199	15	′‖i,+∞	′‖i,+∞	VERB
ma-236	199	16	:	:	PUNCT
ma-236	199	17	=	=	SYM
ma-236	199	18	supt∈i	supt∈i	PROPN
ma-236	199	19	|f	|f	PROPN
ma-236	200	1	′(t)|	′(t)|	X
ma-236	200	2	<	<	X
ma-236	201	1	+	+	NOUN
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ma-236	201	5	,	,	PUNCT
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ma-236	201	8	selfadjoint	selfadjoint	VERB
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ma-236	201	10	with	with	ADP
ma-236	201	11	sp(a	sp(a	NOUN
ma-236	201	12	)	)	PUNCT
ma-236	201	13	,	,	PUNCT
ma-236	201	14	sp(b	sp(b	PROPN
ma-236	201	15	)	)	PUNCT
ma-236	202	1	⊂	⊂	PROPN
ma-236	203	1	i	i	PRON
ma-236	203	2	,	,	PUNCT
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ma-236	203	4	[	[	PUNCT
ma-236	203	5	f	f	X
ma-236	203	6	(	(	PUNCT
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ma-236	203	8	1	1	NUM
ma-236	203	9	+	+	NUM
ma-236	203	10	6f	6f	NUM
ma-236	203	11	(	(	PUNCT
ma-236	203	12	a⊗	a⊗	NOUN
ma-236	203	13	1	1	NUM
ma-236	203	14	+	+	CCONJ
ma-236	203	15	1⊗b	1⊗b	NUM
ma-236	203	16	2	2	NUM
ma-236	203	17	)	)	PUNCT
ma-236	203	18	+	+	CCONJ
ma-236	204	1	1⊗	1⊗	NUM
ma-236	204	2	f	f	X
ma-236	204	3	(	(	PUNCT
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ma-236	204	5	)	)	PUNCT
ma-236	204	6	]	]	PUNCT
ma-236	204	7	(	(	PUNCT
ma-236	204	8	5	5	NUM
ma-236	204	9	)	)	PUNCT
ma-236	204	10	−	−	NOUN
ma-236	204	11	∫	∫	PROPN
ma-236	204	12	1	1	NUM
ma-236	204	13	0	0	NUM
ma-236	204	14	f	f	NOUN
ma-236	204	15	(	(	PUNCT
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ma-236	204	17	(	(	PUNCT
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ma-236	204	19	λ)a⊗	λ)a⊗	X
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ma-236	205	2	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
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ma-236	207	2	.	.	PUNCT
ma-236	208	1	10.28924	10.28924	NUM
ma-236	208	2	/	/	SYM
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ma-236	208	4	/	/	SYM
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ma-236	208	6	7	7	NUM
ma-236	208	7	≤	≤	NUM
ma-236	208	8	5	5	NUM
ma-236	208	9	‖1⊗b−	‖1⊗b−	NOUN
ma-236	208	10	a⊗	a⊗	NOUN
ma-236	208	11	1‖	1‖	NUM
ma-236	208	12	32	32	NUM
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ma-236	209	2	.	.	PUNCT
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ma-236	210	2	we	we	PRON
ma-236	210	3	take	take	VERB
ma-236	210	4	the	the	DET
ma-236	210	5	operator	operator	NOUN
ma-236	210	6	norm	norm	NOUN
ma-236	210	7	of	of	ADP
ma-236	210	8	the	the	DET
ma-236	210	9	previously	previously	ADV
ma-236	210	10	obtained	obtain	VERB
ma-236	210	11	lemma	lemma	PROPN
ma-236	210	12	(	(	PUNCT
ma-236	210	13	4	4	NUM
ma-236	210	14	)	)	PUNCT
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ma-236	210	17	the	the	DET
ma-236	210	18	triangleinequality	triangleinequality	NOUN
ma-236	210	19	,	,	PUNCT
ma-236	210	20	we	we	PRON
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ma-236	210	22	∥∥∥∥18	∥∥∥∥18	ADJ
ma-236	210	23	[	[	PUNCT
ma-236	210	24	f	f	X
ma-236	210	25	(	(	PUNCT
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ma-236	210	27	1	1	NUM
ma-236	210	28	+	+	NUM
ma-236	210	29	6f	6f	NUM
ma-236	210	30	(	(	PUNCT
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ma-236	210	32	1	1	NUM
ma-236	210	33	+	+	CCONJ
ma-236	210	34	1⊗b	1⊗b	NUM
ma-236	210	35	2	2	NUM
ma-236	210	36	)	)	PUNCT
ma-236	210	37	+	+	CCONJ
ma-236	211	1	1⊗	1⊗	NUM
ma-236	211	2	f	f	X
ma-236	211	3	(	(	PUNCT
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ma-236	211	5	)	)	PUNCT
ma-236	211	6	]	]	PUNCT
ma-236	212	1	−	−	PROPN
ma-236	212	2	∫	∫	PROPN
ma-236	212	3	1	1	NUM
ma-236	212	4	0	0	NUM
ma-236	212	5	f	f	NOUN
ma-236	212	6	(	(	PUNCT
ma-236	212	7	λ1⊗b+	λ1⊗b+	NOUN
ma-236	212	8	(	(	PUNCT
ma-236	212	9	1−	1−	NUM
ma-236	212	10	λ)a⊗	λ)a⊗	X
ma-236	212	11	1)dλ	1)dλ	NUM
ma-236	212	12	∥∥∥∥	∥∥∥∥	NUM
ma-236	212	13	≤	≤	NUM
ma-236	212	14	‖1⊗b−	‖1⊗b−	NOUN
ma-236	212	15	a⊗	a⊗	PROPN
ma-236	213	1	1‖	1‖	NUM
ma-236	213	2	2	2	NUM
ma-236	213	3	∫	∫	NOUN
ma-236	213	4	1	1	NUM
ma-236	213	5	0	0	NUM
ma-236	213	6	∣∣∣∣34	∣∣∣∣34	NOUN
ma-236	213	7	−	−	PROPN
ma-236	213	8	k	k	PROPN
ma-236	213	9	∣∣∣∣	∣∣∣∣	PROPN
ma-236	213	10	∥∥∥∥f	∥∥∥∥f	NOUN
ma-236	213	11	′(a⊗	′(a⊗	VERB
ma-236	213	12	1(1	1(1	NUM
ma-236	213	13	+	+	SYM
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ma-236	214	1	+	+	CCONJ
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ma-236	215	2	(	(	PUNCT
ma-236	215	3	1−	1−	NUM
ma-236	215	4	k	k	NOUN
ma-236	215	5	2	2	NUM
ma-236	215	6	)	)	PUNCT
ma-236	215	7	)	)	PUNCT
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ma-236	216	1	+	+	CCONJ
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ma-236	216	3	−	−	PROPN
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ma-236	216	5	∣∣∣∣	∣∣∣∣	PROPN
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ma-236	216	7	′(k2a⊗	′(k2a⊗	PROPN
ma-236	216	8	1	1	NUM
ma-236	216	9	+	+	CCONJ
ma-236	216	10	1⊗b	1⊗b	NUM
ma-236	216	11	(	(	PUNCT
ma-236	216	12	2−	2−	NUM
ma-236	216	13	k	k	NOUN
ma-236	216	14	2	2	NUM
ma-236	216	15	)	)	PUNCT
ma-236	216	16	)	)	PUNCT
ma-236	216	17	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	216	18	]	]	PUNCT
ma-236	216	19	dk	dk	NOUN
ma-236	216	20	realize	realize	VERB
ma-236	216	21	here	here	ADV
ma-236	216	22	that	that	SCONJ
ma-236	216	23	by	by	ADP
ma-236	216	24	lemma	lemma	PROPN
ma-236	216	25	1,∣∣∣∣f	1,∣∣∣∣f	NUM
ma-236	216	26	′(a⊗	′(a⊗	PROPN
ma-236	216	27	1(1	1(1	NUM
ma-236	216	28	+	+	SYM
ma-236	216	29	k2	k2	NOUN
ma-236	216	30	)	)	PUNCT
ma-236	217	1	+	+	CCONJ
ma-236	217	2	1⊗b	1⊗b	NUM
ma-236	217	3	(	(	PUNCT
ma-236	217	4	1−	1−	NUM
ma-236	217	5	k	k	NOUN
ma-236	217	6	2	2	NUM
ma-236	217	7	)	)	PUNCT
ma-236	217	8	)	)	PUNCT
ma-236	217	9	∣∣∣∣	∣∣∣∣	PROPN
ma-236	218	1	=	=	SYM
ma-236	218	2	∫	∫	PROPN
ma-236	219	1	i	i	PRON
ma-236	219	2	∫	∫	VERB
ma-236	220	1	i	i	PRON
ma-236	220	2	∣∣∣∣f	∣∣∣∣f	PROPN
ma-236	221	1	′(t	′(t	NOUN
ma-236	221	2	(	(	PUNCT
ma-236	221	3	1	1	NUM
ma-236	221	4	+	+	CCONJ
ma-236	221	5	k2	k2	ADJ
ma-236	221	6	)	)	PUNCT
ma-236	222	1	+	+	SYM
ma-236	222	2	s	s	X
ma-236	222	3	(	(	PUNCT
ma-236	222	4	1−	1−	NUM
ma-236	222	5	k	k	NOUN
ma-236	222	6	2	2	NUM
ma-236	222	7	)	)	PUNCT
ma-236	222	8	)	)	PUNCT
ma-236	223	1	∣∣∣∣det	∣∣∣∣det	PROPN
ma-236	223	2	⊗	⊗	PROPN
ma-236	223	3	dfs	dfs	INTJ
ma-236	223	4	.	.	PUNCT
ma-236	224	1	since	since	SCONJ
ma-236	224	2	∣∣∣∣f	∣∣∣∣f	PROPN
ma-236	224	3	′(t	′(t	NOUN
ma-236	224	4	(	(	PUNCT
ma-236	224	5	1	1	NUM
ma-236	224	6	+	+	CCONJ
ma-236	224	7	k2	k2	ADJ
ma-236	224	8	)	)	PUNCT
ma-236	225	1	+	+	SYM
ma-236	225	2	s	s	X
ma-236	225	3	(	(	PUNCT
ma-236	225	4	1−	1−	NUM
ma-236	225	5	k	k	NOUN
ma-236	225	6	2	2	NUM
ma-236	225	7	)	)	PUNCT
ma-236	225	8	)	)	PUNCT
ma-236	225	9	∣∣∣∣	∣∣∣∣	NOUN
ma-236	225	10	6	6	NUM
ma-236	225	11	∥∥f	∥∥f	NOUN
ma-236	225	12	′∥∥i,+∞	′∥∥i,+∞	PROPN
ma-236	225	13	.	.	PUNCT
ma-236	226	1	holds	hold	VERB
ma-236	226	2	for	for	ADP
ma-236	226	3	all	all	DET
ma-236	226	4	t	t	NOUN
ma-236	226	5	,	,	PUNCT
ma-236	226	6	s	s	VERB
ma-236	226	7	∈	∈	PROPN
ma-236	227	1	i	i	PRON
ma-236	227	2	.	.	PUNCT
ma-236	228	1	if	if	SCONJ
ma-236	228	2	we	we	PRON
ma-236	228	3	take	take	VERB
ma-236	228	4	the	the	DET
ma-236	228	5	integral	integral	ADJ
ma-236	228	6	∫i	∫i	VERB
ma-236	228	7	∫i	∫i	VERB
ma-236	228	8	over	over	ADP
ma-236	228	9	det	det	PROPN
ma-236	228	10	⊗	⊗	PROPN
ma-236	228	11	dfs	dfs	PROPN
ma-236	228	12	,	,	PUNCT
ma-236	228	13	then	then	ADV
ma-236	228	14	we	we	PRON
ma-236	228	15	get∣∣∣∣f	get∣∣∣∣f	VERB
ma-236	228	16	′(a⊗	′(a⊗	NUM
ma-236	228	17	1(1	1(1	NUM
ma-236	228	18	+	+	SYM
ma-236	228	19	k2	k2	NOUN
ma-236	228	20	)	)	PUNCT
ma-236	229	1	+	+	CCONJ
ma-236	229	2	1⊗b	1⊗b	NUM
ma-236	229	3	(	(	PUNCT
ma-236	229	4	1−	1−	NUM
ma-236	229	5	k	k	NOUN
ma-236	229	6	2	2	NUM
ma-236	229	7	)	)	PUNCT
ma-236	229	8	)	)	PUNCT
ma-236	229	9	∣∣∣∣	∣∣∣∣	PROPN
ma-236	230	1	=	=	SYM
ma-236	230	2	∫	∫	PROPN
ma-236	231	1	i	i	PRON
ma-236	231	2	∫	∫	VERB
ma-236	232	1	i	i	PRON
ma-236	232	2	∣∣∣∣f	∣∣∣∣f	PROPN
ma-236	233	1	′(t	′(t	NOUN
ma-236	233	2	(	(	PUNCT
ma-236	233	3	1	1	NUM
ma-236	233	4	+	+	CCONJ
ma-236	233	5	k2	k2	ADJ
ma-236	233	6	)	)	PUNCT
ma-236	234	1	+	+	SYM
ma-236	234	2	s	s	X
ma-236	234	3	(	(	PUNCT
ma-236	234	4	1−	1−	NUM
ma-236	234	5	k	k	NOUN
ma-236	234	6	2	2	NUM
ma-236	234	7	)	)	PUNCT
ma-236	234	8	)	)	PUNCT
ma-236	235	1	∣∣∣∣det	∣∣∣∣det	PROPN
ma-236	235	2	⊗	⊗	PROPN
ma-236	235	3	dfs	dfs	INTJ
ma-236	235	4	.	.	PROPN
ma-236	236	1	6	6	NUM
ma-236	236	2	∥∥f	∥∥f	NOUN
ma-236	236	3	′∥∥	′∥∥	PROPN
ma-236	237	1	i,+∞	i,+∞	CCONJ
ma-236	237	2	∫	∫	PROPN
ma-236	238	1	i	i	PRON
ma-236	238	2	∫	∫	VERB
ma-236	239	1	i	i	PROPN
ma-236	239	2	det	det	PROPN
ma-236	240	1	⊗	⊗	PROPN
ma-236	241	1	dfs	dfs	PROPN
ma-236	242	1	=	=	NOUN
ma-236	242	2	∥∥f	∥∥f	PROPN
ma-236	242	3	′∥∥	′∥∥	VERB
ma-236	242	4	i,+∞	i,+∞	ADV
ma-236	242	5	.from	.from	ADP
ma-236	242	6	which	which	PRON
ma-236	242	7	we	we	PRON
ma-236	242	8	get	get	VERB
ma-236	242	9	the	the	DET
ma-236	242	10	following,∫	following,∫	ADJ
ma-236	242	11	1	1	NUM
ma-236	242	12	0	0	NUM
ma-236	242	13	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	242	14	−	−	PROPN
ma-236	243	1	k	k	NOUN
ma-236	243	2	∥∥∥∥∥∥∥∥f	∥∥∥∥∥∥∥∥f	VERB
ma-236	243	3	′(a⊗	′(a⊗	PROPN
ma-236	243	4	1(1	1(1	NUM
ma-236	243	5	+	+	SYM
ma-236	243	6	k2	k2	NOUN
ma-236	243	7	)	)	PUNCT
ma-236	244	1	+	+	CCONJ
ma-236	245	1	1⊗b	1⊗b	NUM
ma-236	245	2	(	(	PUNCT
ma-236	245	3	1−	1−	NUM
ma-236	245	4	k	k	NOUN
ma-236	245	5	2	2	NUM
ma-236	245	6	)	)	PUNCT
ma-236	245	7	)	)	PUNCT
ma-236	245	8	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	245	9	dk	dk	PROPN
ma-236	245	10	6	6	NUM
ma-236	245	11	∥∥f	∥∥f	NOUN
ma-236	245	12	′∥∥	′∥∥	PROPN
ma-236	245	13	i,+∞	i,+∞	CCONJ
ma-236	245	14	∫	∫	PROPN
ma-236	245	15	1	1	NUM
ma-236	245	16	0	0	NUM
ma-236	245	17	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	245	18	−	−	PROPN
ma-236	246	1	k	k	X
ma-236	246	2	∥∥∥∥	∥∥∥∥	PROPN
ma-236	246	3	dk	dk	X
ma-236	246	4	=	=	SYM
ma-236	246	5	5	5	NUM
ma-236	246	6	‖f’‖i,+∞16evaluation	‖f’‖i,+∞16evaluation	NOUN
ma-236	246	7	of	of	ADP
ma-236	246	8	the	the	DET
ma-236	246	9	second	second	ADJ
ma-236	246	10	part	part	NOUN
ma-236	246	11	is	be	AUX
ma-236	246	12	analogous	analogous	ADJ
ma-236	246	13	,	,	PUNCT
ma-236	246	14	summing	sum	VERB
ma-236	246	15	everything	everything	PRON
ma-236	246	16	up	up	ADP
ma-236	246	17	we	we	PRON
ma-236	246	18	obtain	obtain	VERB
ma-236	246	19	the	the	DET
ma-236	246	20	desired	desire	VERB
ma-236	246	21	equality	equality	NOUN
ma-236	246	22	.	.	PUNCT
ma-236	247	1	�	�	PROPN
ma-236	247	2	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	247	3	eur	eur	PROPN
ma-236	247	4	.	.	PUNCT
ma-236	248	1	j.	j.	PROPN
ma-236	248	2	math	math	PROPN
ma-236	248	3	.	.	PUNCT
ma-236	249	1	anal	anal	PROPN
ma-236	249	2	.	.	PUNCT
ma-236	250	1	10.28924	10.28924	NUM
ma-236	250	2	/	/	SYM
ma-236	250	3	ada	ada	PROPN
ma-236	250	4	/	/	SYM
ma-236	250	5	ma.4.17	ma.4.17	NOUN
ma-236	250	6	8	8	NUM
ma-236	250	7	theorem	theorem	NOUN
ma-236	250	8	9	9	NUM
ma-236	250	9	.	.	PUNCT
ma-236	250	10	assume	assume	VERB
ma-236	250	11	that	that	SCONJ
ma-236	250	12	f	f	PROPN
ma-236	250	13	is	be	AUX
ma-236	250	14	continuously	continuously	ADV
ma-236	250	15	differentiable	differentiable	ADJ
ma-236	250	16	on	on	ADP
ma-236	250	17	i	i	PRON
ma-236	250	18	and	and	CCONJ
ma-236	250	19	|f	|f	PRON
ma-236	250	20	′|	′|	NUM
ma-236	250	21	is	be	AUX
ma-236	250	22	convex	convex	ADJ
ma-236	250	23	and	and	CCONJ
ma-236	250	24	a	a	DET
ma-236	250	25	,	,	PUNCT
ma-236	250	26	b	b	NOUN
ma-236	251	1	are	be	AUX
ma-236	251	2	selfadjoint	selfadjoint	VERB
ma-236	251	3	operators	operator	NOUN
ma-236	251	4	with	with	ADP
ma-236	251	5	sp(a	sp(a	NOUN
ma-236	251	6	)	)	PUNCT
ma-236	251	7	,	,	PUNCT
ma-236	251	8	sp(b	sp(b	PROPN
ma-236	251	9	)	)	PUNCT
ma-236	252	1	⊂	⊂	PROPN
ma-236	253	1	i	i	PRON
ma-236	253	2	,	,	PUNCT
ma-236	253	3	then∣∣∣∣∣∣∣∣18	then∣∣∣∣∣∣∣∣18	X
ma-236	253	4	[	[	PUNCT
ma-236	253	5	f	f	X
ma-236	253	6	(	(	PUNCT
ma-236	253	7	a)⊗	a)⊗	NOUN
ma-236	253	8	1	1	NUM
ma-236	253	9	+	+	NUM
ma-236	253	10	6f	6f	NUM
ma-236	253	11	(	(	PUNCT
ma-236	253	12	a⊗	a⊗	NOUN
ma-236	253	13	1	1	NUM
ma-236	253	14	+	+	CCONJ
ma-236	253	15	1⊗b	1⊗b	NUM
ma-236	253	16	2	2	NUM
ma-236	253	17	)	)	PUNCT
ma-236	253	18	+	+	CCONJ
ma-236	254	1	1⊗	1⊗	NUM
ma-236	254	2	f	f	X
ma-236	254	3	(	(	PUNCT
ma-236	254	4	b	b	NOUN
ma-236	254	5	)	)	PUNCT
ma-236	254	6	]	]	PUNCT
ma-236	254	7	(	(	PUNCT
ma-236	254	8	6	6	NUM
ma-236	254	9	)	)	PUNCT
ma-236	254	10	−	−	NOUN
ma-236	254	11	∫	∫	PROPN
ma-236	254	12	1	1	NUM
ma-236	254	13	0	0	NUM
ma-236	254	14	f	f	NOUN
ma-236	254	15	(	(	PUNCT
ma-236	254	16	λ1⊗b+	λ1⊗b+	NOUN
ma-236	254	17	(	(	PUNCT
ma-236	254	18	1−	1−	NUM
ma-236	254	19	λ)a⊗	λ)a⊗	X
ma-236	255	1	1)dλ	1)dλ	NUM
ma-236	255	2	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	255	3	≤	≤	ADV
ma-236	255	4	5	5	NUM
ma-236	255	5	‖1⊗b−	‖1⊗b−	NOUN
ma-236	255	6	a⊗	a⊗	NOUN
ma-236	256	1	1‖	1‖	NUM
ma-236	256	2	64	64	NUM
ma-236	256	3	(	(	PUNCT
ma-236	256	4	∥∥f	∥∥f	PROPN
ma-236	256	5	′(a)∥∥+	′(a)∥∥+	NOUN
ma-236	256	6	∥∥f	∥∥f	PROPN
ma-236	256	7	′(b)∥∥	′(b)∥∥	PROPN
ma-236	256	8	)	)	PUNCT
ma-236	256	9	.	.	PUNCT
ma-236	257	1	proof	proof	NOUN
ma-236	257	2	.	.	PUNCT
ma-236	258	1	since	since	SCONJ
ma-236	258	2	|f	|f	PRON
ma-236	258	3	′|	′|	NUM
ma-236	258	4	is	be	AUX
ma-236	258	5	convex	convex	ADJ
ma-236	258	6	on	on	ADP
ma-236	258	7	i	i	PRON
ma-236	258	8	,	,	PUNCT
ma-236	258	9	then	then	ADV
ma-236	258	10	we	we	PRON
ma-236	258	11	get∣∣∣∣f	get∣∣∣∣f	VERB
ma-236	258	12	′(t	′(t	NOUN
ma-236	258	13	(	(	PUNCT
ma-236	258	14	1	1	NUM
ma-236	258	15	+	+	CCONJ
ma-236	258	16	k2	k2	ADJ
ma-236	258	17	)	)	PUNCT
ma-236	259	1	+	+	SYM
ma-236	259	2	s	s	X
ma-236	259	3	(	(	PUNCT
ma-236	259	4	1−	1−	NUM
ma-236	259	5	k	k	NOUN
ma-236	259	6	2	2	NUM
ma-236	259	7	)	)	PUNCT
ma-236	259	8	)	)	PUNCT
ma-236	259	9	∣∣∣∣	∣∣∣∣	NOUN
ma-236	259	10	6	6	NUM
ma-236	259	11	(	(	PUNCT
ma-236	259	12	1	1	NUM
ma-236	259	13	+	+	CCONJ
ma-236	259	14	k2	k2	PROPN
ma-236	259	15	)	)	PUNCT
ma-236	259	16	|f	|f	PROPN
ma-236	260	1	′(t)|+	′(t)|+	PROPN
ma-236	260	2	(	(	PUNCT
ma-236	260	3	1−	1−	NUM
ma-236	260	4	k	k	NOUN
ma-236	260	5	2	2	X
ma-236	260	6	)	)	PUNCT
ma-236	260	7	|f	|f	PROPN
ma-236	260	8	′(s)|	′(s)|	PUNCT
ma-236	261	1	for	for	ADP
ma-236	261	2	all	all	DET
ma-236	261	3	k	k	PROPN
ma-236	261	4	∈	∈	PROPN
ma-236	262	1	[	[	X
ma-236	262	2	0	0	NUM
ma-236	262	3	,	,	PUNCT
ma-236	262	4	1	1	NUM
ma-236	262	5	]	]	PUNCT
ma-236	262	6	and	and	CCONJ
ma-236	262	7	t	t	PROPN
ma-236	262	8	,	,	PUNCT
ma-236	262	9	s	s	VERB
ma-236	262	10	∈	∈	PROPN
ma-236	263	1	i	i	PRON
ma-236	263	2	.if	.if	PUNCT
ma-236	264	1	we	we	PRON
ma-236	264	2	take	take	VERB
ma-236	264	3	the	the	DET
ma-236	264	4	integral	integral	ADJ
ma-236	264	5	∫i	∫i	VERB
ma-236	264	6	∫i	∫i	VERB
ma-236	264	7	over	over	ADP
ma-236	264	8	det	det	PROPN
ma-236	264	9	⊗	⊗	PROPN
ma-236	264	10	dfs	dfs	PROPN
ma-236	264	11	,	,	PUNCT
ma-236	264	12	then	then	ADV
ma-236	264	13	we	we	PRON
ma-236	264	14	get∣∣∣∣f	get∣∣∣∣f	VERB
ma-236	264	15	′(a⊗	′(a⊗	NUM
ma-236	264	16	1(1	1(1	NUM
ma-236	264	17	+	+	SYM
ma-236	264	18	k2	k2	NOUN
ma-236	264	19	)	)	PUNCT
ma-236	265	1	+	+	CCONJ
ma-236	265	2	1⊗b	1⊗b	NUM
ma-236	265	3	(	(	PUNCT
ma-236	265	4	1−	1−	NUM
ma-236	265	5	k	k	NOUN
ma-236	265	6	2	2	NUM
ma-236	265	7	)	)	PUNCT
ma-236	265	8	)	)	PUNCT
ma-236	265	9	∣∣∣∣	∣∣∣∣	PROPN
ma-236	266	1	=	=	SYM
ma-236	266	2	∫	∫	PROPN
ma-236	267	1	i	i	PRON
ma-236	267	2	∫	∫	VERB
ma-236	268	1	i	i	PRON
ma-236	268	2	∣∣∣∣f’((1	∣∣∣∣f’((1	PROPN
ma-236	268	3	+	+	CCONJ
ma-236	268	4	k2	k2	PROPN
ma-236	268	5	)	)	PUNCT
ma-236	268	6	t	t	NOUN
ma-236	268	7	+	+	CCONJ
ma-236	268	8	(	(	PUNCT
ma-236	268	9	1−	1−	NUM
ma-236	268	10	k	k	NOUN
ma-236	268	11	2	2	X
ma-236	268	12	)	)	PUNCT
ma-236	268	13	s	s	PART
ma-236	268	14	)	)	PUNCT
ma-236	268	15	∣∣∣∣det	∣∣∣∣det	PROPN
ma-236	268	16	⊗	⊗	PROPN
ma-236	268	17	dfs	dfs	PROPN
ma-236	268	18	6	6	NUM
ma-236	268	19	∫	∫	NOUN
ma-236	269	1	i	i	PRON
ma-236	269	2	∫	∫	VERB
ma-236	270	1	i	i	PRON
ma-236	270	2	[	[	X
ma-236	270	3	(	(	PUNCT
ma-236	270	4	1	1	NUM
ma-236	270	5	+	+	CCONJ
ma-236	270	6	k	k	PROPN
ma-236	270	7	2	2	X
ma-236	270	8	)	)	PUNCT
ma-236	270	9	|f	|f	PROPN
ma-236	271	1	′(t)|+	′(t)|+	PROPN
ma-236	271	2	(	(	PUNCT
ma-236	271	3	1−	1−	NUM
ma-236	271	4	k	k	NOUN
ma-236	271	5	2	2	X
ma-236	271	6	)	)	PUNCT
ma-236	271	7	|f	|f	PROPN
ma-236	271	8	′(s)|	′(s)|	PUNCT
ma-236	271	9	]	]	PUNCT
ma-236	272	1	det	det	PROPN
ma-236	272	2	⊗	⊗	PROPN
ma-236	272	3	dfs	dfs	PROPN
ma-236	272	4	=	=	PUNCT
ma-236	272	5	(	(	PUNCT
ma-236	272	6	1	1	NUM
ma-236	273	1	+	+	CCONJ
ma-236	273	2	k	k	PROPN
ma-236	273	3	2	2	X
ma-236	273	4	)	)	PUNCT
ma-236	273	5	|f	|f	PROPN
ma-236	273	6	′(a)|	′(a)|	X
ma-236	274	1	⊗	⊗	NUM
ma-236	274	2	1	1	NUM
ma-236	275	1	+	+	CCONJ
ma-236	275	2	(	(	PUNCT
ma-236	275	3	1−	1−	NUM
ma-236	275	4	k	k	NOUN
ma-236	275	5	2	2	NUM
ma-236	275	6	)	)	PUNCT
ma-236	275	7	1⊗	1⊗	PROPN
ma-236	275	8	|f	|f	PROPN
ma-236	275	9	′(b)|	′(b)|	VERB
ma-236	275	10	for	for	ADP
ma-236	275	11	all	all	DET
ma-236	275	12	k	k	PROPN
ma-236	275	13	∈	∈	PROPN
ma-236	276	1	[	[	X
ma-236	276	2	0	0	NUM
ma-236	276	3	,	,	PUNCT
ma-236	276	4	1].if	1].if	NUM
ma-236	276	5	we	we	PRON
ma-236	276	6	take	take	VERB
ma-236	276	7	the	the	DET
ma-236	276	8	norm	norm	NOUN
ma-236	276	9	in	in	ADP
ma-236	276	10	the	the	DET
ma-236	276	11	inequality	inequality	NOUN
ma-236	276	12	,	,	PUNCT
ma-236	276	13	we	we	PRON
ma-236	276	14	get	get	VERB
ma-236	276	15	the	the	DET
ma-236	276	16	following∥∥∥∥f	following∥∥∥∥f	PROPN
ma-236	276	17	′(a⊗	′(a⊗	VERB
ma-236	276	18	1(1	1(1	NUM
ma-236	276	19	+	+	SYM
ma-236	276	20	k2	k2	NOUN
ma-236	276	21	)	)	PUNCT
ma-236	277	1	+	+	CCONJ
ma-236	278	1	1⊗b	1⊗b	NUM
ma-236	278	2	(	(	PUNCT
ma-236	278	3	1−	1−	NUM
ma-236	278	4	k	k	NOUN
ma-236	278	5	2	2	NUM
ma-236	278	6	)	)	PUNCT
ma-236	278	7	)	)	PUNCT
ma-236	278	8	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	278	9	6	6	NUM
ma-236	278	10	∥∥∥∥(1	∥∥∥∥(1	NUM
ma-236	278	11	+	+	ADJ
ma-236	278	12	k2	k2	PROPN
ma-236	278	13	)	)	PUNCT
ma-236	278	14	|f	|f	PROPN
ma-236	278	15	′(a)|	′(a)|	X
ma-236	279	1	⊗	⊗	NUM
ma-236	279	2	1	1	NUM
ma-236	280	1	+	+	CCONJ
ma-236	280	2	(	(	PUNCT
ma-236	280	3	1−	1−	NUM
ma-236	280	4	k	k	NOUN
ma-236	280	5	2	2	NUM
ma-236	280	6	)	)	PUNCT
ma-236	280	7	1⊗	1⊗	PROPN
ma-236	280	8	|f	|f	PROPN
ma-236	281	1	′(b)|	′(b)|	VERB
ma-236	281	2	∥∥∥∥	∥∥∥∥	PROPN
ma-236	281	3	6	6	NUM
ma-236	281	4	(	(	PUNCT
ma-236	281	5	1	1	NUM
ma-236	281	6	+	+	CCONJ
ma-236	281	7	k	k	PROPN
ma-236	281	8	2	2	NUM
ma-236	281	9	)	)	PUNCT
ma-236	281	10	∥∥|f	∥∥|f	NOUN
ma-236	281	11	′(a)|	′(a)|	PUNCT
ma-236	282	1	⊗	⊗	NUM
ma-236	282	2	1∥∥+	1∥∥+	PROPN
ma-236	282	3	(	(	PUNCT
ma-236	282	4	1−	1−	NUM
ma-236	282	5	k	k	NOUN
ma-236	282	6	2	2	NUM
ma-236	282	7	)	)	PUNCT
ma-236	282	8	∥∥1⊗	∥∥1⊗	NOUN
ma-236	282	9	|f	|f	PROPN
ma-236	283	1	′(b)|∥∥	′(b)|∥∥	NOUN
ma-236	283	2	=	=	PUNCT
ma-236	283	3	(	(	PUNCT
ma-236	283	4	1	1	NUM
ma-236	283	5	+	+	CCONJ
ma-236	283	6	k	k	PROPN
ma-236	283	7	2	2	X
ma-236	283	8	)	)	PUNCT
ma-236	283	9	∥∥f	∥∥f	PROPN
ma-236	283	10	′(a)∥∥+	′(a)∥∥+	NOUN
ma-236	283	11	(	(	PUNCT
ma-236	283	12	1−	1−	NUM
ma-236	283	13	k	k	NOUN
ma-236	283	14	2	2	X
ma-236	283	15	)	)	PUNCT
ma-236	283	16	∥∥f	∥∥f	PROPN
ma-236	283	17	′(b)∥∥	′(b)∥∥	NOUN
ma-236	283	18	.therefore	.therefore	NOUN
ma-236	283	19	,	,	PUNCT
ma-236	283	20	we	we	PRON
ma-236	283	21	obtain∫	obtain∫	VERB
ma-236	283	22	1	1	NUM
ma-236	283	23	0	0	NUM
ma-236	283	24	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	284	1	−	−	PROPN
ma-236	285	1	k	k	NOUN
ma-236	285	2	∥∥∥∥∥∥∥∥f	∥∥∥∥∥∥∥∥f	VERB
ma-236	285	3	′(a⊗	′(a⊗	PROPN
ma-236	285	4	1(1	1(1	NUM
ma-236	285	5	+	+	SYM
ma-236	285	6	k2	k2	NOUN
ma-236	285	7	)	)	PUNCT
ma-236	286	1	+	+	CCONJ
ma-236	287	1	1⊗b	1⊗b	NUM
ma-236	287	2	(	(	PUNCT
ma-236	287	3	1−	1−	NUM
ma-236	287	4	k	k	NOUN
ma-236	287	5	2	2	NUM
ma-236	287	6	)	)	PUNCT
ma-236	287	7	)	)	PUNCT
ma-236	287	8	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	288	1	dk	dk	PROPN
ma-236	288	2	6	6	NUM
ma-236	288	3	∫	∫	PROPN
ma-236	288	4	1	1	NUM
ma-236	288	5	0	0	NUM
ma-236	288	6	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	288	7	−	−	PROPN
ma-236	288	8	k	k	PROPN
ma-236	288	9	∥∥∥∥((1	∥∥∥∥((1	PROPN
ma-236	289	1	+	+	CCONJ
ma-236	289	2	k2	k2	ADJ
ma-236	289	3	)	)	PUNCT
ma-236	289	4	∥∥f	∥∥f	PROPN
ma-236	289	5	′(a)∥∥+	′(a)∥∥+	NOUN
ma-236	289	6	(	(	PUNCT
ma-236	289	7	1−	1−	NUM
ma-236	289	8	k	k	NOUN
ma-236	289	9	2	2	NUM
ma-236	289	10	)	)	PUNCT
ma-236	289	11	∥∥f	∥∥f	PROPN
ma-236	289	12	′(b)∥∥	′(b)∥∥	PROPN
ma-236	289	13	)	)	PUNCT
ma-236	289	14	dk	dk	PROPN
ma-236	289	15	=	=	SYM
ma-236	289	16	79	79	NUM
ma-236	289	17	‖f’(a)‖+	‖f’(a)‖+	PROPN
ma-236	289	18	41	41	NUM
ma-236	289	19	‖f’(b)‖	‖f’(b)‖	NOUN
ma-236	289	20	384	384	NUM
ma-236	289	21	.simplifying	.simplifye	VERB
ma-236	289	22	the	the	DET
ma-236	289	23	other	other	ADJ
ma-236	289	24	term	term	NOUN
ma-236	289	25	and	and	CCONJ
ma-236	289	26	adding	add	VERB
ma-236	289	27	them	they	PRON
ma-236	289	28	,	,	PUNCT
ma-236	289	29	we	we	PRON
ma-236	289	30	obtain	obtain	VERB
ma-236	289	31	the	the	DET
ma-236	289	32	desired	desire	VERB
ma-236	289	33	inequality	inequality	NOUN
ma-236	289	34	.	.	PUNCT
ma-236	290	1	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	290	2	eur	eur	PROPN
ma-236	290	3	.	.	PUNCT
ma-236	291	1	j.	j.	PROPN
ma-236	291	2	math	math	PROPN
ma-236	291	3	.	.	PUNCT
ma-236	292	1	anal	anal	PROPN
ma-236	292	2	.	.	PUNCT
ma-236	293	1	10.28924	10.28924	NUM
ma-236	293	2	/	/	SYM
ma-236	293	3	ada	ada	PROPN
ma-236	293	4	/	/	SYM
ma-236	293	5	ma.4.17	ma.4.17	NOUN
ma-236	293	6	9	9	NUM
ma-236	293	7	�	�	NOUN
ma-236	293	8	we	we	PRON
ma-236	293	9	recall	recall	VERB
ma-236	293	10	that	that	SCONJ
ma-236	293	11	the	the	DET
ma-236	293	12	function	function	NOUN
ma-236	293	13	f	f	NOUN
ma-236	293	14	:	:	PUNCT
ma-236	293	15	i	i	PRON
ma-236	293	16	→	→	PUNCT
ma-236	293	17	r	r	NOUN
ma-236	293	18	is	be	AUX
ma-236	293	19	quasi	quasi	ADJ
ma-236	293	20	-	-	VERB
ma-236	293	21	convex	convex	ADJ
ma-236	293	22	,	,	PUNCT
ma-236	293	23	if	if	SCONJ
ma-236	293	24	f	f	PROPN
ma-236	293	25	(	(	PUNCT
ma-236	293	26	(	(	PUNCT
ma-236	293	27	1−	1−	NUM
ma-236	293	28	λ)t	λ)t	NOUN
ma-236	293	29	+	+	X
ma-236	293	30	λs	λs	NOUN
ma-236	293	31	)	)	PUNCT
ma-236	293	32	6	6	NUM
ma-236	293	33	max(f	max(f	NOUN
ma-236	293	34	(	(	PUNCT
ma-236	293	35	t	t	PROPN
ma-236	293	36	)	)	PUNCT
ma-236	293	37	,	,	PUNCT
ma-236	293	38	f	f	PROPN
ma-236	293	39	(	(	PUNCT
ma-236	293	40	s	s	NOUN
ma-236	293	41	)	)	PUNCT
ma-236	293	42	)	)	PUNCT
ma-236	294	1	=	=	SYM
ma-236	294	2	1	1	NUM
ma-236	294	3	2	2	NUM
ma-236	294	4	(	(	PUNCT
ma-236	294	5	f	f	PROPN
ma-236	294	6	(	(	PUNCT
ma-236	294	7	t	t	PROPN
ma-236	294	8	)	)	PUNCT
ma-236	295	1	+	+	NUM
ma-236	295	2	f	f	X
ma-236	295	3	(	(	PUNCT
ma-236	295	4	s	s	X
ma-236	295	5	)	)	PUNCT
ma-236	295	6	+	+	CCONJ
ma-236	295	7	|f	|f	PROPN
ma-236	295	8	(	(	PUNCT
ma-236	295	9	s)−	s)−	PROPN
ma-236	295	10	f	f	PROPN
ma-236	295	11	(	(	PUNCT
ma-236	295	12	t)|	t)|	NOUN
ma-236	295	13	)	)	PUNCT
ma-236	295	14	holds	hold	VERB
ma-236	295	15	for	for	ADP
ma-236	295	16	all	all	DET
ma-236	295	17	t	t	NOUN
ma-236	295	18	,	,	PUNCT
ma-236	295	19	s	s	VERB
ma-236	295	20	∈	∈	PROPN
ma-236	296	1	i	i	PRON
ma-236	296	2	and	and	CCONJ
ma-236	296	3	λ	λ	X
ma-236	296	4	∈	∈	PROPN
ma-236	297	1	[	[	X
ma-236	297	2	0	0	NUM
ma-236	297	3	,	,	PUNCT
ma-236	297	4	1	1	NUM
ma-236	297	5	]	]	PUNCT
ma-236	297	6	.	.	PUNCT
ma-236	298	1	theorem	theorem	ADJ
ma-236	298	2	10	10	NUM
ma-236	298	3	.	.	PUNCT
ma-236	299	1	assume	assume	VERB
ma-236	299	2	that	that	SCONJ
ma-236	299	3	f	f	PROPN
ma-236	299	4	is	be	AUX
ma-236	299	5	continuously	continuously	ADV
ma-236	299	6	differentiable	differentiable	ADJ
ma-236	299	7	on	on	ADP
ma-236	299	8	i	i	PRON
ma-236	299	9	with	with	ADP
ma-236	299	10	|f	|f	PRON
ma-236	299	11	′|	′|	NUM
ma-236	299	12	is	be	AUX
ma-236	299	13	quasi	quasi	ADJ
ma-236	299	14	-	-	NOUN
ma-236	299	15	convex	convex	ADJ
ma-236	299	16	on	on	ADP
ma-236	299	17	i	i	PRON
ma-236	299	18	,	,	PUNCT
ma-236	299	19	a	a	PRON
ma-236	299	20	and	and	CCONJ
ma-236	299	21	b	b	NOUN
ma-236	299	22	are	be	AUX
ma-236	299	23	selfadjoint	selfadjoint	VERB
ma-236	299	24	operators	operator	NOUN
ma-236	299	25	with	with	ADP
ma-236	299	26	sp(a	sp(a	NOUN
ma-236	299	27	)	)	PUNCT
ma-236	299	28	,	,	PUNCT
ma-236	299	29	sp(b	sp(b	PROPN
ma-236	299	30	)	)	PUNCT
ma-236	300	1	⊂	⊂	PROPN
ma-236	301	1	i	i	PRON
ma-236	301	2	,	,	PUNCT
ma-236	301	3	then∣∣∣∣∣∣∣∣18	then∣∣∣∣∣∣∣∣18	X
ma-236	301	4	[	[	PUNCT
ma-236	301	5	f	f	X
ma-236	301	6	(	(	PUNCT
ma-236	301	7	a)⊗	a)⊗	NOUN
ma-236	301	8	1	1	NUM
ma-236	301	9	+	+	NUM
ma-236	301	10	6f	6f	NUM
ma-236	301	11	(	(	PUNCT
ma-236	301	12	a⊗	a⊗	NOUN
ma-236	301	13	1	1	NUM
ma-236	301	14	+	+	CCONJ
ma-236	301	15	1⊗b	1⊗b	NUM
ma-236	301	16	2	2	NUM
ma-236	301	17	)	)	PUNCT
ma-236	301	18	+	+	CCONJ
ma-236	302	1	1⊗	1⊗	NUM
ma-236	302	2	f	f	X
ma-236	302	3	(	(	PUNCT
ma-236	302	4	b	b	NOUN
ma-236	302	5	)	)	PUNCT
ma-236	302	6	]	]	PUNCT
ma-236	302	7	(	(	PUNCT
ma-236	302	8	7	7	X
ma-236	302	9	)	)	PUNCT
ma-236	302	10	−	−	NOUN
ma-236	302	11	∫	∫	PROPN
ma-236	302	12	1	1	NUM
ma-236	302	13	0	0	NUM
ma-236	302	14	f	f	NOUN
ma-236	302	15	(	(	PUNCT
ma-236	302	16	λ1⊗b+	λ1⊗b+	NOUN
ma-236	302	17	(	(	PUNCT
ma-236	302	18	1−	1−	NUM
ma-236	302	19	λ)a⊗	λ)a⊗	X
ma-236	303	1	1)dλ	1)dλ	NUM
ma-236	303	2	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	303	3	≤	≤	ADV
ma-236	303	4	5	5	NUM
ma-236	303	5	‖1⊗b−	‖1⊗b−	NOUN
ma-236	303	6	a⊗	a⊗	NOUN
ma-236	304	1	1‖	1‖	NUM
ma-236	304	2	64	64	NUM
ma-236	305	1	∥∥|f	∥∥|f	ADJ
ma-236	305	2	′(a)|	′(a)|	PUNCT
ma-236	306	1	⊗	⊗	NUM
ma-236	306	2	1	1	NUM
ma-236	307	1	+	+	SYM
ma-236	307	2	1⊗	1⊗	NUM
ma-236	307	3	|f	|f	PRON
ma-236	307	4	′(b)|∥∥+	′(b)|∥∥+	PROPN
ma-236	307	5	∥∥|f	∥∥|f	PRON
ma-236	307	6	′(a)|	′(a)|	SYM
ma-236	308	1	⊗	⊗	NOUN
ma-236	308	2	1−	1−	NUM
ma-236	309	1	1⊗	1⊗	NUM
ma-236	309	2	|f	|f	PROPN
ma-236	309	3	′(b∥∥	′(b∥∥	NUM
ma-236	309	4	.	.	PUNCT
ma-236	310	1	proof	proof	NOUN
ma-236	310	2	.	.	PUNCT
ma-236	311	1	since	since	SCONJ
ma-236	311	2	|f	|f	PRON
ma-236	311	3	′|	′|	NUM
ma-236	311	4	is	be	AUX
ma-236	311	5	quasi	quasi	ADJ
ma-236	311	6	-	-	NOUN
ma-236	311	7	convex	convex	ADJ
ma-236	311	8	on	on	ADP
ma-236	311	9	i	i	PRON
ma-236	311	10	,	,	PUNCT
ma-236	311	11	then	then	ADV
ma-236	311	12	we	we	PRON
ma-236	311	13	get	get	VERB
ma-236	311	14	|f	|f	PRON
ma-236	311	15	′(t(1	′(t(1	NOUN
ma-236	311	16	+	+	CCONJ
ma-236	311	17	k)/(2	k)/(2	NOUN
ma-236	311	18	)	)	PUNCT
ma-236	312	1	+	+	NUM
ma-236	312	2	s(1−	s(1−	ADJ
ma-236	312	3	k)/(2))|	k)/(2))|	PROPN
ma-236	312	4	≤	≤	NOUN
ma-236	312	5	1/2(|f	1/2(|f	NUM
ma-236	312	6	′(t)|+	′(t)|+	PROPN
ma-236	312	7	|f	|f	PROPN
ma-236	313	1	′(s)|+	′(s)|+	PROPN
ma-236	314	1	||f	||f	VERB
ma-236	314	2	′(t)−	′(t)−	PROPN
ma-236	314	3	f	f	PROPN
ma-236	314	4	′(s)||	′(s)||	PROPN
ma-236	314	5	)	)	PUNCT
ma-236	314	6	for	for	ADP
ma-236	314	7	all	all	DET
ma-236	314	8	k	k	PROPN
ma-236	314	9	∈	∈	PROPN
ma-236	315	1	[	[	X
ma-236	315	2	0	0	NUM
ma-236	315	3	,	,	PUNCT
ma-236	315	4	1	1	NUM
ma-236	315	5	]	]	PUNCT
ma-236	315	6	and	and	CCONJ
ma-236	315	7	t	t	PROPN
ma-236	315	8	,	,	PUNCT
ma-236	315	9	s	s	PROPN
ma-236	315	10	∈	∈	PROPN
ma-236	315	11	i.	i.	NOUN
ma-236	315	12	if	if	SCONJ
ma-236	315	13	we	we	PRON
ma-236	315	14	take	take	VERB
ma-236	315	15	the	the	DET
ma-236	315	16	integral	integral	ADJ
ma-236	315	17	∫i	∫i	VERB
ma-236	315	18	∫i	∫i	VERB
ma-236	315	19	over	over	ADP
ma-236	315	20	det	det	PROPN
ma-236	315	21	⊗	⊗	PROPN
ma-236	315	22	dfs	dfs	PROPN
ma-236	315	23	,	,	PUNCT
ma-236	315	24	then	then	ADV
ma-236	315	25	we	we	PRON
ma-236	315	26	get∣∣∣∣f	get∣∣∣∣f	VERB
ma-236	315	27	′(a⊗	′(a⊗	NUM
ma-236	315	28	1(1	1(1	NUM
ma-236	315	29	+	+	SYM
ma-236	315	30	k2	k2	NOUN
ma-236	315	31	)	)	PUNCT
ma-236	316	1	+	+	CCONJ
ma-236	316	2	1⊗b	1⊗b	NUM
ma-236	316	3	(	(	PUNCT
ma-236	316	4	1−	1−	NUM
ma-236	316	5	k	k	NOUN
ma-236	316	6	2	2	NUM
ma-236	316	7	)	)	PUNCT
ma-236	316	8	)	)	PUNCT
ma-236	316	9	∣∣∣∣	∣∣∣∣	PROPN
ma-236	317	1	=	=	SYM
ma-236	317	2	∫	∫	PROPN
ma-236	318	1	i	i	PRON
ma-236	318	2	∫	∫	VERB
ma-236	319	1	i	i	PRON
ma-236	319	2	f	f	PROPN
ma-236	319	3	′(t(1	′(t(1	X
ma-236	319	4	+	+	CCONJ
ma-236	319	5	k)/(2	k)/(2	X
ma-236	319	6	)	)	PUNCT
ma-236	320	1	+	+	NUM
ma-236	320	2	s(1−	s(1−	ADJ
ma-236	320	3	k)/(2))det	k)/(2))det	PROPN
ma-236	320	4	⊗	⊗	PROPN
ma-236	320	5	dfs	dfs	NOUN
ma-236	320	6	6	6	NUM
ma-236	320	7	1	1	NUM
ma-236	320	8	2	2	NUM
ma-236	320	9	∫	∫	NOUN
ma-236	321	1	i	i	PRON
ma-236	321	2	∫	∫	VERB
ma-236	322	1	i	i	PRON
ma-236	322	2	(	(	PUNCT
ma-236	322	3	|f	|f	PROPN
ma-236	322	4	′(t)|+	′(t)|+	PROPN
ma-236	322	5	|f	|f	PROPN
ma-236	322	6	′(s)|+	′(s)|+	PROPN
ma-236	322	7	||f	||f	NOUN
ma-236	322	8	′(t)|	′(t)|	NOUN
ma-236	322	9	−	−	PROPN
ma-236	322	10	|f	|f	PROPN
ma-236	322	11	′(s)||)det	′(s)||)det	PROPN
ma-236	323	1	⊗	⊗	PROPN
ma-236	323	2	dfs	dfs	PROPN
ma-236	323	3	=	=	NOUN
ma-236	323	4	1	1	NUM
ma-236	323	5	2	2	NUM
ma-236	323	6	(	(	PUNCT
ma-236	323	7	|f	|f	PROPN
ma-236	323	8	′(a)|	′(a)|	X
ma-236	324	1	⊗	⊗	NOUN
ma-236	324	2	1	1	NUM
ma-236	325	1	+	+	SYM
ma-236	325	2	1⊗	1⊗	NUM
ma-236	325	3	|f	|f	PROPN
ma-236	325	4	′(b)|+	′(b)|+	PROPN
ma-236	325	5	||f	||f	PROPN
ma-236	325	6	′(a)|	′(a)|	PROPN
ma-236	326	1	⊗	⊗	NUM
ma-236	326	2	1−	1−	NUM
ma-236	327	1	1⊗	1⊗	NUM
ma-236	327	2	|f	|f	PROPN
ma-236	327	3	′(b)||)for	′(b)||)for	ADP
ma-236	327	4	all	all	DET
ma-236	327	5	k	k	PROPN
ma-236	327	6	∈	∈	PROPN
ma-236	328	1	[	[	X
ma-236	328	2	0	0	NUM
ma-236	328	3	,	,	PUNCT
ma-236	328	4	1].if	1].if	NUM
ma-236	328	5	we	we	PRON
ma-236	328	6	take	take	VERB
ma-236	328	7	the	the	DET
ma-236	328	8	norm	norm	NOUN
ma-236	328	9	,	,	PUNCT
ma-236	328	10	then	then	ADV
ma-236	328	11	we	we	PRON
ma-236	328	12	get∥∥∥∥f	get∥∥∥∥f	VERB
ma-236	328	13	′(a⊗	′(a⊗	NUM
ma-236	328	14	1(1	1(1	NUM
ma-236	328	15	+	+	SYM
ma-236	328	16	k2	k2	NOUN
ma-236	328	17	)	)	PUNCT
ma-236	329	1	+	+	CCONJ
ma-236	330	1	1⊗b	1⊗b	NUM
ma-236	330	2	(	(	PUNCT
ma-236	330	3	1−	1−	NUM
ma-236	330	4	k	k	NOUN
ma-236	330	5	2	2	NUM
ma-236	330	6	)	)	PUNCT
ma-236	330	7	)	)	PUNCT
ma-236	330	8	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	330	9	6	6	NUM
ma-236	330	10	∥∥∥∥12(|f	∥∥∥∥12(|f	PROPN
ma-236	330	11	′(a)|	′(a)|	X
ma-236	331	1	⊗	⊗	NOUN
ma-236	331	2	1	1	NUM
ma-236	332	1	+	+	SYM
ma-236	332	2	1⊗	1⊗	NUM
ma-236	332	3	|f	|f	PROPN
ma-236	332	4	′(b)|+	′(b)|+	PROPN
ma-236	332	5	||f	||f	PROPN
ma-236	332	6	′(a)|	′(a)|	PROPN
ma-236	333	1	⊗	⊗	NUM
ma-236	333	2	1−	1−	NUM
ma-236	334	1	1⊗	1⊗	NUM
ma-236	334	2	|f	|f	PRON
ma-236	334	3	′(b)||	′(b)||	PROPN
ma-236	334	4	)	)	PUNCT
ma-236	334	5	∥∥∥∥	∥∥∥∥	NUM
ma-236	335	1	6	6	NUM
ma-236	335	2	1	1	NUM
ma-236	335	3	2	2	NUM
ma-236	335	4	(	(	PUNCT
ma-236	335	5	∥∥|f	∥∥|f	ADJ
ma-236	335	6	′(a)|	′(a)|	X
ma-236	336	1	⊗	⊗	NUM
ma-236	336	2	1	1	NUM
ma-236	337	1	+	+	SYM
ma-236	337	2	1⊗	1⊗	NUM
ma-236	337	3	|f	|f	PRON
ma-236	337	4	′(b)|∥∥+	′(b)|∥∥+	PROPN
ma-236	337	5	∥∥|f	∥∥|f	PRON
ma-236	337	6	′(a)|	′(a)|	SYM
ma-236	338	1	⊗	⊗	NOUN
ma-236	338	2	1−	1−	NUM
ma-236	339	1	1⊗	1⊗	NUM
ma-236	339	2	|f	|f	PRON
ma-236	339	3	′(b)|∥∥)which	′(b)|∥∥)which	ADV
ma-236	339	4	when	when	SCONJ
ma-236	339	5	applied	apply	VERB
ma-236	339	6	in	in	ADP
ma-236	339	7	our	our	PRON
ma-236	339	8	case	case	NOUN
ma-236	339	9	,	,	PUNCT
ma-236	339	10	we	we	PRON
ma-236	339	11	get∫	get∫	VERB
ma-236	339	12	1	1	NUM
ma-236	339	13	0	0	NUM
ma-236	339	14	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	340	1	−	−	PROPN
ma-236	340	2	k	k	NOUN
ma-236	340	3	∥∥∥∥∥∥∥∥f	∥∥∥∥∥∥∥∥f	VERB
ma-236	340	4	′(a⊗	′(a⊗	PROPN
ma-236	340	5	1(1	1(1	NUM
ma-236	340	6	+	+	SYM
ma-236	340	7	k2	k2	NOUN
ma-236	340	8	)	)	PUNCT
ma-236	341	1	+	+	CCONJ
ma-236	342	1	1⊗b	1⊗b	NUM
ma-236	342	2	(	(	PUNCT
ma-236	342	3	1−	1−	NUM
ma-236	342	4	k	k	NOUN
ma-236	342	5	2	2	NUM
ma-236	342	6	)	)	PUNCT
ma-236	342	7	)	)	PUNCT
ma-236	342	8	∥∥∥∥	∥∥∥∥	PUNCT
ma-236	343	1	dk	dk	PROPN
ma-236	343	2	6	6	NUM
ma-236	343	3	∫	∫	PROPN
ma-236	343	4	1	1	NUM
ma-236	343	5	0	0	NUM
ma-236	343	6	∥∥∥∥34	∥∥∥∥34	NOUN
ma-236	343	7	−	−	PROPN
ma-236	344	1	k	k	NOUN
ma-236	344	2	∥∥∥∥(12	∥∥∥∥(12	PROPN
ma-236	344	3	(	(	PUNCT
ma-236	344	4	∥∥|f	∥∥|f	PROPN
ma-236	344	5	′(a)|	′(a)|	SYM
ma-236	345	1	⊗	⊗	NUM
ma-236	345	2	1	1	NUM
ma-236	346	1	+	+	SYM
ma-236	346	2	1⊗	1⊗	NUM
ma-236	346	3	|f	|f	PRON
ma-236	346	4	′(b)|∥∥+	′(b)|∥∥+	PROPN
ma-236	346	5	∥∥|f	∥∥|f	PRON
ma-236	346	6	′(a)|	′(a)|	SYM
ma-236	347	1	⊗	⊗	NOUN
ma-236	347	2	1−	1−	NUM
ma-236	348	1	1⊗	1⊗	NUM
ma-236	348	2	|f	|f	PROPN
ma-236	348	3	′(b)|∥∥	′(b)|∥∥	NOUN
ma-236	348	4	)	)	PUNCT
ma-236	348	5	)	)	PUNCT
ma-236	349	1	dk	dk	PROPN
ma-236	349	2	.	.	PUNCT
ma-236	349	3	which	which	PRON
ma-236	349	4	when	when	SCONJ
ma-236	349	5	simplified	simplify	VERB
ma-236	349	6	,	,	PUNCT
ma-236	349	7	we	we	PRON
ma-236	349	8	obtain	obtain	VERB
ma-236	349	9	the	the	DET
ma-236	349	10	desired	desire	VERB
ma-236	349	11	inequality	inequality	NOUN
ma-236	349	12	.	.	PUNCT
ma-236	350	1	�	�	PROPN
ma-236	350	2	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	350	3	eur	eur	PROPN
ma-236	350	4	.	.	PUNCT
ma-236	351	1	j.	j.	PROPN
ma-236	351	2	math	math	PROPN
ma-236	351	3	.	.	PUNCT
ma-236	352	1	anal	anal	PROPN
ma-236	352	2	.	.	PUNCT
ma-236	353	1	10.28924	10.28924	NUM
ma-236	353	2	/	/	SYM
ma-236	353	3	ada	ada	PROPN
ma-236	353	4	/	/	SYM
ma-236	353	5	ma.4.17	ma.4.17	NOUN
ma-236	353	6	103	103	NUM
ma-236	353	7	.	.	PUNCT
ma-236	354	1	some	some	DET
ma-236	354	2	examples	example	NOUN
ma-236	354	3	and	and	CCONJ
ma-236	354	4	consequences	consequence	NOUN
ma-236	354	5	it	it	PRON
ma-236	354	6	is	be	AUX
ma-236	354	7	known	know	VERB
ma-236	354	8	that	that	SCONJ
ma-236	354	9	if	if	SCONJ
ma-236	354	10	u	u	PROPN
ma-236	354	11	and	and	CCONJ
ma-236	354	12	v	v	NOUN
ma-236	354	13	are	be	AUX
ma-236	354	14	commuting	commute	VERB
ma-236	354	15	,	,	PUNCT
ma-236	354	16	that	that	PRON
ma-236	354	17	is	be	AUX
ma-236	354	18	uv	uv	NOUN
ma-236	354	19	=	=	PUNCT
ma-236	354	20	v	v	NOUN
ma-236	354	21	u	u	NOUN
ma-236	354	22	,	,	PUNCT
ma-236	354	23	then	then	ADV
ma-236	354	24	the	the	DET
ma-236	354	25	exponential	exponential	ADJ
ma-236	354	26	functionsatisfies	functionsatisfie	VERB
ma-236	354	27	the	the	DET
ma-236	354	28	property	property	NOUN
ma-236	354	29	exp(u	exp(u	PROPN
ma-236	354	30	)	)	PUNCT
ma-236	354	31	exp(v	exp(v	NOUN
ma-236	354	32	)	)	PUNCT
ma-236	355	1	=	=	SYM
ma-236	355	2	exp(v	exp(v	X
ma-236	355	3	)	)	PUNCT
ma-236	355	4	exp(u	exp(u	PROPN
ma-236	355	5	)	)	PUNCT
ma-236	355	6	=	=	SYM
ma-236	356	1	exp(u	exp(u	PROPN
ma-236	357	1	+	+	CCONJ
ma-236	357	2	v	v	NOUN
ma-236	357	3	)	)	PUNCT
ma-236	357	4	.	.	PUNCT
ma-236	358	1	also	also	ADV
ma-236	358	2	,	,	PUNCT
ma-236	358	3	if	if	SCONJ
ma-236	358	4	u	u	NOUN
ma-236	358	5	is	be	AUX
ma-236	358	6	invertible	invertible	ADJ
ma-236	358	7	and	and	CCONJ
ma-236	358	8	a	a	DET
ma-236	358	9	,	,	PUNCT
ma-236	358	10	b	b	X
ma-236	358	11	∈	∈	PROPN
ma-236	358	12	r	r	NOUN
ma-236	358	13	and	and	CCONJ
ma-236	358	14	a	a	DET
ma-236	358	15	<	<	X
ma-236	358	16	b	b	NOUN
ma-236	358	17	then∫	then∫	NOUN
ma-236	358	18	b	b	PROPN
ma-236	358	19	a	a	DET
ma-236	358	20	exp(tu)dt	exp(tu)dt	NOUN
ma-236	358	21	=	=	PUNCT
ma-236	358	22	u−1[exp(bu)−	u−1[exp(bu)−	ADJ
ma-236	358	23	exp(au	exp(au	NOUN
ma-236	358	24	)	)	PUNCT
ma-236	358	25	]	]	PUNCT
ma-236	358	26	.	.	PUNCT
ma-236	359	1	moreover	moreover	ADV
ma-236	359	2	,	,	PUNCT
ma-236	359	3	if	if	SCONJ
ma-236	359	4	u	u	NOUN
ma-236	359	5	and	and	CCONJ
ma-236	359	6	v	v	NOUN
ma-236	359	7	are	be	AUX
ma-236	359	8	commuting	commute	VERB
ma-236	359	9	and	and	CCONJ
ma-236	359	10	v	v	ADP
ma-236	359	11	−	−	PROPN
ma-236	359	12	u	u	NOUN
ma-236	359	13	is	be	AUX
ma-236	359	14	invertible	invertible	ADJ
ma-236	359	15	,	,	PUNCT
ma-236	359	16	then∫	then∫	NOUN
ma-236	359	17	1	1	NUM
ma-236	359	18	0	0	NUM
ma-236	359	19	exp((1−	exp((1−	ADJ
ma-236	359	20	k)u	k)u	NOUN
ma-236	360	1	+	+	CCONJ
ma-236	360	2	kv	kv	PROPN
ma-236	360	3	)	)	PUNCT
ma-236	360	4	dk	dk	PROPN
ma-236	360	5	=	=	PUNCT
ma-236	360	6	∫	∫	PROPN
ma-236	360	7	1	1	NUM
ma-236	360	8	0	0	NUM
ma-236	360	9	exp(k(v	exp(k(v	PROPN
ma-236	360	10	−	−	PROPN
ma-236	360	11	u	u	NOUN
ma-236	360	12	)	)	PUNCT
ma-236	360	13	)	)	PUNCT
ma-236	360	14	exp(u)dk	exp(u)dk	X
ma-236	361	1	=	=	SYM
ma-236	361	2	∫	∫	PROPN
ma-236	361	3	1	1	NUM
ma-236	361	4	0	0	NUM
ma-236	361	5	(	(	PUNCT
ma-236	361	6	exp(k(v	exp(k(v	PROPN
ma-236	361	7	−	−	PROPN
ma-236	361	8	u))dk)exp(u	u))dk)exp(u	NUM
ma-236	361	9	)	)	PUNCT
ma-236	362	1	=	=	PRON
ma-236	362	2	(	(	PUNCT
ma-236	362	3	v	v	NUM
ma-236	362	4	−	−	PROPN
ma-236	362	5	u)−1[exp(v	u)−1[exp(v	PROPN
ma-236	362	6	−	−	PROPN
ma-236	362	7	u)−	u)−	PROPN
ma-236	362	8	i	i	PROPN
ma-236	362	9	]	]	X
ma-236	362	10	exp(u	exp(u	PROPN
ma-236	362	11	)	)	PUNCT
ma-236	362	12	=	=	SYM
ma-236	363	1	(	(	PUNCT
ma-236	363	2	v	v	NOUN
ma-236	363	3	−	−	PROPN
ma-236	363	4	u)−1[exp(v	u)−1[exp(v	PROPN
ma-236	363	5	)	)	PUNCT
ma-236	363	6	−	−	PROPN
ma-236	364	1	exp(u)].since	exp(u)].since	NOUN
ma-236	364	2	the	the	DET
ma-236	364	3	operators	operator	NOUN
ma-236	364	4	u	u	NOUN
ma-236	364	5	=	=	NOUN
ma-236	364	6	a⊗	a⊗	NOUN
ma-236	364	7	1	1	NUM
ma-236	364	8	and	and	CCONJ
ma-236	364	9	v	v	NOUN
ma-236	364	10	=	=	SYM
ma-236	364	11	1⊗b	1⊗b	NUM
ma-236	364	12	are	be	AUX
ma-236	364	13	commutative	commutative	ADJ
ma-236	364	14	and	and	CCONJ
ma-236	364	15	if	if	SCONJ
ma-236	364	16	1⊗b−a⊗	1⊗b−a⊗	PROPN
ma-236	364	17	1	1	NUM
ma-236	364	18	is	be	AUX
ma-236	364	19	invertible	invertible	ADJ
ma-236	364	20	,	,	PUNCT
ma-236	364	21	then	then	ADV
ma-236	364	22	∫	∫	PROPN
ma-236	364	23	1	1	NUM
ma-236	364	24	0	0	NUM
ma-236	364	25	exp((1−	exp((1−	VERB
ma-236	364	26	k)a⊗	k)a⊗	NOUN
ma-236	364	27	1	1	NUM
ma-236	365	1	+	+	CCONJ
ma-236	365	2	k1⊗b)dk	k1⊗b)dk	NOUN
ma-236	365	3	=	=	SYM
ma-236	365	4	(	(	PUNCT
ma-236	365	5	1⊗b−	1⊗b−	NUM
ma-236	365	6	a⊗	a⊗	NOUN
ma-236	365	7	1)−1[exp(1⊗b)−	1)−1[exp(1⊗b)−	NUM
ma-236	366	1	exp(a⊗	exp(a⊗	PROPN
ma-236	366	2	1)].in	1)].in	NUM
ma-236	366	3	the	the	DET
ma-236	366	4	following	following	ADJ
ma-236	366	5	sequel	sequel	NOUN
ma-236	366	6	we	we	PRON
ma-236	366	7	provide	provide	VERB
ma-236	366	8	examples	example	NOUN
ma-236	366	9	to	to	ADP
ma-236	366	10	the	the	DET
ma-236	366	11	obtained	obtain	VERB
ma-236	366	12	theorems	theorem	NOUN
ma-236	366	13	in	in	ADP
ma-236	366	14	main	main	ADJ
ma-236	366	15	section	section	NOUN
ma-236	366	16	.	.	PUNCT
ma-236	367	1	examplesconsist	examplesconsist	NOUN
ma-236	367	2	of	of	ADP
ma-236	367	3	taking	take	VERB
ma-236	367	4	f	f	PROPN
ma-236	367	5	to	to	PART
ma-236	367	6	be	be	AUX
ma-236	367	7	an	an	DET
ma-236	367	8	exponential	exponential	ADJ
ma-236	367	9	operator	operator	NOUN
ma-236	367	10	and	and	CCONJ
ma-236	367	11	applying	apply	VERB
ma-236	367	12	various	various	ADJ
ma-236	367	13	conditions	condition	NOUN
ma-236	367	14	as	as	SCONJ
ma-236	367	15	given	give	VERB
ma-236	367	16	by	by	ADP
ma-236	367	17	thetheorems	thetheorem	NOUN
ma-236	367	18	.	.	PUNCT
ma-236	368	1	corollary	corollary	ADJ
ma-236	368	2	1	1	NUM
ma-236	368	3	.	.	PUNCT
ma-236	369	1	if	if	SCONJ
ma-236	369	2	a	a	DET
ma-236	369	3	,	,	PUNCT
ma-236	369	4	b	b	NOUN
ma-236	369	5	are	be	AUX
ma-236	369	6	selfadjoint	selfadjoint	VERB
ma-236	369	7	operators	operator	NOUN
ma-236	369	8	with	with	ADP
ma-236	369	9	sp(a	sp(a	NOUN
ma-236	369	10	)	)	PUNCT
ma-236	369	11	,	,	PUNCT
ma-236	369	12	sp(b	sp(b	PROPN
ma-236	369	13	)	)	PUNCT
ma-236	370	1	⊂	⊂	PROPN
ma-236	371	1	[	[	X
ma-236	371	2	m	m	X
ma-236	371	3	,	,	PUNCT
ma-236	371	4	m	m	X
ma-236	371	5	]	]	PUNCT
ma-236	371	6	and	and	CCONJ
ma-236	371	7	1⊗b−	1⊗b−	NUM
ma-236	371	8	a⊗	a⊗	NOUN
ma-236	371	9	1	1	NUM
ma-236	371	10	is	be	AUX
ma-236	371	11	invertible	invertible	ADJ
ma-236	371	12	,	,	PUNCT
ma-236	371	13	then	then	ADV
ma-236	371	14	by	by	ADP
ma-236	371	15	(	(	PUNCT
ma-236	371	16	5	5	NUM
ma-236	371	17	)	)	PUNCT
ma-236	371	18	,	,	PUNCT
ma-236	371	19	we	we	PRON
ma-236	371	20	get∣∣∣∣∣∣∣∣18	get∣∣∣∣∣∣∣∣18	VERB
ma-236	371	21	[	[	PUNCT
ma-236	371	22	exp(a)⊗	exp(a)⊗	X
ma-236	371	23	1	1	NUM
ma-236	371	24	+	+	SYM
ma-236	371	25	6	6	NUM
ma-236	371	26	exp	exp	NOUN
ma-236	371	27	(	(	PUNCT
ma-236	371	28	a⊗	a⊗	NOUN
ma-236	371	29	1	1	NUM
ma-236	371	30	+	+	CCONJ
ma-236	371	31	1⊗b	1⊗b	NUM
ma-236	371	32	2	2	NUM
ma-236	371	33	)	)	PUNCT
ma-236	372	1	+	+	CCONJ
ma-236	373	1	1⊗	1⊗	NUM
ma-236	373	2	exp(b	exp(b	NUM
ma-236	373	3	)	)	PUNCT
ma-236	373	4	]	]	PUNCT
ma-236	374	1	(	(	PUNCT
ma-236	374	2	8)	8)	NUM
ma-236	374	3	−(1⊗b−	−(1⊗b−	NOUN
ma-236	374	4	a⊗	a⊗	NOUN
ma-236	374	5	1)−1[exp(1⊗b)−	1)−1[exp(1⊗b)−	NUM
ma-236	374	6	exp(a⊗	exp(a⊗	PROPN
ma-236	374	7	1	1	NUM
ma-236	374	8	)	)	PUNCT
ma-236	374	9	]	]	PUNCT
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ma-236	374	11	≤	≤	ADJ
ma-236	374	12	5	5	NUM
ma-236	374	13	‖1⊗b−	‖1⊗b−	NOUN
ma-236	374	14	a⊗	a⊗	NOUN
ma-236	374	15	1‖	1‖	NUM
ma-236	374	16	32	32	NUM
ma-236	374	17	exp(m	exp(m	NOUN
ma-236	374	18	)	)	PUNCT
ma-236	374	19	.	.	PUNCT
ma-236	375	1	corollary	corollary	ADJ
ma-236	375	2	2	2	NUM
ma-236	375	3	.	.	PUNCT
ma-236	376	1	since	since	SCONJ
ma-236	376	2	for	for	ADP
ma-236	376	3	f	f	PROPN
ma-236	376	4	(	(	PUNCT
ma-236	376	5	t	t	PROPN
ma-236	376	6	)	)	PUNCT
ma-236	376	7	=	=	PUNCT
ma-236	376	8	exp(t	exp(t	PROPN
ma-236	376	9	)	)	PUNCT
ma-236	376	10	,	,	PUNCT
ma-236	376	11	t	t	PROPN
ma-236	376	12	∈	∈	PROPN
ma-236	376	13	r	r	PROPN
ma-236	376	14	,	,	PUNCT
ma-236	376	15	|f	|f	PROPN
ma-236	376	16	′|	′|	NUM
ma-236	376	17	is	be	AUX
ma-236	376	18	convex	convex	ADJ
ma-236	376	19	,	,	PUNCT
ma-236	376	20	then	then	ADV
ma-236	376	21	by	by	ADP
ma-236	376	22	(	(	PUNCT
ma-236	376	23	6)∣∣∣∣∣∣∣∣18	6)∣∣∣∣∣∣∣∣18	NUM
ma-236	376	24	[	[	PUNCT
ma-236	376	25	exp(a)⊗	exp(a)⊗	X
ma-236	376	26	1	1	NUM
ma-236	376	27	+	+	SYM
ma-236	376	28	6	6	NUM
ma-236	376	29	exp	exp	NOUN
ma-236	376	30	(	(	PUNCT
ma-236	376	31	a⊗	a⊗	NOUN
ma-236	376	32	1	1	NUM
ma-236	376	33	+	+	CCONJ
ma-236	376	34	1⊗b	1⊗b	NUM
ma-236	376	35	2	2	NUM
ma-236	376	36	)	)	PUNCT
ma-236	377	1	+	+	CCONJ
ma-236	378	1	1⊗	1⊗	NUM
ma-236	378	2	exp(b	exp(b	NUM
ma-236	378	3	)	)	PUNCT
ma-236	378	4	]	]	PUNCT
ma-236	379	1	(	(	PUNCT
ma-236	379	2	9	9	X
ma-236	379	3	)	)	PUNCT
ma-236	379	4	−(1⊗b−	−(1⊗b−	NOUN
ma-236	379	5	a⊗	a⊗	NOUN
ma-236	379	6	1)−1[exp(1⊗b)−	1)−1[exp(1⊗b)−	NUM
ma-236	379	7	exp(a⊗	exp(a⊗	PROPN
ma-236	379	8	1	1	NUM
ma-236	379	9	)	)	PUNCT
ma-236	379	10	]	]	PUNCT
ma-236	380	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	380	2	≤	≤	ADJ
ma-236	380	3	5	5	NUM
ma-236	380	4	‖1⊗b−	‖1⊗b−	NOUN
ma-236	380	5	a⊗	a⊗	NOUN
ma-236	380	6	1‖	1‖	NUM
ma-236	380	7	64	64	NUM
ma-236	380	8	(	(	PUNCT
ma-236	380	9	‖exp(a)‖+	‖exp(a)‖+	X
ma-236	380	10	‖exp(b)‖	‖exp(b)‖	NUM
ma-236	380	11	)	)	PUNCT
ma-236	380	12	.	.	PUNCT
ma-236	381	1	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	381	2	eur	eur	PROPN
ma-236	381	3	.	.	PUNCT
ma-236	382	1	j.	j.	PROPN
ma-236	382	2	math	math	PROPN
ma-236	382	3	.	.	PUNCT
ma-236	383	1	anal	anal	PROPN
ma-236	383	2	.	.	PUNCT
ma-236	384	1	10.28924	10.28924	NUM
ma-236	384	2	/	/	SYM
ma-236	384	3	ada	ada	PROPN
ma-236	384	4	/	/	SYM
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ma-236	384	6	11	11	NUM
ma-236	384	7	∣∣∣∣∣∣∣∣18	∣∣∣∣∣∣∣∣18	PROPN
ma-236	384	8	[	[	PUNCT
ma-236	384	9	exp(a)⊗	exp(a)⊗	X
ma-236	384	10	1	1	NUM
ma-236	384	11	+	+	SYM
ma-236	384	12	6	6	NUM
ma-236	384	13	exp	exp	NOUN
ma-236	384	14	(	(	PUNCT
ma-236	384	15	a⊗	a⊗	NOUN
ma-236	384	16	1	1	NUM
ma-236	384	17	+	+	CCONJ
ma-236	384	18	1⊗b	1⊗b	NUM
ma-236	384	19	2	2	NUM
ma-236	384	20	)	)	PUNCT
ma-236	384	21	+	+	CCONJ
ma-236	384	22	1⊗	1⊗	NUM
ma-236	384	23	exp(b	exp(b	NUM
ma-236	384	24	)	)	PUNCT
ma-236	384	25	]	]	PUNCT
ma-236	384	26	(	(	PUNCT
ma-236	384	27	10	10	NUM
ma-236	384	28	)	)	PUNCT
ma-236	384	29	−(1⊗b−	−(1⊗b−	NOUN
ma-236	384	30	a⊗	a⊗	NOUN
ma-236	384	31	1)−1[exp(1⊗b)−	1)−1[exp(1⊗b)−	NUM
ma-236	384	32	exp(a⊗	exp(a⊗	PROPN
ma-236	384	33	1	1	NUM
ma-236	384	34	)	)	PUNCT
ma-236	384	35	]	]	PUNCT
ma-236	385	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ma-236	385	2	≤	≤	ADJ
ma-236	385	3	5	5	NUM
ma-236	385	4	‖1⊗b−	‖1⊗b−	NOUN
ma-236	385	5	a⊗	a⊗	NOUN
ma-236	385	6	1‖	1‖	NUM
ma-236	385	7	64	64	NUM
ma-236	385	8	(	(	PUNCT
ma-236	385	9	‖|	‖|	PROPN
ma-236	385	10	exp(a)|	exp(a)|	PROPN
ma-236	385	11	⊗	⊗	PROPN
ma-236	385	12	1	1	NUM
ma-236	386	1	+	+	SYM
ma-236	386	2	1⊗	1⊗	NUM
ma-236	386	3	|	|	ADV
ma-236	386	4	exp(b)|‖+	exp(b)|‖+	NOUN
ma-236	386	5	‖exp(a)|	‖exp(a)|	PROPN
ma-236	386	6	⊗	⊗	NUM
ma-236	386	7	1−	1−	NUM
ma-236	387	1	1⊗	1⊗	NUM
ma-236	387	2	|	|	ADV
ma-236	387	3	exp(b‖	exp(b‖	PRON
ma-236	387	4	)	)	PUNCT
ma-236	387	5	.	.	PUNCT
ma-236	388	1	4	4	X
ma-236	388	2	.	.	X
ma-236	388	3	conclusion	conclusion	NOUN
ma-236	388	4	tensors	tensor	NOUN
ma-236	388	5	have	have	AUX
ma-236	388	6	become	become	VERB
ma-236	388	7	important	important	ADJ
ma-236	388	8	in	in	ADP
ma-236	388	9	various	various	ADJ
ma-236	388	10	fields	field	NOUN
ma-236	388	11	,	,	PUNCT
ma-236	388	12	for	for	ADP
ma-236	388	13	example	example	NOUN
ma-236	388	14	in	in	ADP
ma-236	388	15	physics	physics	NOUN
ma-236	388	16	because	because	SCONJ
ma-236	388	17	they	they	PRON
ma-236	388	18	providea	providea	VERB
ma-236	388	19	concise	concise	ADJ
ma-236	388	20	mathematical	mathematical	ADJ
ma-236	388	21	framework	framework	NOUN
ma-236	388	22	for	for	ADP
ma-236	388	23	formulating	formulate	VERB
ma-236	388	24	and	and	CCONJ
ma-236	388	25	solving	solve	VERB
ma-236	388	26	physical	physical	ADJ
ma-236	388	27	problems	problem	NOUN
ma-236	388	28	in	in	ADP
ma-236	388	29	fields	field	NOUN
ma-236	388	30	suchas	sucha	NOUN
ma-236	388	31	mechanics	mechanic	NOUN
ma-236	388	32	,	,	PUNCT
ma-236	388	33	electromagnetism	electromagnetism	NOUN
ma-236	388	34	,	,	PUNCT
ma-236	388	35	quantum	quantum	NOUN
ma-236	388	36	mechanics	mechanic	NOUN
ma-236	388	37	,	,	PUNCT
ma-236	388	38	and	and	CCONJ
ma-236	388	39	many	many	ADJ
ma-236	388	40	others	other	NOUN
ma-236	388	41	.	.	PUNCT
ma-236	389	1	as	as	SCONJ
ma-236	389	2	such	such	ADJ
ma-236	389	3	inequalities	inequality	NOUN
ma-236	389	4	arecrucial	arecrucial	ADJ
ma-236	389	5	in	in	ADP
ma-236	389	6	numerical	numerical	ADJ
ma-236	389	7	aspects	aspect	NOUN
ma-236	389	8	.	.	PUNCT
ma-236	389	9	reflected	reflect	VERB
ma-236	389	10	in	in	ADP
ma-236	389	11	this	this	DET
ma-236	389	12	work	work	NOUN
ma-236	389	13	is	be	AUX
ma-236	389	14	the	the	DET
ma-236	389	15	tensorial	tensorial	PROPN
ma-236	389	16	shuang	shuang	PROPN
ma-236	389	17	’s	’s	PROPN
ma-236	389	18	lemma	lemma	PROPN
ma-236	389	19	,	,	PUNCT
ma-236	389	20	which	which	PRON
ma-236	389	21	asa	asa	PROPN
ma-236	389	22	consequence	consequence	NOUN
ma-236	389	23	enabled	enable	VERB
ma-236	389	24	us	we	PRON
ma-236	389	25	to	to	PART
ma-236	389	26	obtain	obtain	VERB
ma-236	389	27	simpson	simpson	NOUN
ma-236	389	28	type	type	NOUN
ma-236	389	29	inequalities	inequality	NOUN
ma-236	389	30	in	in	ADP
ma-236	389	31	hilbert	hilbert	NOUN
ma-236	389	32	space	space	NOUN
ma-236	389	33	.	.	PUNCT
ma-236	390	1	new	new	ADJ
ma-236	390	2	simpsontype	simpsontype	NOUN
ma-236	390	3	inequalities	inequality	NOUN
ma-236	390	4	are	be	AUX
ma-236	390	5	given	give	VERB
ma-236	390	6	,	,	PUNCT
ma-236	390	7	examples	example	NOUN
ma-236	390	8	of	of	ADP
ma-236	390	9	specific	specific	ADJ
ma-236	390	10	convex	convex	NOUN
ma-236	390	11	functions	function	NOUN
ma-236	390	12	and	and	CCONJ
ma-236	390	13	their	their	PRON
ma-236	390	14	inequalities	inequality	NOUN
ma-236	390	15	using	use	VERB
ma-236	390	16	ourresults	ourresult	NOUN
ma-236	390	17	are	be	AUX
ma-236	390	18	given	give	VERB
ma-236	390	19	in	in	ADP
ma-236	390	20	the	the	DET
ma-236	390	21	section	section	NOUN
ma-236	390	22	some	some	DET
ma-236	390	23	examples	example	NOUN
ma-236	390	24	and	and	CCONJ
ma-236	390	25	consequences	consequence	NOUN
ma-236	390	26	.	.	PUNCT
ma-236	391	1	plans	plan	NOUN
ma-236	391	2	for	for	ADP
ma-236	391	3	future	future	ADJ
ma-236	391	4	research	research	NOUN
ma-236	391	5	can	can	AUX
ma-236	391	6	bereflected	bereflecte	VERB
ma-236	391	7	in	in	ADP
ma-236	391	8	the	the	DET
ma-236	391	9	fact	fact	NOUN
ma-236	391	10	that	that	SCONJ
ma-236	391	11	the	the	DET
ma-236	391	12	obtained	obtain	VERB
ma-236	391	13	inequalities	inequality	NOUN
ma-236	391	14	in	in	ADP
ma-236	391	15	this	this	DET
ma-236	391	16	work	work	NOUN
ma-236	391	17	can	can	AUX
ma-236	391	18	be	be	AUX
ma-236	391	19	sharpened	sharpen	VERB
ma-236	391	20	or	or	CCONJ
ma-236	391	21	generalized	generalized	ADJ
ma-236	391	22	byusing	byuse	VERB
ma-236	391	23	other	other	ADJ
ma-236	391	24	methods	method	NOUN
ma-236	391	25	.	.	PUNCT
ma-236	392	1	an	an	DET
ma-236	392	2	interesting	interesting	ADJ
ma-236	392	3	perspective	perspective	NOUN
ma-236	392	4	can	can	AUX
ma-236	392	5	be	be	AUX
ma-236	392	6	seen	see	VERB
ma-236	392	7	in	in	ADP
ma-236	392	8	incorporating	incorporate	VERB
ma-236	392	9	other	other	ADJ
ma-236	392	10	techniques	technique	NOUN
ma-236	392	11	forhilbert	forhilbert	ADJ
ma-236	392	12	space	space	NOUN
ma-236	392	13	inequalities	inequality	NOUN
ma-236	392	14	with	with	ADP
ma-236	392	15	the	the	DET
ma-236	392	16	techniques	technique	NOUN
ma-236	392	17	shown	show	VERB
ma-236	392	18	in	in	ADP
ma-236	392	19	this	this	DET
ma-236	392	20	paper	paper	NOUN
ma-236	392	21	.	.	PUNCT
ma-236	393	1	one	one	NUM
ma-236	393	2	direction	direction	NOUN
ma-236	393	3	is	be	AUX
ma-236	393	4	the	the	DET
ma-236	393	5	techniqueof	techniqueof	NOUN
ma-236	393	6	the	the	DET
ma-236	393	7	mond	mond	NOUN
ma-236	393	8	-	-	PUNCT
ma-236	393	9	pecaric	pecaric	ADJ
ma-236	393	10	inequality	inequality	NOUN
ma-236	393	11	,	,	PUNCT
ma-236	393	12	on	on	ADP
ma-236	393	13	which	which	PRON
ma-236	393	14	we	we	PRON
ma-236	393	15	will	will	AUX
ma-236	393	16	work	work	VERB
ma-236	393	17	on	on	ADP
ma-236	393	18	.	.	PUNCT
ma-236	394	1	references	reference	NOUN
ma-236	394	2	[	[	X
ma-236	394	3	1	1	NUM
ma-236	394	4	]	]	PUNCT
ma-236	394	5	w.	w.	PROPN
ma-236	394	6	afzal	afzal	PROPN
ma-236	394	7	,	,	PUNCT
ma-236	394	8	m.	m.	NOUN
ma-236	394	9	abbas	abbas	PROPN
ma-236	394	10	,	,	PUNCT
ma-236	394	11	j.e	j.e	PROPN
ma-236	394	12	.	.	PROPN
ma-236	394	13	macías	macías	PROPN
ma-236	394	14	-	-	PUNCT
ma-236	394	15	díaz	díaz	NOUN
ma-236	394	16	,	,	PUNCT
ma-236	394	17	s.	s.	PROPN
ma-236	394	18	treanţă	treanţă	PROPN
ma-236	394	19	.	.	PUNCT
ma-236	395	1	some	some	DET
ma-236	395	2	h	h	NOUN
ma-236	395	3	-	-	PUNCT
ma-236	395	4	godunova	godunova	ADJ
ma-236	395	5	–	–	PUNCT
ma-236	395	6	levin	levin	PROPN
ma-236	395	7	function	function	PROPN
ma-236	395	8	inequalities	inequality	NOUN
ma-236	395	9	using	use	VERB
ma-236	395	10	center	center	ADJ
ma-236	395	11	radius(cr	radius(cr	NOUN
ma-236	395	12	)	)	PUNCT
ma-236	395	13	order	order	NOUN
ma-236	395	14	relation	relation	NOUN
ma-236	395	15	.	.	PUNCT
ma-236	396	1	fractal	fractal	ADJ
ma-236	396	2	fract	fract	NOUN
ma-236	396	3	.	.	PUNCT
ma-236	397	1	6	6	NUM
ma-236	397	2	(	(	PUNCT
ma-236	397	3	2022	2022	NUM
ma-236	397	4	)	)	PUNCT
ma-236	397	5	518	518	NUM
ma-236	397	6	.	.	PUNCT
ma-236	397	7	https://doi.org/10.3390/fractalfract6090518.[2	https://doi.org/10.3390/fractalfract6090518.[2	PROPN
ma-236	397	8	]	]	PUNCT
ma-236	397	9	w.	w.	PROPN
ma-236	397	10	afzal	afzal	PROPN
ma-236	397	11	,	,	PUNCT
ma-236	397	12	a.a	a.a	PROPN
ma-236	397	13	.	.	PROPN
ma-236	397	14	lupas	lupas	PROPN
ma-236	397	15	,	,	PUNCT
ma-236	397	16	k.	k.	PROPN
ma-236	397	17	shabbir	shabbir	PROPN
ma-236	397	18	.	.	PUNCT
ma-236	398	1	hermite	hermite	PROPN
ma-236	398	2	–	–	PUNCT
ma-236	398	3	hadamard	hadamard	PROPN
ma-236	398	4	and	and	CCONJ
ma-236	398	5	jensen	jensen	PROPN
ma-236	398	6	-	-	PUNCT
ma-236	398	7	type	type	NOUN
ma-236	398	8	inequalities	inequality	NOUN
ma-236	398	9	for	for	ADP
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ma-236	398	11	(	(	PUNCT
ma-236	398	12	h1,h2)-godunova	h1,h2)-godunova	ADJ
ma-236	398	13	–	–	PUNCT
ma-236	398	14	levin	levin	NOUN
ma-236	398	15	interval	interval	NOUN
ma-236	398	16	-	-	PUNCT
ma-236	398	17	valued	value	VERB
ma-236	398	18	functions	function	NOUN
ma-236	398	19	.	.	PUNCT
ma-236	399	1	mathematics	mathematic	NOUN
ma-236	399	2	,	,	PUNCT
ma-236	399	3	10	10	NUM
ma-236	399	4	(	(	PUNCT
ma-236	399	5	2022	2022	NUM
ma-236	399	6	)	)	PUNCT
ma-236	399	7	2970	2970	NUM
ma-236	399	8	.	.	PUNCT
ma-236	400	1	https://doi.org/10.3390/	https://doi.org/10.3390/	PROPN
ma-236	400	2	math10162970.[3	math10162970.[3	PROPN
ma-236	400	3	]	]	X
ma-236	400	4	w.	w.	PROPN
ma-236	400	5	afzal	afzal	PROPN
ma-236	400	6	,	,	PUNCT
ma-236	400	7	k.	k.	PROPN
ma-236	400	8	shabbir	shabbir	PROPN
ma-236	400	9	,	,	PUNCT
ma-236	400	10	s.	s.	PROPN
ma-236	400	11	treanţă	treanţă	PROPN
ma-236	400	12	,	,	PUNCT
ma-236	400	13	k.	k.	PROPN
ma-236	400	14	nonlaopon	nonlaopon	PROPN
ma-236	400	15	.	.	PUNCT
ma-236	401	1	jensen	jensen	PROPN
ma-236	401	2	and	and	CCONJ
ma-236	401	3	hermite	hermite	PROPN
ma-236	401	4	-	-	PUNCT
ma-236	401	5	hadamard	hadamard	ADJ
ma-236	401	6	type	type	NOUN
ma-236	401	7	inclusions	inclusion	NOUN
ma-236	401	8	for	for	ADP
ma-236	401	9	harmonicalh	harmonicalh	NOUN
ma-236	401	10	-	-	PUNCT
ma-236	401	11	godunova	godunova	PROPN
ma-236	401	12	-	-	PUNCT
ma-236	401	13	levin	levin	PROPN
ma-236	401	14	functions	function	NOUN
ma-236	401	15	.	.	PUNCT
ma-236	402	1	aims	aim	VERB
ma-236	402	2	math	math	NOUN
ma-236	402	3	.	.	PUNCT
ma-236	403	1	8	8	NUM
ma-236	403	2	(	(	PUNCT
ma-236	403	3	2023	2023	NUM
ma-236	403	4	)	)	PUNCT
ma-236	403	5	3303	3303	NUM
ma-236	403	6	-	-	SYM
ma-236	403	7	3321	3321	NUM
ma-236	403	8	.	.	PUNCT
ma-236	404	1	https://doi.org/10.3934/math.2023170.[4	https://doi.org/10.3934/math.2023170.[4	PROPN
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ma-236	404	3	w.	w.	PROPN
ma-236	404	4	afzal	afzal	PROPN
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ma-236	405	7	-	-	PUNCT
ma-236	405	8	hadamard	hadamard	ADJ
ma-236	405	9	inequalities	inequality	NOUN
ma-236	405	10	for	for	ADP
ma-236	405	11	interval	interval	NOUN
ma-236	405	12	-	-	PUNCT
ma-236	405	13	valued	value	VERB
ma-236	405	14	(	(	PUNCT
ma-236	405	15	h1	h1	PROPN
ma-236	405	16	,	,	PUNCT
ma-236	405	17	h2)godunova	h2)godunova	PROPN
ma-236	405	18	-	-	PUNCT
ma-236	405	19	levin	levin	PROPN
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ma-236	405	21	.	.	PUNCT
ma-236	406	1	aims	aim	VERB
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ma-236	406	3	.	.	PUNCT
ma-236	407	1	7	7	NUM
ma-236	407	2	(	(	PUNCT
ma-236	407	3	2022	2022	NUM
ma-236	407	4	)	)	PUNCT
ma-236	407	5	19372	19372	NUM
ma-236	407	6	-	-	SYM
ma-236	407	7	19387	19387	NUM
ma-236	407	8	.	.	PUNCT
ma-236	408	1	https://doi.org/10.3934/math	https://doi.org/10.3934/math	PROPN
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ma-236	409	2	]	]	X
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ma-236	409	5	,	,	PUNCT
ma-236	409	6	w.	w.	PROPN
ma-236	409	7	nazeer	nazeer	PROPN
ma-236	409	8	,	,	PUNCT
ma-236	409	9	t.	t.	NOUN
ma-236	409	10	botmart	botmart	NOUN
ma-236	409	11	,	,	PUNCT
ma-236	409	12	s.	s.	PROPN
ma-236	409	13	treanţă	treanţă	PROPN
ma-236	409	14	.	.	PUNCT
ma-236	410	1	some	some	DET
ma-236	410	2	properties	property	NOUN
ma-236	410	3	and	and	CCONJ
ma-236	410	4	inequalities	inequality	NOUN
ma-236	410	5	for	for	ADP
ma-236	410	6	generalized	generalized	ADJ
ma-236	410	7	class	class	NOUN
ma-236	410	8	of	of	ADP
ma-236	410	9	harmonicalgodunova	harmonicalgodunova	PROPN
ma-236	410	10	-	-	PUNCT
ma-236	410	11	levin	levin	PROPN
ma-236	410	12	function	function	PROPN
ma-236	410	13	via	via	ADP
ma-236	410	14	center	center	ADJ
ma-236	410	15	radius	radius	NOUN
ma-236	410	16	order	order	NOUN
ma-236	410	17	relation	relation	NOUN
ma-236	410	18	.	.	PUNCT
ma-236	411	1	aims	aim	VERB
ma-236	411	2	math	math	NOUN
ma-236	411	3	.	.	PUNCT
ma-236	412	1	8	8	NUM
ma-236	412	2	(	(	PUNCT
ma-236	412	3	2023	2023	NUM
ma-236	412	4	)	)	PUNCT
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ma-236	412	6	-	-	SYM
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ma-236	412	8	.	.	PUNCT
ma-236	413	1	https://doi.org/10	https://doi.org/10	PROPN
ma-236	413	2	.	.	PUNCT
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ma-236	414	2	/	/	SYM
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ma-236	414	4	]	]	PUNCT
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ma-236	414	7	,	,	PUNCT
ma-236	414	8	f.	f.	PROPN
ma-236	414	9	hansen	hansen	PROPN
ma-236	414	10	,	,	PUNCT
ma-236	414	11	jensenís	jensenís	NOUN
ma-236	414	12	operator	operator	NOUN
ma-236	414	13	inequality	inequality	NOUN
ma-236	414	14	for	for	ADP
ma-236	414	15	functions	function	NOUN
ma-236	414	16	of	of	ADP
ma-236	414	17	several	several	ADJ
ma-236	414	18	variables	variable	NOUN
ma-236	414	19	,	,	PUNCT
ma-236	414	20	proc	proc	NOUN
ma-236	414	21	.	.	PUNCT
ma-236	415	1	amer	amer	PROPN
ma-236	415	2	.	.	PUNCT
ma-236	415	3	math	math	PROPN
ma-236	415	4	.	.	PUNCT
ma-236	416	1	soc	soc	PROPN
ma-236	416	2	.	.	PUNCT
ma-236	417	1	128(2000	128(2000	NUM
ma-236	417	2	)	)	PUNCT
ma-236	417	3	2075	2075	NUM
ma-236	417	4	-	-	SYM
ma-236	417	5	2084.[7	2084.[7	NUM
ma-236	417	6	]	]	X
ma-236	417	7	s.i	s.i	PROPN
ma-236	417	8	butt	butt	PROPN
ma-236	417	9	,	,	PUNCT
ma-236	417	10	m.	m.	NOUN
ma-236	417	11	tariq	tariq	PROPN
ma-236	417	12	,	,	PUNCT
ma-236	417	13	a.	a.	PROPN
ma-236	417	14	aslam	aslam	PROPN
ma-236	417	15	,	,	PUNCT
ma-236	417	16	h.	h.	PROPN
ma-236	417	17	ahmad	ahmad	PROPN
ma-236	417	18	,	,	PUNCT
ma-236	417	19	t.a	t.a	PROPN
ma-236	417	20	.	.	PROPN
ma-236	417	21	nofal	nofal	PROPN
ma-236	417	22	.	.	PUNCT
ma-236	418	1	hermite	hermite	PROPN
ma-236	418	2	–	–	PUNCT
ma-236	418	3	hadamard	hadamard	ADJ
ma-236	418	4	type	type	NOUN
ma-236	418	5	inequalities	inequality	NOUN
ma-236	418	6	via	via	ADP
ma-236	418	7	generalized	generalized	ADJ
ma-236	418	8	harmonicexponential	harmonicexponential	ADJ
ma-236	418	9	convexity	convexity	NOUN
ma-236	418	10	and	and	CCONJ
ma-236	418	11	applications	application	NOUN
ma-236	418	12	.	.	PUNCT
ma-236	419	1	j.	j.	PROPN
ma-236	419	2	funct	funct	PROPN
ma-236	419	3	.	.	PUNCT
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ma-236	420	2	,	,	PUNCT
ma-236	420	3	2021	2021	NUM
ma-236	420	4	(	(	PUNCT
ma-236	420	5	2021	2021	NUM
ma-236	420	6	)	)	PUNCT
ma-236	420	7	5533491	5533491	NUM
ma-236	420	8	.	.	PUNCT
ma-236	421	1	https://doi.org/10.1155/2021/	https://doi.org/10.1155/2021/	ADJ
ma-236	421	2	5533491	5533491	NUM
ma-236	421	3	.	.	PUNCT
ma-236	422	1	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	422	2	https://doi.org/10.3390/fractalfract6090518	https://doi.org/10.3390/fractalfract6090518	PROPN
ma-236	422	3	https://doi.org/10.3390/math10162970	https://doi.org/10.3390/math10162970	PROPN
ma-236	422	4	https://doi.org/10.3390/math10162970	https://doi.org/10.3390/math10162970	PROPN
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ma-236	422	6	https://doi.org/10.3934/math.20221064	https://doi.org/10.3934/math.20221064	ADP
ma-236	422	7	https://doi.org/10.3934/math.20221064	https://doi.org/10.3934/math.20221064	NOUN
ma-236	422	8	https://doi.org/10.3934/math.2023087	https://doi.org/10.3934/math.2023087	NOUN
ma-236	422	9	https://doi.org/10.3934/math.2023087	https://doi.org/10.3934/math.2023087	NOUN
ma-236	422	10	https://doi.org/10.1155/2021/5533491	https://doi.org/10.1155/2021/5533491	PROPN
ma-236	422	11	https://doi.org/10.1155/2021/5533491	https://doi.org/10.1155/2021/5533491	PROPN
ma-236	422	12	eur	eur	PROPN
ma-236	422	13	.	.	PUNCT
ma-236	423	1	j.	j.	PROPN
ma-236	423	2	math	math	PROPN
ma-236	423	3	.	.	PUNCT
ma-236	424	1	anal	anal	PROPN
ma-236	424	2	.	.	PUNCT
ma-236	425	1	10.28924	10.28924	NUM
ma-236	425	2	/	/	SYM
ma-236	425	3	ada	ada	PROPN
ma-236	425	4	/	/	SYM
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ma-236	425	6	12	12	NUM
ma-236	426	1	[	[	SYM
ma-236	426	2	8	8	NUM
ma-236	426	3	]	]	PUNCT
ma-236	426	4	a.	a.	NOUN
ma-236	426	5	chandola	chandola	PROPN
ma-236	426	6	,	,	PUNCT
ma-236	426	7	r.	r.	PROPN
ma-236	426	8	agarwal	agarwal	PROPN
ma-236	426	9	,	,	PUNCT
ma-236	426	10	m.r	m.r	PROPN
ma-236	426	11	.	.	PROPN
ma-236	426	12	pandey	pandey	PROPN
ma-236	426	13	.	.	PUNCT
ma-236	427	1	some	some	DET
ma-236	427	2	new	new	ADJ
ma-236	427	3	hermite	hermite	ADJ
ma-236	427	4	–	–	PUNCT
ma-236	427	5	hadamard	hadamard	ADJ
ma-236	427	6	,	,	PUNCT
ma-236	427	7	hermite	hermite	ADJ
ma-236	427	8	–	–	PUNCT
ma-236	427	9	hadamard	hadamard	NOUN
ma-236	427	10	fejer	fejer	ADJ
ma-236	427	11	and	and	CCONJ
ma-236	427	12	weightedhardy	weightedhardy	ADJ
ma-236	427	13	type	type	NOUN
ma-236	427	14	inequalities	inequality	NOUN
ma-236	427	15	involving	involve	VERB
ma-236	427	16	(	(	PUNCT
ma-236	427	17	k	k	X
ma-236	427	18	-	-	ADJ
ma-236	427	19	p	p	ADJ
ma-236	427	20	)	)	PUNCT
ma-236	427	21	riemann	riemann	PROPN
ma-236	427	22	–	–	PUNCT
ma-236	427	23	liouville	liouville	VERB
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ma-236	427	25	integral	integral	ADJ
ma-236	427	26	operator	operator	NOUN
ma-236	427	27	,	,	PUNCT
ma-236	427	28	appl	appl	PROPN
ma-236	427	29	.	.	PROPN
ma-236	427	30	math	math	PROPN
ma-236	427	31	.	.	PUNCT
ma-236	428	1	inf	inf	PROPN
ma-236	428	2	.	.	PUNCT
ma-236	429	1	sci	sci	PROPN
ma-236	429	2	.	.	PROPN
ma-236	430	1	16	16	NUM
ma-236	430	2	(	(	PUNCT
ma-236	430	3	2022)287–297	2022)287–297	NUM
ma-236	430	4	.	.	PUNCT
ma-236	431	1	https://doi.org/10.18576/amis/160216.[9	https://doi.org/10.18576/amis/160216.[9	NOUN
ma-236	431	2	]	]	PUNCT
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ma-236	431	7	.	.	PROPN
ma-236	431	8	katugampola	katugampola	PROPN
ma-236	431	9	.	.	PUNCT
ma-236	432	1	hermite	hermite	PROPN
ma-236	432	2	–	–	PUNCT
ma-236	432	3	hadamard	hadamard	ADJ
ma-236	432	4	and	and	CCONJ
ma-236	432	5	hermite	hermite	ADJ
ma-236	432	6	–	–	PUNCT
ma-236	432	7	hadamard	hadamard	ADJ
ma-236	432	8	–	–	PUNCT
ma-236	432	9	fejer	fejer	ADJ
ma-236	432	10	type	type	NOUN
ma-236	432	11	inequalities	inequality	NOUN
ma-236	432	12	for	for	ADP
ma-236	432	13	generalizedfractional	generalizedfractional	ADJ
ma-236	432	14	integrals	integral	NOUN
ma-236	432	15	.	.	PUNCT
ma-236	433	1	j.	j.	PROPN
ma-236	433	2	math	math	PROPN
ma-236	433	3	.	.	PUNCT
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ma-236	434	2	.	.	PUNCT
ma-236	435	1	appl	appl	PROPN
ma-236	435	2	.	.	PROPN
ma-236	436	1	446	446	NUM
ma-236	436	2	(	(	PUNCT
ma-236	436	3	2017	2017	NUM
ma-236	436	4	)	)	PUNCT
ma-236	436	5	1274–1291	1274–1291	NUM
ma-236	436	6	.	.	PUNCT
ma-236	437	1	https://doi.org/10.1016/j.jmaa.2016.09	https://doi.org/10.1016/j.jmaa.2016.09	PROPN
ma-236	437	2	.	.	PUNCT
ma-236	438	1	018.[10	018.[10	NUM
ma-236	438	2	]	]	X
ma-236	438	3	s.s	s.s	PROPN
ma-236	438	4	.	.	PROPN
ma-236	438	5	dragomir	dragomir	PROPN
ma-236	438	6	.	.	PROPN
ma-236	439	1	inequalities	inequality	NOUN
ma-236	439	2	for	for	ADP
ma-236	439	3	normal	normal	ADJ
ma-236	439	4	operators	operator	NOUN
ma-236	439	5	in	in	ADP
ma-236	439	6	hilbert	hilbert	PROPN
ma-236	439	7	spaces	space	NOUN
ma-236	439	8	,	,	PUNCT
ma-236	439	9	appl	appl	PROPN
ma-236	439	10	.	.	PROPN
ma-236	440	1	anal	anal	PROPN
ma-236	440	2	.	.	PUNCT
ma-236	441	1	discr	discr	PROPN
ma-236	441	2	.	.	PUNCT
ma-236	442	1	math	math	NOUN
ma-236	442	2	.	.	PUNCT
ma-236	443	1	1	1	NUM
ma-236	443	2	(	(	PUNCT
ma-236	443	3	2007	2007	NUM
ma-236	443	4	)	)	PUNCT
ma-236	444	1	92–110	92–110	NUM
ma-236	444	2	.	.	PUNCT
ma-236	445	1	https://doi.org/10.2298/aadm0701092d.[11	https://doi.org/10.2298/aadm0701092d.[11	ADP
ma-236	445	2	]	]	X
ma-236	445	3	s.s	s.s	PROPN
ma-236	445	4	.	.	PROPN
ma-236	445	5	dragomir	dragomir	PROPN
ma-236	445	6	,	,	PUNCT
ma-236	445	7	the	the	DET
ma-236	445	8	hermite	hermite	PROPN
ma-236	445	9	-	-	PUNCT
ma-236	445	10	hadamard	hadamard	ADJ
ma-236	445	11	type	type	NOUN
ma-236	445	12	inequalities	inequality	NOUN
ma-236	445	13	for	for	ADP
ma-236	445	14	operator	operator	NOUN
ma-236	445	15	convex	convex	NOUN
ma-236	445	16	functions	function	NOUN
ma-236	445	17	,	,	PUNCT
ma-236	445	18	appl	appl	PROPN
ma-236	445	19	.	.	PROPN
ma-236	445	20	math	math	PROPN
ma-236	445	21	.	.	PUNCT
ma-236	446	1	comp	comp	NOUN
ma-236	446	2	.	.	PUNCT
ma-236	447	1	218(2011	218(2011	NUM
ma-236	447	2	)	)	PUNCT
ma-236	447	3	766	766	NUM
ma-236	447	4	-	-	SYM
ma-236	447	5	772.[12	772.[12	PROPN
ma-236	447	6	]	]	X
ma-236	447	7	s.s	s.s	PROPN
ma-236	447	8	dragomir	dragomir	ADJ
ma-236	447	9	,	,	PUNCT
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ma-236	447	11	norm	norm	NOUN
ma-236	447	12	inequalities	inequality	NOUN
ma-236	447	13	for	for	ADP
ma-236	447	14	taylor	taylor	PROPN
ma-236	447	15	’s	’s	PART
ma-236	447	16	expansions	expansion	NOUN
ma-236	447	17	of	of	ADP
ma-236	447	18	functions	function	NOUN
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ma-236	447	21	operators	operator	NOUN
ma-236	447	22	in	in	ADP
ma-236	447	23	hilbertspaces	hilbertspace	NOUN
ma-236	447	24	,	,	PUNCT
ma-236	447	25	researchgate	researchgate	NOUN
ma-236	447	26	,	,	PUNCT
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ma-236	447	30	s.s	s.s	PROPN
ma-236	447	31	dragomir	dragomir	PROPN
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ma-236	447	33	an	an	DET
ma-236	447	34	ostrowski	ostrowski	ADJ
ma-236	447	35	type	type	NOUN
ma-236	447	36	tensorial	tensorial	ADJ
ma-236	447	37	norm	norm	NOUN
ma-236	447	38	inequality	inequality	NOUN
ma-236	447	39	for	for	ADP
ma-236	447	40	continuous	continuous	ADJ
ma-236	447	41	functions	function	NOUN
ma-236	447	42	of	of	ADP
ma-236	447	43	selfadjoint	selfadjoint	NOUN
ma-236	447	44	operators	operator	NOUN
ma-236	447	45	inhilbert	inhilbert	PROPN
ma-236	447	46	spaces	space	NOUN
ma-236	447	47	,	,	PUNCT
ma-236	447	48	researchgate	researchgate	NOUN
ma-236	447	49	,	,	PUNCT
ma-236	447	50	november	november	PROPN
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ma-236	447	52	]	]	X
ma-236	447	53	h.	h.	PROPN
ma-236	447	54	guo	guo	PROPN
ma-236	447	55	,	,	PUNCT
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ma-236	447	57	are	be	AUX
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ma-236	447	60	?	?	PUNCT
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ma-236	447	65	2021	2021	NUM
ma-236	447	66	.	.	PUNCT
ma-236	448	1	https://doi.org/10.1142/12388.[15	https://doi.org/10.1142/12388.[15	PROPN
ma-236	448	2	]	]	PUNCT
ma-236	448	3	f.	f.	PROPN
ma-236	448	4	hezenci	hezenci	PROPN
ma-236	448	5	,	,	PUNCT
ma-236	448	6	h.	h.	PROPN
ma-236	448	7	budak	budak	PROPN
ma-236	448	8	,	,	PUNCT
ma-236	448	9	h.	h.	PROPN
ma-236	448	10	kara	kara	PROPN
ma-236	448	11	.	.	PUNCT
ma-236	449	1	new	new	ADJ
ma-236	449	2	version	version	NOUN
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ma-236	449	4	fractional	fractional	PROPN
ma-236	449	5	simpson	simpson	PROPN
ma-236	449	6	type	type	PROPN
ma-236	449	7	inequalities	inequality	NOUN
ma-236	449	8	for	for	ADP
ma-236	449	9	twice	twice	ADV
ma-236	449	10	differentiable	differentiable	ADJ
ma-236	449	11	functions.adv	functions.adv	PROPN
ma-236	449	12	.	.	PROPN
ma-236	449	13	diff	diff	PROPN
ma-236	449	14	.	.	PUNCT
ma-236	450	1	equ	equ	PROPN
ma-236	450	2	.	.	PROPN
ma-236	450	3	2021	2021	NUM
ma-236	450	4	(	(	PUNCT
ma-236	450	5	2021	2021	NUM
ma-236	450	6	)	)	PUNCT
ma-236	450	7	460	460	NUM
ma-236	450	8	.	.	PUNCT
ma-236	451	1	https://doi.org/10.1186/s13662-021-03615-2.[16	https://doi.org/10.1186/s13662-021-03615-2.[16	PROPN
ma-236	451	2	]	]	PUNCT
ma-236	451	3	a.	a.	NOUN
ma-236	451	4	koranyi	koranyi	PROPN
ma-236	451	5	.	.	PUNCT
ma-236	452	1	on	on	ADP
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ma-236	452	5	analytic	analytic	ADJ
ma-236	452	6	functions	function	NOUN
ma-236	452	7	of	of	ADP
ma-236	452	8	several	several	ADJ
ma-236	452	9	variables	variable	NOUN
ma-236	452	10	.	.	PUNCT
ma-236	453	1	trans	trans	PROPN
ma-236	453	2	.	.	PUNCT
ma-236	454	1	amer	amer	PROPN
ma-236	454	2	.	.	PUNCT
ma-236	454	3	math	math	PROPN
ma-236	454	4	.	.	PUNCT
ma-236	455	1	soc	soc	PROPN
ma-236	455	2	.	.	PUNCT
ma-236	456	1	101	101	NUM
ma-236	456	2	(	(	PUNCT
ma-236	456	3	1961	1961	NUM
ma-236	456	4	)	)	PUNCT
ma-236	456	5	520	520	NUM
ma-236	456	6	-	-	SYM
ma-236	456	7	554.[17	554.[17	PROPN
ma-236	456	8	]	]	X
ma-236	456	9	d.s	d.s	PROPN
ma-236	456	10	.	.	PROPN
ma-236	456	11	mitrinović	mitrinović	PROPN
ma-236	456	12	,	,	PUNCT
ma-236	456	13	analytic	analytic	ADJ
ma-236	456	14	inequalities	inequality	NOUN
ma-236	456	15	,	,	PUNCT
ma-236	456	16	springer	springer	NOUN
ma-236	456	17	-	-	PUNCT
ma-236	456	18	verlag	verlag	PROPN
ma-236	456	19	,	,	PUNCT
ma-236	456	20	berlin	berlin	PROPN
ma-236	456	21	,	,	PUNCT
ma-236	456	22	1970.[18	1970.[18	NUM
ma-236	456	23	]	]	PUNCT
ma-236	456	24	j.	j.	PROPN
ma-236	456	25	pečarić	pečarić	PROPN
ma-236	456	26	,	,	PUNCT
ma-236	456	27	f.	f.	PROPN
ma-236	456	28	proschan	proschan	PROPN
ma-236	456	29	,	,	PUNCT
ma-236	456	30	y.	y.	PROPN
ma-236	456	31	tong	tong	PROPN
ma-236	456	32	,	,	PUNCT
ma-236	456	33	convex	convex	NOUN
ma-236	456	34	functions	function	NOUN
ma-236	456	35	,	,	PUNCT
ma-236	456	36	partial	partial	ADJ
ma-236	456	37	orderings	ordering	NOUN
ma-236	456	38	,	,	PUNCT
ma-236	456	39	and	and	CCONJ
ma-236	456	40	statistical	statistical	ADJ
ma-236	456	41	applications	application	NOUN
ma-236	456	42	,	,	PUNCT
ma-236	456	43	academic	academic	ADJ
ma-236	456	44	press,1992.[19	press,1992.[19	PROPN
ma-236	456	45	]	]	PUNCT
ma-236	456	46	m.z	m.z	PROPN
ma-236	456	47	.	.	PROPN
ma-236	456	48	sarikaya	sarikaya	PROPN
ma-236	456	49	,	,	PUNCT
ma-236	456	50	e.	e.	PROPN
ma-236	456	51	set	set	PROPN
ma-236	456	52	,	,	PUNCT
ma-236	456	53	m.e	m.e	PROPN
ma-236	456	54	.	.	PROPN
ma-236	456	55	özdemir	özdemir	PROPN
ma-236	456	56	,	,	PUNCT
ma-236	456	57	on	on	ADP
ma-236	456	58	new	new	ADJ
ma-236	456	59	inequalities	inequality	NOUN
ma-236	456	60	of	of	ADP
ma-236	456	61	simpson	simpson	PROPN
ma-236	456	62	’s	’s	PART
ma-236	456	63	type	type	NOUN
ma-236	456	64	for	for	ADP
ma-236	456	65	convex	convex	NOUN
ma-236	456	66	functions	function	NOUN
ma-236	456	67	,	,	PUNCT
ma-236	456	68	rgmia	rgmia	NOUN
ma-236	456	69	res	re	NOUN
ma-236	456	70	.	.	PUNCT
ma-236	457	1	rep.coll	rep.coll	PROPN
ma-236	457	2	.	.	PROPN
ma-236	457	3	13	13	NUM
ma-236	457	4	(	(	PUNCT
ma-236	457	5	2010	2010	NUM
ma-236	457	6	)	)	PUNCT
ma-236	458	1	2.[20	2.[20	NUM
ma-236	458	2	]	]	X
ma-236	458	3	y.	y.	PROPN
ma-236	458	4	shuang	shuang	PROPN
ma-236	458	5	,	,	PUNCT
ma-236	458	6	y.	y.	PROPN
ma-236	458	7	wang	wang	PROPN
ma-236	458	8	,	,	PUNCT
ma-236	458	9	f.	f.	PROPN
ma-236	458	10	qi	qi	PROPN
ma-236	458	11	,	,	PUNCT
ma-236	458	12	integral	integral	ADJ
ma-236	458	13	inequalities	inequality	NOUN
ma-236	458	14	of	of	ADP
ma-236	458	15	simpson	simpson	PROPN
ma-236	458	16	’s	’s	PART
ma-236	458	17	type	type	NOUN
ma-236	458	18	for	for	ADP
ma-236	458	19	(	(	PUNCT
ma-236	458	20	α	α	X
ma-236	458	21	,	,	PUNCT
ma-236	458	22	m)-convex	m)-convex	NOUN
ma-236	458	23	functions	function	NOUN
ma-236	458	24	,	,	PUNCT
ma-236	458	25	j.	j.	PROPN
ma-236	458	26	nonlinear	nonlinear	PROPN
ma-236	458	27	sci	sci	PROPN
ma-236	458	28	.	.	PUNCT
ma-236	459	1	appl.9	appl.9	PROPN
ma-236	459	2	(	(	PUNCT
ma-236	459	3	2016	2016	NUM
ma-236	459	4	)	)	PUNCT
ma-236	459	5	6364	6364	NUM
ma-236	459	6	-	-	SYM
ma-236	459	7	6370	6370	NUM
ma-236	459	8	.	.	PUNCT
ma-236	460	1	https://doi.org/10.22436/jnsa.009.12.36.[21	https://doi.org/10.22436/jnsa.009.12.36.[21	X
ma-236	460	2	]	]	PUNCT
ma-236	461	1	v.	v.	CCONJ
ma-236	461	2	stojiljkovic	stojiljkovic	PROPN
ma-236	461	3	,	,	PUNCT
ma-236	461	4	simpson	simpson	PROPN
ma-236	461	5	type	type	PROPN
ma-236	461	6	tensorial	tensorial	ADJ
ma-236	461	7	norm	norm	NOUN
ma-236	461	8	inequalities	inequality	NOUN
ma-236	461	9	for	for	ADP
ma-236	461	10	continuous	continuous	ADJ
ma-236	461	11	functions	function	NOUN
ma-236	461	12	of	of	ADP
ma-236	461	13	´	´	NOUN
ma-236	461	14	selfadjoint	selfadjoint	VERB
ma-236	461	15	operators	operator	NOUN
ma-236	461	16	in	in	ADP
ma-236	461	17	hilbertspaces	hilbertspace	NOUN
ma-236	461	18	,	,	PUNCT
ma-236	461	19	creat	creat	PROPN
ma-236	461	20	.	.	PUNCT
ma-236	462	1	math	math	PROPN
ma-236	462	2	.	.	PUNCT
ma-236	463	1	inf	inf	PROPN
ma-236	463	2	.	.	PUNCT
ma-236	464	1	33	33	NUM
ma-236	464	2	(	(	PUNCT
ma-236	464	3	2024	2024	NUM
ma-236	464	4	)	)	PUNCT
ma-236	464	5	105–117	105–117	NUM
ma-236	464	6	.	.	PUNCT
ma-236	465	1	https://doi.org/10.37193/cmi.2024.01.10.[22	https://doi.org/10.37193/cmi.2024.01.10.[22	PROPN
ma-236	465	2	]	]	PUNCT
ma-236	466	1	v.	v.	CCONJ
ma-236	466	2	stojiljković	stojiljković	PROPN
ma-236	466	3	,	,	PUNCT
ma-236	466	4	r.	r.	PROPN
ma-236	466	5	ramaswamy	ramaswamy	PROPN
ma-236	466	6	,	,	PUNCT
ma-236	466	7	o.a.a	o.a.a	PROPN
ma-236	466	8	.	.	PROPN
ma-236	466	9	abdelnaby	abdelnaby	PROPN
ma-236	466	10	,	,	PUNCT
ma-236	467	1	s.	s.	PROPN
ma-236	467	2	radenović	radenović	PROPN
ma-236	467	3	.	.	PUNCT
ma-236	468	1	some	some	DET
ma-236	468	2	refinements	refinement	NOUN
ma-236	468	3	of	of	ADP
ma-236	468	4	the	the	DET
ma-236	468	5	tensorial	tensorial	ADJ
ma-236	468	6	inequalities	inequality	NOUN
ma-236	468	7	inhilbert	inhilbert	PROPN
ma-236	468	8	spaces	space	NOUN
ma-236	468	9	.	.	PUNCT
ma-236	469	1	symmetry	symmetry	NOUN
ma-236	469	2	,	,	PUNCT
ma-236	469	3	15	15	NUM
ma-236	469	4	(	(	PUNCT
ma-236	469	5	2023	2023	NUM
ma-236	469	6	)	)	PUNCT
ma-236	469	7	925	925	NUM
ma-236	469	8	.	.	PUNCT
ma-236	470	1	https://doi.org/10.3390/sym15040925.[23	https://doi.org/10.3390/sym15040925.[23	PROPN
ma-236	470	2	]	]	PUNCT
ma-236	470	3	v.	v.	CCONJ
ma-236	470	4	stojiljković	stojiljković	PROPN
ma-236	470	5	.	.	PUNCT
ma-236	471	1	hermite	hermite	PROPN
ma-236	471	2	–	–	PUNCT
ma-236	471	3	hadamard	hadamard	ADJ
ma-236	471	4	–	–	PUNCT
ma-236	471	5	type	type	NOUN
ma-236	471	6	fractional	fractional	ADJ
ma-236	471	7	–	–	PUNCT
ma-236	471	8	integral	integral	ADJ
ma-236	471	9	inequalities	inequality	NOUN
ma-236	471	10	for	for	ADP
ma-236	471	11	(	(	PUNCT
ma-236	471	12	p	p	X
ma-236	471	13	,	,	PUNCT
ma-236	471	14	h)-convex	h)-convex	NOUN
ma-236	471	15	fuzzy	fuzzy	ADJ
ma-236	471	16	-	-	PUNCT
ma-236	471	17	interval	interval	NOUN
ma-236	471	18	-	-	PUNCT
ma-236	471	19	valued	value	VERB
ma-236	471	20	map	map	NOUN
ma-236	471	21	-	-	PUNCT
ma-236	471	22	pings	ping	NOUN
ma-236	471	23	,	,	PUNCT
ma-236	471	24	elec	elec	PROPN
ma-236	471	25	.	.	PUNCT
ma-236	472	1	j.	j.	PROPN
ma-236	472	2	math	math	PROPN
ma-236	472	3	.	.	PUNCT
ma-236	473	1	5	5	NUM
ma-236	473	2	(	(	PUNCT
ma-236	473	3	2023	2023	NUM
ma-236	473	4	)	)	PUNCT
ma-236	473	5	18	18	NUM
ma-236	473	6	-	-	SYM
ma-236	473	7	28	28	NUM
ma-236	473	8	.	.	PUNCT
ma-236	474	1	https://doi.org/10.47443/ejm.2023.004.[24	https://doi.org/10.47443/ejm.2023.004.[24	NOUN
ma-236	474	2	]	]	PUNCT
ma-236	474	3	v.	v.	X
ma-236	474	4	stojiljković	stojiljković	PROPN
ma-236	474	5	.	.	PUNCT
ma-236	475	1	twice	twice	DET
ma-236	475	2	differentiable	differentiable	ADJ
ma-236	475	3	ostrowski	ostrowski	ADJ
ma-236	475	4	type	type	NOUN
ma-236	475	5	tensorial	tensorial	ADJ
ma-236	475	6	norm	norm	NOUN
ma-236	475	7	inequality	inequality	NOUN
ma-236	475	8	for	for	ADP
ma-236	475	9	continuous	continuous	ADJ
ma-236	475	10	functions	function	NOUN
ma-236	475	11	of	of	ADP
ma-236	475	12	selfadjointoperators	selfadjointoperator	NOUN
ma-236	475	13	in	in	ADP
ma-236	475	14	hilbert	hilbert	PROPN
ma-236	475	15	spaces	space	NOUN
ma-236	475	16	,	,	PUNCT
ma-236	475	17	elec	elec	PROPN
ma-236	475	18	.	.	PUNCT
ma-236	476	1	j.	j.	PROPN
ma-236	476	2	math	math	PROPN
ma-236	476	3	.	.	PUNCT
ma-236	477	1	anal	anal	PROPN
ma-236	477	2	.	.	PUNCT
ma-236	478	1	appl	appl	PROPN
ma-236	478	2	.	.	PROPN
ma-236	479	1	11	11	NUM
ma-236	479	2	(	(	PUNCT
ma-236	479	3	2023	2023	NUM
ma-236	479	4	)	)	PUNCT
ma-236	479	5	1	1	NUM
ma-236	479	6	-	-	SYM
ma-236	479	7	15	15	NUM
ma-236	479	8	.	.	PUNCT
ma-236	480	1	https://doi.org/10.21608/ejmaa.2023	https://doi.org/10.21608/ejmaa.2023	PROPN
ma-236	480	2	.	.	PUNCT
ma-236	481	1	199881.1014.[25	199881.1014.[25	PROPN
ma-236	481	2	]	]	PUNCT
ma-236	481	3	v.	v.	CCONJ
ma-236	481	4	stojiljković	stojiljković	PROPN
ma-236	481	5	.	.	PUNCT
ma-236	482	1	twice	twice	DET
ma-236	482	2	differentiable	differentiable	ADJ
ma-236	482	3	ostrowski	ostrowski	ADJ
ma-236	482	4	type	type	NOUN
ma-236	482	5	tensorial	tensorial	ADJ
ma-236	482	6	norm	norm	NOUN
ma-236	482	7	inequality	inequality	NOUN
ma-236	482	8	for	for	ADP
ma-236	482	9	continuous	continuous	ADJ
ma-236	482	10	functions	function	NOUN
ma-236	482	11	of	of	ADP
ma-236	482	12	selfadjointoperators	selfadjointoperator	NOUN
ma-236	482	13	in	in	ADP
ma-236	482	14	hilbert	hilbert	PROPN
ma-236	482	15	spaces	space	NOUN
ma-236	482	16	.	.	PUNCT
ma-236	483	1	eur	eur	PROPN
ma-236	483	2	.	.	PUNCT
ma-236	484	1	j.	j.	PROPN
ma-236	484	2	pure	pure	PROPN
ma-236	484	3	appl	appl	PROPN
ma-236	484	4	.	.	PUNCT
ma-236	484	5	math	math	NOUN
ma-236	484	6	.	.	PUNCT
ma-236	485	1	16	16	NUM
ma-236	485	2	(	(	PUNCT
ma-236	485	3	2023	2023	NUM
ma-236	485	4	)	)	PUNCT
ma-236	485	5	1421–1433	1421–1433	NUM
ma-236	485	6	.	.	PUNCT
ma-236	486	1	https://doi.org/10.29020/nybg	https://doi.org/10.29020/nybg	NOUN
ma-236	486	2	.	.	PUNCT
ma-236	487	1	ejpam.v16i3.4843.[26	ejpam.v16i3.4843.[26	NUM
ma-236	487	2	]	]	PUNCT
ma-236	487	3	v.	v.	CCONJ
ma-236	487	4	stojiljković	stojiljković	PROPN
ma-236	487	5	,	,	PUNCT
ma-236	487	6	s.s	s.s	PROPN
ma-236	487	7	.	.	PROPN
ma-236	487	8	dragomir	dragomir	PROPN
ma-236	487	9	.	.	PUNCT
ma-236	488	1	differentiable	differentiable	ADJ
ma-236	488	2	ostrowski	ostrowski	ADJ
ma-236	488	3	type	type	NOUN
ma-236	488	4	tensorial	tensorial	ADJ
ma-236	488	5	norm	norm	NOUN
ma-236	488	6	inequality	inequality	NOUN
ma-236	488	7	for	for	ADP
ma-236	488	8	continuous	continuous	ADJ
ma-236	488	9	functions	function	NOUN
ma-236	488	10	ofselfadjoint	ofselfadjoint	NOUN
ma-236	488	11	operators	operator	NOUN
ma-236	488	12	in	in	ADP
ma-236	488	13	hilbert	hilbert	PROPN
ma-236	488	14	spaces	space	NOUN
ma-236	488	15	.	.	PUNCT
ma-236	489	1	gulf	gulf	PROPN
ma-236	489	2	j.	j.	PROPN
ma-236	489	3	math	math	PROPN
ma-236	489	4	.	.	PUNCT
ma-236	490	1	15	15	NUM
ma-236	490	2	(	(	PUNCT
ma-236	490	3	2023	2023	NUM
ma-236	490	4	)	)	PUNCT
ma-236	490	5	40	40	NUM
ma-236	490	6	-	-	SYM
ma-236	490	7	55	55	NUM
ma-236	490	8	.	.	PUNCT
ma-236	491	1	https://doi.org/10.56947/gjom.v15i2	https://doi.org/10.56947/gjom.v15i2	PROPN
ma-236	491	2	.	.	PUNCT
ma-236	492	1	1247.[27	1247.[27	NUM
ma-236	492	2	]	]	X
ma-236	492	3	v.	v.	CCONJ
ma-236	492	4	stojiljković	stojiljković	PROPN
ma-236	492	5	,	,	PUNCT
ma-236	492	6	n.	n.	PROPN
ma-236	492	7	mirkov	mirkov	PROPN
ma-236	492	8	,	,	PUNCT
ma-236	492	9	s.	s.	PROPN
ma-236	492	10	radenović	radenović	PROPN
ma-236	492	11	.	.	PUNCT
ma-236	493	1	variations	variation	NOUN
ma-236	493	2	in	in	ADP
ma-236	493	3	the	the	DET
ma-236	493	4	tensorial	tensorial	ADJ
ma-236	493	5	trapezoid	trapezoid	ADJ
ma-236	493	6	type	type	NOUN
ma-236	493	7	inequalities	inequality	NOUN
ma-236	493	8	for	for	ADP
ma-236	493	9	convex	convex	ADJ
ma-236	493	10	functionsof	functionsof	VERB
ma-236	493	11	self	self	NOUN
ma-236	493	12	-	-	PUNCT
ma-236	493	13	adjoint	adjoint	NOUN
ma-236	493	14	operators	operator	NOUN
ma-236	493	15	in	in	ADP
ma-236	493	16	hilbert	hilbert	PROPN
ma-236	493	17	spaces	space	NOUN
ma-236	493	18	.	.	PUNCT
ma-236	494	1	symmetry	symmetry	NOUN
ma-236	494	2	,	,	PUNCT
ma-236	494	3	16	16	NUM
ma-236	494	4	(	(	PUNCT
ma-236	494	5	2024	2024	NUM
ma-236	494	6	)	)	PUNCT
ma-236	494	7	121	121	NUM
ma-236	494	8	.	.	PUNCT
ma-236	495	1	https://doi.org/10.3390/sym16010121	https://doi.org/10.3390/sym16010121	PROPN
ma-236	495	2	.	.	PUNCT
ma-236	496	1	https://doi.org/10.28924/ada/ma.4.17	https://doi.org/10.28924/ada/ma.4.17	PROPN
ma-236	496	2	https://doi.org/10.18576/amis/160216	https://doi.org/10.18576/amis/160216	VERB
ma-236	496	3	https://doi.org/10.1016/j.jmaa.2016.09.018	https://doi.org/10.1016/j.jmaa.2016.09.018	PROPN
ma-236	496	4	https://doi.org/10.1016/j.jmaa.2016.09.018	https://doi.org/10.1016/j.jmaa.2016.09.018	PROPN
ma-236	496	5	https://doi.org/10.2298/aadm0701092d	https://doi.org/10.2298/aadm0701092d	PROPN
ma-236	496	6	https://doi.org/10.1142/12388	https://doi.org/10.1142/12388	NOUN
ma-236	496	7	https://doi.org/10.1186/s13662-021-03615-2	https://doi.org/10.1186/s13662-021-03615-2	NUM
ma-236	496	8	https://doi.org/10.22436/jnsa.009.12.36	https://doi.org/10.22436/jnsa.009.12.36	NUM
ma-236	496	9	https://doi.org/10.37193/cmi.2024.01.10	https://doi.org/10.37193/cmi.2024.01.10	ADP
ma-236	496	10	https://doi.org/10.3390/sym15040925	https://doi.org/10.3390/sym15040925	NOUN
ma-236	496	11	https://doi.org/10.47443/ejm.2023.004	https://doi.org/10.47443/ejm.2023.004	PROPN
ma-236	496	12	https://doi.org/10.21608/ejmaa.2023.199881.1014	https://doi.org/10.21608/ejmaa.2023.199881.1014	PROPN
ma-236	496	13	https://doi.org/10.21608/ejmaa.2023.199881.1014	https://doi.org/10.21608/ejmaa.2023.199881.1014	PROPN
ma-236	496	14	https://doi.org/10.29020/nybg.ejpam.v16i3.4843	https://doi.org/10.29020/nybg.ejpam.v16i3.4843	PROPN
ma-236	496	15	https://doi.org/10.29020/nybg.ejpam.v16i3.4843	https://doi.org/10.29020/nybg.ejpam.v16i3.4843	PROPN
ma-236	496	16	https://doi.org/10.56947/gjom.v15i2.1247	https://doi.org/10.56947/gjom.v15i2.1247	PRON
ma-236	496	17	https://doi.org/10.56947/gjom.v15i2.1247	https://doi.org/10.56947/gjom.v15i2.1247	ADV
ma-236	496	18	https://doi.org/10.3390/sym16010121	https://doi.org/10.3390/sym16010121	VERB
ma-236	496	19	1	1	NUM
ma-236	496	20	.	.	PUNCT
ma-236	496	21	introduction	introduction	NOUN
ma-236	496	22	and	and	CCONJ
ma-236	496	23	preliminaries	preliminary	NOUN
ma-236	496	24	2	2	NUM
ma-236	496	25	.	.	X
ma-236	496	26	main	main	ADJ
ma-236	496	27	results	result	NOUN
ma-236	496	28	3	3	NUM
ma-236	496	29	.	.	PUNCT
ma-236	497	1	some	some	DET
ma-236	497	2	examples	example	NOUN
ma-236	497	3	and	and	CCONJ
ma-236	497	4	consequences	consequence	NOUN
ma-236	497	5	4	4	NUM
ma-236	497	6	.	.	PUNCT
ma-236	497	7	conclusion	conclusion	NOUN
ma-236	497	8	references	reference	NOUN