id	sid	tid	token	lemma	pos
ma-254	1	1	2025	2025	NUM
ma-254	1	2	ada	ada	PROPN
ma-254	1	3	academica	academica	PROPN
ma-254	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-254	1	5	.	.	PUNCT
ma-254	2	1	j.	j.	PROPN
ma-254	2	2	math	math	PROPN
ma-254	2	3	.	.	PUNCT
ma-254	3	1	anal	anal	ADJ
ma-254	3	2	.	.	PUNCT
ma-254	4	1	5	5	NUM
ma-254	4	2	(	(	PUNCT
ma-254	4	3	2025	2025	NUM
ma-254	4	4	)	)	PUNCT
ma-254	5	1	3doi	3doi	NOUN
ma-254	5	2	:	:	PUNCT
ma-254	5	3	10.28924	10.28924	NUM
ma-254	5	4	/	/	SYM
ma-254	5	5	ada	ada	PROPN
ma-254	5	6	/	/	SYM
ma-254	5	7	ma.5.3	ma.5.3	PROPN
ma-254	5	8	the	the	DET
ma-254	5	9	rellich	rellich	NOUN
ma-254	5	10	-	-	PUNCT
ma-254	5	11	kondrachov	kondrachov	NOUN
ma-254	5	12	theorem	theorem	NOUN
ma-254	5	13	for	for	ADP
ma-254	5	14	gelfand	gelfand	ADJ
ma-254	5	15	pairs	pair	NOUN
ma-254	5	16	over	over	ADP
ma-254	5	17	hypergroups	hypergroup	NOUN
ma-254	5	18	ky	ky	PROPN
ma-254	5	19	t.	t.	PROPN
ma-254	5	20	bataka1	bataka1	PROPN
ma-254	5	21	,	,	PUNCT
ma-254	5	22	yaogan	yaogan	PROPN
ma-254	5	23	mensah1,2,∗	mensah1,2,∗	PROPN
ma-254	5	24	1department	1department	NUM
ma-254	5	25	of	of	ADP
ma-254	5	26	mathematics	mathematic	NOUN
ma-254	5	27	,	,	PUNCT
ma-254	5	28	university	university	NOUN
ma-254	5	29	of	of	ADP
ma-254	5	30	lomé	lomé	NOUN
ma-254	5	31	,	,	PUNCT
ma-254	5	32	pob	pob	PROPN
ma-254	5	33	1515	1515	NUM
ma-254	5	34	lomé	lomé	NOUN
ma-254	5	35	1,togo	1,togo	NUM
ma-254	5	36	btaka.2005@gmail.com	btaka.2005@gmail.com	X
ma-254	6	1	2international	2international	ADJ
ma-254	6	2	chair	chair	NOUN
ma-254	6	3	in	in	ADP
ma-254	6	4	mathematical	mathematical	ADJ
ma-254	6	5	physics	physics	NOUN
ma-254	6	6	and	and	CCONJ
ma-254	6	7	applications	application	NOUN
ma-254	6	8	(	(	PUNCT
ma-254	6	9	icmpa)-unesco	icmpa)-unesco	PROPN
ma-254	6	10	chair	chair	NOUN
ma-254	6	11	,	,	PUNCT
ma-254	6	12	university	university	NOUN
ma-254	6	13	of	of	ADP
ma-254	6	14	abomey	abomey	NOUN
ma-254	6	15	-	-	PUNCT
ma-254	6	16	calavi	calavi	NOUN
ma-254	6	17	,	,	PUNCT
ma-254	6	18	benin	benin	PROPN
ma-254	6	19	mensahyaogan2@gmailcom	mensahyaogan2@gmailcom	NOUN
ma-254	6	20	∗correspondence	∗correspondence	NOUN
ma-254	6	21	:	:	PUNCT
ma-254	6	22	mensahyaogan2@gmailcom	mensahyaogan2@gmailcom	PROPN
ma-254	6	23	abstract	abstract	NOUN
ma-254	6	24	.	.	PUNCT
ma-254	7	1	embedding	embed	VERB
ma-254	7	2	results	result	NOUN
ma-254	7	3	play	play	VERB
ma-254	7	4	important	important	ADJ
ma-254	7	5	rôles	rôle	NOUN
ma-254	7	6	in	in	ADP
ma-254	7	7	mathematical	mathematical	ADJ
ma-254	7	8	analysis	analysis	NOUN
ma-254	7	9	.	.	PUNCT
ma-254	8	1	this	this	DET
ma-254	8	2	paper	paper	NOUN
ma-254	8	3	addressessome	addressessome	NOUN
ma-254	8	4	embedding	embed	VERB
ma-254	8	5	theorems	theorem	NOUN
ma-254	8	6	in	in	ADP
ma-254	8	7	the	the	DET
ma-254	8	8	context	context	NOUN
ma-254	8	9	of	of	ADP
ma-254	8	10	sobolev	sobolev	NOUN
ma-254	8	11	spaces	space	NOUN
ma-254	8	12	theory	theory	NOUN
ma-254	8	13	on	on	ADP
ma-254	8	14	gelfand	gelfand	ADJ
ma-254	8	15	pairs	pair	NOUN
ma-254	8	16	over	over	ADP
ma-254	8	17	hypergroups.mainly	hypergroups.mainly	ADV
ma-254	8	18	,	,	PUNCT
ma-254	8	19	the	the	DET
ma-254	8	20	analogue	analogue	NOUN
ma-254	8	21	of	of	ADP
ma-254	8	22	the	the	DET
ma-254	8	23	rellich	rellich	NOUN
ma-254	8	24	-	-	PUNCT
ma-254	8	25	kondrachov	kondrachov	NOUN
ma-254	8	26	theorem	theorem	NOUN
ma-254	8	27	is	be	AUX
ma-254	8	28	proved	prove	VERB
ma-254	8	29	.	.	PUNCT
ma-254	9	1	1	1	X
ma-254	9	2	.	.	X
ma-254	9	3	introduction	introduction	NOUN
ma-254	9	4	sobolev	sobolev	NOUN
ma-254	9	5	spaces	space	NOUN
ma-254	9	6	are	be	AUX
ma-254	9	7	well	well	ADV
ma-254	9	8	studied	study	VERB
ma-254	9	9	on	on	ADP
ma-254	9	10	subsets	subset	NOUN
ma-254	9	11	of	of	ADP
ma-254	9	12	rn	rn	PROPN
ma-254	10	1	[	[	X
ma-254	10	2	1	1	NUM
ma-254	10	3	,	,	PUNCT
ma-254	10	4	4	4	NUM
ma-254	10	5	]	]	PUNCT
ma-254	10	6	and	and	CCONJ
ma-254	10	7	on	on	ADP
ma-254	10	8	other	other	ADJ
ma-254	10	9	classical	classical	ADJ
ma-254	10	10	spaces	space	NOUN
ma-254	10	11	such	such	ADJ
ma-254	10	12	asriemannian	asriemannian	ADJ
ma-254	10	13	manifolds	manifold	NOUN
ma-254	11	1	[	[	X
ma-254	11	2	13	13	NUM
ma-254	11	3	,	,	PUNCT
ma-254	11	4	14	14	NUM
ma-254	11	5	]	]	PUNCT
ma-254	11	6	,	,	PUNCT
ma-254	11	7	metric	metric	ADJ
ma-254	11	8	measure	measure	NOUN
ma-254	11	9	spaces	space	VERB
ma-254	11	10	[	[	X
ma-254	11	11	12	12	NUM
ma-254	11	12	]	]	PUNCT
ma-254	11	13	,	,	PUNCT
ma-254	11	14	etc	etc	X
ma-254	11	15	.	.	X
ma-254	11	16	more	more	ADV
ma-254	11	17	recently	recently	ADV
ma-254	11	18	,	,	PUNCT
ma-254	11	19	these	these	DET
ma-254	11	20	studies	study	NOUN
ma-254	11	21	areextended	areextende	VERB
ma-254	11	22	to	to	ADP
ma-254	11	23	other	other	ADJ
ma-254	11	24	topological	topological	ADJ
ma-254	11	25	algebraic	algebraic	ADJ
ma-254	11	26	structures	structure	NOUN
ma-254	11	27	such	such	ADJ
ma-254	11	28	as	as	ADP
ma-254	11	29	topological	topological	ADJ
ma-254	11	30	abelian	abelian	ADJ
ma-254	11	31	groups	group	NOUN
ma-254	11	32	,	,	PUNCT
ma-254	11	33	locally	locally	ADV
ma-254	11	34	com	com	NOUN
ma-254	11	35	-	-	PUNCT
ma-254	11	36	pact	pact	NOUN
ma-254	11	37	groups	group	NOUN
ma-254	11	38	,	,	PUNCT
ma-254	11	39	gelfand	gelfand	ADJ
ma-254	11	40	pairs	pair	NOUN
ma-254	11	41	over	over	ADP
ma-254	11	42	locally	locally	ADV
ma-254	11	43	compact	compact	ADJ
ma-254	11	44	groups	group	NOUN
ma-254	11	45	,	,	PUNCT
ma-254	11	46	locally	locally	ADV
ma-254	11	47	compact	compact	ADJ
ma-254	11	48	commutative	commutative	ADJ
ma-254	11	49	hypergroups	hypergroup	NOUN
ma-254	11	50	,	,	PUNCT
ma-254	11	51	etc	etc	X
ma-254	11	52	.	.	X
ma-254	12	1	more	more	ADV
ma-254	12	2	precisely	precisely	ADV
ma-254	12	3	,	,	PUNCT
ma-254	12	4	in	in	ADP
ma-254	12	5	[	[	PUNCT
ma-254	12	6	10	10	NUM
ma-254	12	7	,	,	PUNCT
ma-254	12	8	11	11	NUM
ma-254	12	9	]	]	PUNCT
ma-254	12	10	,	,	PUNCT
ma-254	12	11	górka	górka	PROPN
ma-254	12	12	et	et	PROPN
ma-254	12	13	al	al	PROPN
ma-254	12	14	.	.	PROPN
ma-254	12	15	constructed	construct	VERB
ma-254	12	16	a	a	DET
ma-254	12	17	class	class	NOUN
ma-254	12	18	of	of	ADP
ma-254	12	19	sobolev	sobolev	NOUN
ma-254	12	20	spaces	space	NOUN
ma-254	12	21	on	on	ADP
ma-254	12	22	hausdorfflocally	hausdorfflocally	ADV
ma-254	12	23	compact	compact	ADJ
ma-254	12	24	abelian	abelian	ADJ
ma-254	12	25	groups	group	NOUN
ma-254	12	26	by	by	ADP
ma-254	12	27	the	the	DET
ma-254	12	28	means	mean	NOUN
ma-254	12	29	of	of	ADP
ma-254	12	30	the	the	DET
ma-254	12	31	fourier	fourier	NOUN
ma-254	12	32	transform	transform	NOUN
ma-254	12	33	.	.	PUNCT
ma-254	13	1	this	this	DET
ma-254	13	2	construction	construction	NOUN
ma-254	13	3	is	be	AUX
ma-254	13	4	gener	gener	NOUN
ma-254	13	5	-	-	PUNCT
ma-254	13	6	alized	alized	ADJ
ma-254	13	7	to	to	PART
ma-254	13	8	gelfand	gelfand	VERB
ma-254	13	9	pairs	pair	NOUN
ma-254	13	10	over	over	ADP
ma-254	13	11	locally	locally	ADV
ma-254	13	12	compact	compact	ADJ
ma-254	13	13	groups	group	NOUN
ma-254	13	14	by	by	ADP
ma-254	13	15	krukowski	krukowski	NOUN
ma-254	14	1	[	[	X
ma-254	14	2	16	16	NUM
ma-254	14	3	]	]	PUNCT
ma-254	14	4	,	,	PUNCT
ma-254	14	5	to	to	ADP
ma-254	14	6	compact	compact	ADJ
ma-254	14	7	groups	group	NOUN
ma-254	14	8	by	by	ADP
ma-254	14	9	kumarand	kumarand	PROPN
ma-254	14	10	kumar	kumar	PROPN
ma-254	15	1	[	[	X
ma-254	15	2	17	17	NUM
ma-254	15	3	]	]	PUNCT
ma-254	15	4	,	,	PUNCT
ma-254	15	5	to	to	PART
ma-254	15	6	noncommutative	noncommutative	VERB
ma-254	15	7	locally	locally	ADV
ma-254	15	8	compact	compact	ADJ
ma-254	15	9	groups	group	NOUN
ma-254	15	10	by	by	ADP
ma-254	15	11	mensah	mensah	PROPN
ma-254	15	12	[	[	X
ma-254	15	13	18	18	NUM
ma-254	15	14	]	]	PUNCT
ma-254	15	15	and	and	CCONJ
ma-254	15	16	to	to	ADP
ma-254	15	17	noncommutativehypergroups	noncommutativehypergroup	NOUN
ma-254	15	18	by	by	ADP
ma-254	15	19	bataka	bataka	PROPN
ma-254	15	20	et	et	PROPN
ma-254	15	21	al	al	PROPN
ma-254	15	22	.	.	PUNCT
ma-254	16	1	[	[	X
ma-254	16	2	2].in	2].in	NUM
ma-254	16	3	sobolev	sobolev	NOUN
ma-254	16	4	spaces	space	NOUN
ma-254	16	5	theory	theory	NOUN
ma-254	16	6	,	,	PUNCT
ma-254	16	7	embedding	embed	VERB
ma-254	16	8	theorems	theorem	NOUN
ma-254	16	9	are	be	AUX
ma-254	16	10	among	among	ADP
ma-254	16	11	the	the	DET
ma-254	16	12	useful	useful	ADJ
ma-254	16	13	results	result	NOUN
ma-254	16	14	that	that	SCONJ
ma-254	16	15	one	one	PRON
ma-254	16	16	may	may	AUX
ma-254	16	17	ex	ex	NOUN
ma-254	16	18	-	-	VERB
ma-254	16	19	pect	pect	ADJ
ma-254	16	20	.	.	PUNCT
ma-254	17	1	they	they	PRON
ma-254	17	2	appear	appear	VERB
ma-254	17	3	as	as	ADP
ma-254	17	4	support	support	NOUN
ma-254	17	5	points	point	NOUN
ma-254	17	6	in	in	ADP
ma-254	17	7	the	the	DET
ma-254	17	8	analysis	analysis	NOUN
ma-254	17	9	of	of	ADP
ma-254	17	10	partial	partial	ADJ
ma-254	17	11	differential	differential	ADJ
ma-254	17	12	equations	equation	NOUN
ma-254	17	13	and	and	CCONJ
ma-254	17	14	integralequations	integralequation	NOUN
ma-254	17	15	.	.	PUNCT
ma-254	18	1	among	among	ADP
ma-254	18	2	such	such	ADJ
ma-254	18	3	embedding	embed	VERB
ma-254	18	4	theorems	theorem	NOUN
ma-254	18	5	is	be	AUX
ma-254	18	6	the	the	DET
ma-254	18	7	rellich	rellich	NOUN
ma-254	18	8	-	-	PUNCT
ma-254	18	9	kondrachov	kondrachov	NOUN
ma-254	18	10	theorem	theorem	NOUN
ma-254	18	11	.	.	PUNCT
ma-254	19	1	it	it	PRON
ma-254	19	2	is	be	AUX
ma-254	19	3	a	a	DET
ma-254	19	4	com	com	NOUN
ma-254	19	5	-	-	PUNCT
ma-254	19	6	pact	pact	NOUN
ma-254	19	7	embedding	embed	VERB
ma-254	19	8	theorem	theorem	NOUN
ma-254	19	9	in	in	ADP
ma-254	19	10	sobolev	sobolev	PROPN
ma-254	19	11	spaces	space	NOUN
ma-254	19	12	theory	theory	NOUN
ma-254	19	13	which	which	PRON
ma-254	19	14	intervenes	intervene	VERB
ma-254	19	15	for	for	ADP
ma-254	19	16	instance	instance	NOUN
ma-254	19	17	in	in	ADP
ma-254	19	18	the	the	DET
ma-254	19	19	proof	proof	NOUN
ma-254	19	20	ofthe	ofthe	PRON
ma-254	19	21	poincaré	poincaré	PROPN
ma-254	19	22	inequality	inequality	PROPN
ma-254	19	23	.	.	PUNCT
ma-254	20	1	the	the	DET
ma-254	20	2	rellich	rellich	NOUN
ma-254	20	3	-	-	PUNCT
ma-254	20	4	kondrachov	kondrachov	NOUN
ma-254	20	5	theorem	theorem	NOUN
ma-254	20	6	took	take	VERB
ma-254	20	7	it	it	PRON
ma-254	20	8	origin	origin	NOUN
ma-254	20	9	in	in	ADP
ma-254	20	10	a	a	DET
ma-254	20	11	special	special	ADJ
ma-254	20	12	result	result	NOUN
ma-254	20	13	by	by	ADP
ma-254	20	14	received	receive	VERB
ma-254	20	15	:	:	PUNCT
ma-254	20	16	3	3	NUM
ma-254	20	17	jul	jul	PROPN
ma-254	20	18	2024	2024	NUM
ma-254	20	19	.	.	PUNCT
ma-254	21	1	key	key	ADJ
ma-254	21	2	words	word	NOUN
ma-254	21	3	and	and	CCONJ
ma-254	21	4	phrases	phrase	NOUN
ma-254	21	5	.	.	PUNCT
ma-254	22	1	hypergroup	hypergroup	PROPN
ma-254	22	2	;	;	PUNCT
ma-254	22	3	sobolev	sobolev	NOUN
ma-254	22	4	space	space	NOUN
ma-254	22	5	;	;	PUNCT
ma-254	22	6	sobolev	sobolev	NOUN
ma-254	22	7	embedding	embed	VERB
ma-254	22	8	theorem	theorem	NOUN
ma-254	22	9	;	;	PUNCT
ma-254	22	10	rellich	rellich	NOUN
ma-254	22	11	-	-	PUNCT
ma-254	22	12	kondrachov	kondrachov	NOUN
ma-254	22	13	theorem.1	theorem.1	PROPN
ma-254	22	14	https://adac.ee	https://adac.ee	PROPN
ma-254	22	15	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	22	16	eur	eur	PROPN
ma-254	22	17	.	.	PUNCT
ma-254	23	1	j.	j.	PROPN
ma-254	23	2	math	math	PROPN
ma-254	23	3	.	.	PUNCT
ma-254	24	1	anal	anal	PROPN
ma-254	24	2	.	.	PUNCT
ma-254	25	1	10.28924	10.28924	NUM
ma-254	25	2	/	/	SYM
ma-254	25	3	ada	ada	PROPN
ma-254	25	4	/	/	SYM
ma-254	25	5	ma.5.3	ma.5.3	PROPN
ma-254	25	6	2rellich	2rellich	PROPN
ma-254	26	1	[	[	X
ma-254	26	2	19	19	NUM
ma-254	26	3	]	]	PUNCT
ma-254	26	4	and	and	CCONJ
ma-254	26	5	the	the	DET
ma-254	26	6	general	general	ADJ
ma-254	26	7	case	case	NOUN
ma-254	26	8	was	be	AUX
ma-254	26	9	obtained	obtain	VERB
ma-254	26	10	by	by	ADP
ma-254	26	11	kondrachov	kondrachov	NOUN
ma-254	26	12	[	[	X
ma-254	26	13	15	15	NUM
ma-254	26	14	]	]	PUNCT
ma-254	26	15	.	.	PUNCT
ma-254	27	1	such	such	ADJ
ma-254	27	2	compact	compact	ADJ
ma-254	27	3	embedding	embed	VERB
ma-254	27	4	the	the	DET
ma-254	27	5	-	-	PUNCT
ma-254	27	6	orem	orem	PROPN
ma-254	27	7	has	have	VERB
ma-254	27	8	many	many	ADJ
ma-254	27	9	important	important	ADJ
ma-254	27	10	applications	application	NOUN
ma-254	27	11	in	in	ADP
ma-254	27	12	analysis	analysis	NOUN
ma-254	27	13	for	for	ADP
ma-254	27	14	instance	instance	NOUN
ma-254	27	15	in	in	ADP
ma-254	27	16	linear	linear	PROPN
ma-254	27	17	elliptic	elliptic	ADJ
ma-254	27	18	partial	partial	ADJ
ma-254	27	19	differentialequations	differentialequation	NOUN
ma-254	27	20	defined	define	VERB
ma-254	27	21	over	over	ADP
ma-254	27	22	bounded	bounded	ADJ
ma-254	27	23	domains	domain	NOUN
ma-254	27	24	[	[	X
ma-254	27	25	8	8	NUM
ma-254	27	26	,	,	PUNCT
ma-254	27	27	9	9	NUM
ma-254	27	28	]	]	PUNCT
ma-254	27	29	,	,	PUNCT
ma-254	27	30	in	in	ADP
ma-254	27	31	engineering	engineering	NOUN
ma-254	27	32	applications	application	NOUN
ma-254	27	33	[	[	X
ma-254	27	34	20	20	NUM
ma-254	27	35	]	]	PUNCT
ma-254	27	36	,	,	PUNCT
ma-254	27	37	etc.in	etc.in	PROPN
ma-254	27	38	this	this	DET
ma-254	27	39	paper	paper	NOUN
ma-254	27	40	,	,	PUNCT
ma-254	27	41	we	we	PRON
ma-254	27	42	are	be	AUX
ma-254	27	43	mainly	mainly	ADV
ma-254	27	44	concerned	concerned	ADJ
ma-254	27	45	with	with	ADP
ma-254	27	46	a	a	DET
ma-254	27	47	generalization	generalization	NOUN
ma-254	27	48	of	of	ADP
ma-254	27	49	the	the	DET
ma-254	27	50	rellich	rellich	NOUN
ma-254	27	51	-	-	PUNCT
ma-254	27	52	kondrachov	kondrachov	NOUN
ma-254	27	53	theoremto	theoremto	ADP
ma-254	27	54	a	a	DET
ma-254	27	55	class	class	NOUN
ma-254	27	56	of	of	ADP
ma-254	27	57	sobolev	sobolev	NOUN
ma-254	27	58	spaces	space	NOUN
ma-254	27	59	on	on	ADP
ma-254	27	60	gelfand	gelfand	ADJ
ma-254	27	61	pairs	pair	NOUN
ma-254	27	62	associated	associate	VERB
ma-254	27	63	with	with	ADP
ma-254	27	64	compact	compact	ADJ
ma-254	27	65	hypergroups	hypergroup	NOUN
ma-254	27	66	.	.	PUNCT
ma-254	28	1	we	we	PRON
ma-254	28	2	paved	pave	VERB
ma-254	28	3	theway	theway	PROPN
ma-254	28	4	with	with	ADP
ma-254	28	5	some	some	DET
ma-254	28	6	results	result	NOUN
ma-254	28	7	which	which	PRON
ma-254	28	8	amount	amount	VERB
ma-254	28	9	to	to	ADP
ma-254	28	10	the	the	DET
ma-254	28	11	proof	proof	NOUN
ma-254	28	12	of	of	ADP
ma-254	28	13	the	the	DET
ma-254	28	14	rellich	rellich	NOUN
ma-254	28	15	-	-	PUNCT
ma-254	28	16	kondrachov	kondrachov	NOUN
ma-254	28	17	theorem	theorem	NOUN
ma-254	28	18	in	in	ADP
ma-254	28	19	the	the	DET
ma-254	28	20	presentframework.the	presentframework.the	PRON
ma-254	28	21	paper	paper	NOUN
ma-254	28	22	is	be	AUX
ma-254	28	23	organized	organize	VERB
ma-254	28	24	as	as	SCONJ
ma-254	28	25	follows	follow	VERB
ma-254	28	26	.	.	PUNCT
ma-254	29	1	in	in	ADP
ma-254	29	2	section	section	NOUN
ma-254	29	3	2	2	NUM
ma-254	29	4	,	,	PUNCT
ma-254	29	5	we	we	PRON
ma-254	29	6	recall	recall	VERB
ma-254	29	7	some	some	DET
ma-254	29	8	results	result	NOUN
ma-254	29	9	which	which	PRON
ma-254	29	10	we	we	PRON
ma-254	29	11	may	may	AUX
ma-254	29	12	need	need	VERB
ma-254	29	13	.	.	PUNCT
ma-254	30	1	insection	insection	NOUN
ma-254	30	2	3	3	NUM
ma-254	30	3	,	,	PUNCT
ma-254	30	4	we	we	PRON
ma-254	30	5	present	present	VERB
ma-254	30	6	the	the	DET
ma-254	30	7	main	main	ADJ
ma-254	30	8	results	result	NOUN
ma-254	30	9	,	,	PUNCT
ma-254	30	10	the	the	DET
ma-254	30	11	culmination	culmination	NOUN
ma-254	30	12	of	of	ADP
ma-254	30	13	which	which	PRON
ma-254	30	14	is	be	AUX
ma-254	30	15	the	the	DET
ma-254	30	16	analogue	analogue	NOUN
ma-254	30	17	of	of	ADP
ma-254	30	18	the	the	DET
ma-254	30	19	rellich	rellich	NOUN
ma-254	30	20	-	-	PUNCT
ma-254	30	21	kondrachov	kondrachov	NOUN
ma-254	30	22	theorem	theorem	NOUN
ma-254	30	23	.	.	PROPN
ma-254	30	24	2	2	NUM
ma-254	30	25	.	.	NOUN
ma-254	30	26	preliminaries	preliminary	NOUN
ma-254	30	27	the	the	DET
ma-254	30	28	important	important	ADJ
ma-254	30	29	ingredients	ingredient	NOUN
ma-254	30	30	which	which	PRON
ma-254	30	31	constitute	constitute	VERB
ma-254	30	32	this	this	DET
ma-254	30	33	section	section	NOUN
ma-254	30	34	are	be	AUX
ma-254	30	35	borrowed	borrow	VERB
ma-254	30	36	from	from	ADP
ma-254	30	37	[	[	X
ma-254	30	38	3	3	NUM
ma-254	30	39	,	,	PUNCT
ma-254	30	40	5	5	NUM
ma-254	30	41	,	,	PUNCT
ma-254	30	42	6	6	NUM
ma-254	30	43	]	]	PUNCT
ma-254	30	44	.	.	PUNCT
ma-254	31	1	let	let	VERB
ma-254	31	2	g	g	NOUN
ma-254	31	3	be	be	AUX
ma-254	31	4	alocally	alocally	ADV
ma-254	31	5	compact	compact	ADJ
ma-254	31	6	space	space	NOUN
ma-254	31	7	.	.	PUNCT
ma-254	32	1	denote	denote	VERB
ma-254	32	2	by	by	ADP
ma-254	32	3	•	•	NUM
ma-254	32	4	c(g	c(g	PROPN
ma-254	32	5	)	)	PUNCT
ma-254	32	6	,	,	PUNCT
ma-254	32	7	the	the	DET
ma-254	32	8	set	set	NOUN
ma-254	32	9	of	of	ADP
ma-254	32	10	complex	complex	NOUN
ma-254	32	11	-	-	PUNCT
ma-254	32	12	valued	value	VERB
ma-254	32	13	continuous	continuous	ADJ
ma-254	32	14	functions	function	NOUN
ma-254	32	15	on	on	ADP
ma-254	32	16	g	g	PROPN
ma-254	32	17	,	,	PUNCT
ma-254	32	18	•	•	NUM
ma-254	32	19	m(g	m(g	PROPN
ma-254	32	20	)	)	PUNCT
ma-254	32	21	,	,	PUNCT
ma-254	32	22	the	the	DET
ma-254	32	23	set	set	NOUN
ma-254	32	24	of	of	ADP
ma-254	32	25	radon	radon	ADJ
ma-254	32	26	measures	measure	NOUN
ma-254	32	27	on	on	ADP
ma-254	32	28	g	g	NOUN
ma-254	32	29	,	,	PUNCT
ma-254	32	30	•	•	DET
ma-254	32	31	mb(g	mb(g	NOUN
ma-254	32	32	)	)	PUNCT
ma-254	32	33	,	,	PUNCT
ma-254	32	34	the	the	DET
ma-254	32	35	subset	subset	NOUN
ma-254	32	36	of	of	ADP
ma-254	32	37	m(g	m(g	PROPN
ma-254	32	38	)	)	PUNCT
ma-254	32	39	consisting	consist	VERB
ma-254	32	40	of	of	ADP
ma-254	32	41	bounded	bounded	ADJ
ma-254	32	42	measures	measure	NOUN
ma-254	32	43	,	,	PUNCT
ma-254	32	44	•	•	NUM
ma-254	32	45	m1(g	m1(g	NOUN
ma-254	32	46	)	)	PUNCT
ma-254	32	47	,	,	PUNCT
ma-254	32	48	the	the	DET
ma-254	32	49	subset	subset	NOUN
ma-254	32	50	of	of	ADP
ma-254	32	51	mb(g	mb(g	NOUN
ma-254	32	52	)	)	PUNCT
ma-254	32	53	consisting	consist	VERB
ma-254	32	54	of	of	ADP
ma-254	32	55	probability	probability	NOUN
ma-254	32	56	measures	measure	NOUN
ma-254	32	57	,	,	PUNCT
ma-254	32	58	•	•	NUM
ma-254	32	59	c(g	c(g	PROPN
ma-254	32	60	)	)	PUNCT
ma-254	32	61	,	,	PUNCT
ma-254	32	62	the	the	DET
ma-254	32	63	set	set	NOUN
ma-254	32	64	of	of	ADP
ma-254	32	65	compact	compact	ADJ
ma-254	32	66	subspaces	subspace	NOUN
ma-254	32	67	of	of	ADP
ma-254	32	68	g	g	NOUN
ma-254	32	69	,	,	PUNCT
ma-254	32	70	•	•	NUM
ma-254	32	71	δx	δx	NOUN
ma-254	32	72	,	,	PUNCT
ma-254	32	73	the	the	DET
ma-254	32	74	point	point	NOUN
ma-254	32	75	measure	measure	NOUN
ma-254	32	76	at	at	ADP
ma-254	32	77	the	the	DET
ma-254	32	78	element	element	NOUN
ma-254	32	79	x	x	PUNCT
ma-254	32	80	.the	.the	DET
ma-254	32	81	setm(g	setm(g	PROPN
ma-254	32	82	)	)	PUNCT
ma-254	32	83	is	be	AUX
ma-254	32	84	endowed	endow	VERB
ma-254	32	85	with	with	ADP
ma-254	32	86	the	the	DET
ma-254	32	87	cône	cône	PROPN
ma-254	32	88	topology	topology	NOUN
ma-254	32	89	while	while	SCONJ
ma-254	32	90	c(g	c(g	PROPN
ma-254	32	91	)	)	PUNCT
ma-254	32	92	is	be	AUX
ma-254	32	93	endowed	endow	VERB
ma-254	32	94	with	with	ADP
ma-254	32	95	the	the	DET
ma-254	32	96	michael	michael	PROPN
ma-254	32	97	topology	topology	PROPN
ma-254	32	98	.	.	PUNCT
ma-254	33	1	definition	definition	NOUN
ma-254	33	2	2.1	2.1	NUM
ma-254	33	3	.	.	PUNCT
ma-254	34	1	a	a	DET
ma-254	34	2	locally	locally	ADV
ma-254	34	3	compact	compact	ADJ
ma-254	34	4	space	space	NOUN
ma-254	34	5	g	g	NOUN
ma-254	34	6	is	be	AUX
ma-254	34	7	called	call	VERB
ma-254	34	8	a	a	DET
ma-254	34	9	hypergroup	hypergroup	NOUN
ma-254	34	10	if	if	SCONJ
ma-254	34	11	the	the	DET
ma-254	34	12	following	follow	VERB
ma-254	34	13	properties	property	NOUN
ma-254	34	14	hold.(1	hold.(1	PROPN
ma-254	34	15	)	)	PUNCT
ma-254	34	16	there	there	PRON
ma-254	34	17	exists	exist	VERB
ma-254	34	18	a	a	DET
ma-254	34	19	binary	binary	ADJ
ma-254	34	20	operation	operation	NOUN
ma-254	34	21	∗	∗	NOUN
ma-254	34	22	(	(	PUNCT
ma-254	34	23	the	the	DET
ma-254	34	24	convolution	convolution	NOUN
ma-254	34	25	)	)	PUNCT
ma-254	34	26	on	on	ADP
ma-254	34	27	mb(g	mb(g	NOUN
ma-254	34	28	)	)	PUNCT
ma-254	34	29	which	which	PRON
ma-254	34	30	turns	turn	VERB
ma-254	34	31	it	it	PRON
ma-254	34	32	into	into	ADP
ma-254	34	33	an	an	DET
ma-254	34	34	associative	associative	ADJ
ma-254	34	35	algebra	algebra	NOUN
ma-254	34	36	such	such	ADJ
ma-254	34	37	that(a	that(a	PROPN
ma-254	34	38	)	)	PUNCT
ma-254	34	39	the	the	DET
ma-254	34	40	mapping	mapping	NOUN
ma-254	34	41	(	(	PUNCT
ma-254	34	42	µ	µ	NOUN
ma-254	34	43	,	,	PUNCT
ma-254	34	44	ν	ν	NOUN
ma-254	34	45	)	)	PUNCT
ma-254	34	46	7→	7→	NUM
ma-254	34	47	µ	µ	NOUN
ma-254	34	48	∗	∗	NOUN
ma-254	34	49	ν	ν	NOUN
ma-254	34	50	is	be	AUX
ma-254	34	51	continuous	continuous	ADJ
ma-254	34	52	from	from	ADP
ma-254	34	53	mb(g)×mb(g	mb(g)×mb(g	PROPN
ma-254	34	54	)	)	PUNCT
ma-254	34	55	into	into	ADP
ma-254	34	56	mb(g),(b	mb(g),(b	NOUN
ma-254	34	57	)	)	PUNCT
ma-254	34	58	∀x	∀x	NUM
ma-254	34	59	,	,	PUNCT
ma-254	34	60	y	y	PROPN
ma-254	34	61	∈	∈	PROPN
ma-254	34	62	g	g	PROPN
ma-254	34	63	,	,	PUNCT
ma-254	34	64	δx	δx	PROPN
ma-254	34	65	∗	∗	NOUN
ma-254	34	66	δy	δy	NOUN
ma-254	34	67	is	be	AUX
ma-254	34	68	a	a	DET
ma-254	34	69	probability	probability	NOUN
ma-254	34	70	measure	measure	NOUN
ma-254	34	71	such	such	ADJ
ma-254	34	72	that	that	SCONJ
ma-254	34	73	supp(δx	supp(δx	ADJ
ma-254	34	74	∗	∗	NOUN
ma-254	34	75	δy	δy	NOUN
ma-254	34	76	)	)	PUNCT
ma-254	34	77	is	be	AUX
ma-254	34	78	compact.(c	compact.(c	PRON
ma-254	34	79	)	)	PUNCT
ma-254	34	80	the	the	DET
ma-254	34	81	mapping	mapping	NOUN
ma-254	34	82	(	(	PUNCT
ma-254	34	83	x	x	NOUN
ma-254	34	84	,	,	PUNCT
ma-254	34	85	y)→	y)→	PROPN
ma-254	34	86	supp(δx	supp(δx	ADJ
ma-254	34	87	∗	∗	NOUN
ma-254	34	88	δy	δy	NOUN
ma-254	34	89	)	)	PUNCT
ma-254	34	90	is	be	AUX
ma-254	34	91	continuous	continuous	ADJ
ma-254	34	92	from	from	ADP
ma-254	34	93	g	g	PROPN
ma-254	34	94	×	×	PROPN
ma-254	34	95	g	g	NOUN
ma-254	34	96	into	into	ADP
ma-254	34	97	c(g).(2	c(g).(2	NOUN
ma-254	34	98	)	)	PUNCT
ma-254	34	99	there	there	PRON
ma-254	34	100	exists	exist	VERB
ma-254	34	101	a	a	DET
ma-254	34	102	unique	unique	ADJ
ma-254	34	103	element	element	NOUN
ma-254	34	104	e	e	NOUN
ma-254	34	105	in	in	ADP
ma-254	34	106	g	g	PROPN
ma-254	34	107	(	(	PUNCT
ma-254	34	108	the	the	DET
ma-254	34	109	neutral	neutral	ADJ
ma-254	34	110	element	element	NOUN
ma-254	34	111	)	)	PUNCT
ma-254	35	1	such	such	ADJ
ma-254	35	2	that	that	SCONJ
ma-254	35	3	∀x	∀x	VERB
ma-254	35	4	∈	∈	PROPN
ma-254	35	5	g	g	NOUN
ma-254	35	6	,	,	PUNCT
ma-254	35	7	δx	δx	NOUN
ma-254	35	8	∗	∗	NOUN
ma-254	35	9	δe	δe	NOUN
ma-254	35	10	=	=	NOUN
ma-254	35	11	δe	δe	NOUN
ma-254	35	12	∗	∗	NOUN
ma-254	35	13	δx	δx	NOUN
ma-254	35	14	=	=	NOUN
ma-254	35	15	δx	δx	NOUN
ma-254	35	16	.	.	PUNCT
ma-254	36	1	(	(	PUNCT
ma-254	36	2	3	3	X
ma-254	36	3	)	)	PUNCT
ma-254	36	4	there	there	PRON
ma-254	36	5	exists	exist	VERB
ma-254	36	6	an	an	DET
ma-254	36	7	involutive	involutive	ADJ
ma-254	36	8	homeomorphism	homeomorphism	ADJ
ma-254	36	9	�	�	PROPN
ma-254	36	10	:	:	PUNCT
ma-254	36	11	g	g	PROPN
ma-254	36	12	→	→	SYM
ma-254	36	13	g	g	NOUN
ma-254	36	14	such	such	ADJ
ma-254	36	15	that	that	PRON
ma-254	36	16	for	for	ADP
ma-254	36	17	all	all	DET
ma-254	36	18	x	x	NOUN
ma-254	36	19	,	,	PUNCT
ma-254	36	20	y	y	PROPN
ma-254	36	21	∈	∈	PROPN
ma-254	36	22	g	g	PROPN
ma-254	36	23	,	,	PUNCT
ma-254	36	24	(	(	PUNCT
ma-254	37	1	δx	δx	PROPN
ma-254	37	2	∗	∗	NOUN
ma-254	37	3	δy	δy	PROPN
ma-254	37	4	)	)	PUNCT
ma-254	37	5	�	�	PROPN
ma-254	37	6	=	=	SYM
ma-254	37	7	δy	δy	PROPN
ma-254	37	8	�	�	PROPN
ma-254	37	9	∗	∗	PROPN
ma-254	37	10	δx	δx	ADP
ma-254	37	11	�	�	PROPN
ma-254	37	12	.	.	PUNCT
ma-254	38	1	(	(	PUNCT
ma-254	38	2	4	4	NUM
ma-254	38	3	)	)	PUNCT
ma-254	38	4	∀x	∀x	NUM
ma-254	38	5	,	,	PUNCT
ma-254	38	6	y	y	PROPN
ma-254	38	7	,	,	PUNCT
ma-254	38	8	z	z	PROPN
ma-254	38	9	∈	∈	PROPN
ma-254	38	10	g	g	PROPN
ma-254	38	11	,	,	PUNCT
ma-254	38	12	z	z	PROPN
ma-254	38	13	∈	∈	PROPN
ma-254	38	14	supp(δx	supp(δx	PROPN
ma-254	38	15	∗	∗	X
ma-254	38	16	δy	δy	NOUN
ma-254	38	17	)	)	PUNCT
ma-254	38	18	⇐	⇐	ADJ
ma-254	38	19	⇒	⇒	NOUN
ma-254	38	20	x	x	SYM
ma-254	38	21	∈	∈	PROPN
ma-254	38	22	supp(δz	supp(δz	PROPN
ma-254	38	23	∗	∗	PROPN
ma-254	38	24	δy	δy	PROPN
ma-254	38	25	�	�	PROPN
ma-254	38	26	)	)	PUNCT
ma-254	38	27	.	.	PUNCT
ma-254	39	1	definition	definition	NOUN
ma-254	39	2	2.2	2.2	NUM
ma-254	39	3	.	.	PUNCT
ma-254	40	1	a	a	DET
ma-254	40	2	closed	closed	ADJ
ma-254	40	3	nonempty	nonempty	NOUN
ma-254	40	4	subset	subset	VERB
ma-254	40	5	h	h	NOUN
ma-254	40	6	of	of	ADP
ma-254	40	7	a	a	DET
ma-254	40	8	hypergroup	hypergroup	NOUN
ma-254	40	9	g	g	NOUN
ma-254	40	10	is	be	AUX
ma-254	40	11	called	call	VERB
ma-254	40	12	a	a	DET
ma-254	40	13	subhypergroup	subhypergroup	NOUN
ma-254	40	14	of	of	ADP
ma-254	40	15	g	g	PROPN
ma-254	40	16	if(1	if(1	PROPN
ma-254	40	17	)	)	PUNCT
ma-254	40	18	∀x	∀x	VERB
ma-254	40	19	∈	∈	PROPN
ma-254	40	20	h	h	NOUN
ma-254	40	21	,	,	PUNCT
ma-254	40	22	x	x	X
ma-254	40	23	�	�	PROPN
ma-254	40	24	∈	∈	PROPN
ma-254	40	25	h	h	NOUN
ma-254	40	26	,	,	PUNCT
ma-254	40	27	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	40	28	eur	eur	PROPN
ma-254	40	29	.	.	PUNCT
ma-254	41	1	j.	j.	PROPN
ma-254	41	2	math	math	PROPN
ma-254	41	3	.	.	PUNCT
ma-254	42	1	anal	anal	PROPN
ma-254	42	2	.	.	PUNCT
ma-254	43	1	10.28924	10.28924	NUM
ma-254	43	2	/	/	SYM
ma-254	43	3	ada	ada	PROPN
ma-254	43	4	/	/	SYM
ma-254	43	5	ma.5.3	ma.5.3	PROPN
ma-254	43	6	3(2	3(2	NUM
ma-254	43	7	)	)	PUNCT
ma-254	43	8	∀x	∀x	NUM
ma-254	43	9	,	,	PUNCT
ma-254	43	10	y	y	PROPN
ma-254	43	11	∈	∈	PROPN
ma-254	43	12	h	h	NOUN
ma-254	43	13	,	,	PUNCT
ma-254	43	14	supp(δx	supp(δx	ADJ
ma-254	43	15	∗	∗	NOUN
ma-254	43	16	δy	δy	NOUN
ma-254	43	17	)	)	PUNCT
ma-254	44	1	⊂	⊂	PROPN
ma-254	44	2	h.	h.	PROPN
ma-254	44	3	let	let	VERB
ma-254	44	4	g	g	PRON
ma-254	44	5	be	be	AUX
ma-254	44	6	a	a	DET
ma-254	44	7	hypergroup	hypergroup	NOUN
ma-254	44	8	and	and	CCONJ
ma-254	44	9	let	let	VERB
ma-254	44	10	k	k	PRON
ma-254	44	11	be	be	AUX
ma-254	44	12	a	a	DET
ma-254	44	13	compact	compact	ADJ
ma-254	44	14	subhypergroup	subhypergroup	NOUN
ma-254	44	15	of	of	ADP
ma-254	44	16	g.	g.	PROPN
ma-254	44	17	for	for	ADP
ma-254	44	18	x	x	PROPN
ma-254	44	19	,	,	PUNCT
ma-254	44	20	y	y	PROPN
ma-254	44	21	∈	∈	PROPN
ma-254	44	22	g	g	PROPN
ma-254	44	23	,	,	PUNCT
ma-254	44	24	x	x	PROPN
ma-254	44	25	∗	∗	NOUN
ma-254	44	26	y	y	PROPN
ma-254	44	27	standsfor	standsfor	ADP
ma-254	44	28	the	the	DET
ma-254	44	29	support	support	NOUN
ma-254	44	30	of	of	ADP
ma-254	44	31	δx	δx	PROPN
ma-254	44	32	∗	∗	NOUN
ma-254	44	33	δy	δy	NOUN
ma-254	44	34	.	.	PUNCT
ma-254	45	1	the	the	DET
ma-254	45	2	double	double	ADJ
ma-254	45	3	coset	coset	NOUN
ma-254	45	4	of	of	ADP
ma-254	45	5	x	x	PUNCT
ma-254	45	6	with	with	ADP
ma-254	45	7	respect	respect	NOUN
ma-254	45	8	to	to	ADP
ma-254	45	9	k	k	PROPN
ma-254	45	10	is	be	AUX
ma-254	45	11	kxk	kxk	ADV
ma-254	45	12	=	=	PUNCT
ma-254	45	13	{	{	PUNCT
ma-254	45	14	k1	k1	NOUN
ma-254	45	15	∗	∗	X
ma-254	45	16	x	x	PROPN
ma-254	45	17	∗	∗	NOUN
ma-254	45	18	k2	k2	NOUN
ma-254	45	19	:	:	PUNCT
ma-254	45	20	k1	k1	PROPN
ma-254	45	21	,	,	PUNCT
ma-254	45	22	k2	k2	PROPN
ma-254	45	23	∈	∈	PROPN
ma-254	45	24	k	k	X
ma-254	45	25	}	}	PUNCT
ma-254	45	26	=	=	SYM
ma-254	45	27	⋃	⋃	ADP
ma-254	45	28	k1,k2∈k	k1,k2∈k	VERB
ma-254	45	29	supp(δk1	supp(δk1	PROPN
ma-254	45	30	∗	∗	NOUN
ma-254	45	31	δx	δx	NOUN
ma-254	45	32	∗	∗	NOUN
ma-254	45	33	δk2	δk2	PROPN
ma-254	45	34	)	)	PUNCT
ma-254	45	35	.	.	PUNCT
ma-254	46	1	for	for	ADP
ma-254	46	2	f	f	PROPN
ma-254	46	3	∈	∈	PROPN
ma-254	46	4	c(g	c(g	PROPN
ma-254	46	5	)	)	PUNCT
ma-254	46	6	,	,	PUNCT
ma-254	46	7	we	we	PRON
ma-254	46	8	set	set	VERB
ma-254	46	9	f	f	PROPN
ma-254	46	10	(	(	PUNCT
ma-254	46	11	x	x	PROPN
ma-254	46	12	∗	∗	PROPN
ma-254	46	13	y	y	NOUN
ma-254	46	14	)	)	PUNCT
ma-254	47	1	=	=	SYM
ma-254	48	1	∫	∫	PROPN
ma-254	48	2	g	g	PROPN
ma-254	48	3	f	f	PROPN
ma-254	48	4	(	(	PUNCT
ma-254	48	5	z)d(δx	z)d(δx	NUM
ma-254	48	6	∗	∗	NOUN
ma-254	48	7	δy	δy	NOUN
ma-254	48	8	)	)	PUNCT
ma-254	48	9	(	(	PUNCT
ma-254	48	10	z	z	NOUN
ma-254	48	11	)	)	PUNCT
ma-254	48	12	and	and	CCONJ
ma-254	48	13	f	f	PROPN
ma-254	48	14	�	�	PROPN
ma-254	48	15	(	(	PUNCT
ma-254	48	16	x	x	NOUN
ma-254	48	17	)	)	PUNCT
ma-254	49	1	=	=	SYM
ma-254	49	2	f	f	X
ma-254	49	3	(	(	PUNCT
ma-254	49	4	x	x	X
ma-254	49	5	�	�	PROPN
ma-254	49	6	).a	).a	PUNCT
ma-254	49	7	function	function	PROPN
ma-254	49	8	f	f	PROPN
ma-254	49	9	∈	∈	PROPN
ma-254	49	10	c(g	c(g	PROPN
ma-254	49	11	)	)	PUNCT
ma-254	49	12	is	be	AUX
ma-254	49	13	said	say	VERB
ma-254	49	14	to	to	PART
ma-254	49	15	be	be	AUX
ma-254	49	16	k	k	ADJ
ma-254	49	17	-	-	ADJ
ma-254	49	18	bi	bi	ADJ
ma-254	49	19	-	-	ADJ
ma-254	49	20	invariant	invariant	ADJ
ma-254	49	21	if	if	SCONJ
ma-254	49	22	∀k1	∀k1	ADJ
ma-254	49	23	,	,	PUNCT
ma-254	49	24	k2	k2	PROPN
ma-254	49	25	∈	∈	PROPN
ma-254	49	26	k,∀x	k,∀x	ADP
ma-254	49	27	∈	∈	PROPN
ma-254	49	28	g	g	PROPN
ma-254	49	29	,	,	PUNCT
ma-254	49	30	f	f	PROPN
ma-254	49	31	(	(	PUNCT
ma-254	49	32	k1	k1	NOUN
ma-254	49	33	∗	∗	X
ma-254	49	34	x	x	SYM
ma-254	49	35	∗	∗	NOUN
ma-254	49	36	k2	k2	NOUN
ma-254	49	37	)	)	PUNCT
ma-254	50	1	=	=	SYM
ma-254	50	2	f	f	PROPN
ma-254	50	3	(	(	PUNCT
ma-254	50	4	x	x	NOUN
ma-254	50	5	)	)	PUNCT
ma-254	50	6	.	.	PUNCT
ma-254	51	1	denote	denote	VERB
ma-254	51	2	by	by	ADP
ma-254	51	3	k(g	k(g	NOUN
ma-254	51	4	)	)	PUNCT
ma-254	51	5	the	the	DET
ma-254	51	6	set	set	NOUN
ma-254	51	7	of	of	ADP
ma-254	51	8	continuous	continuous	ADJ
ma-254	51	9	functions	function	NOUN
ma-254	51	10	on	on	ADP
ma-254	51	11	g	g	NOUN
ma-254	51	12	with	with	ADP
ma-254	51	13	compact	compact	ADJ
ma-254	51	14	support	support	NOUN
ma-254	51	15	and	and	CCONJ
ma-254	51	16	by	by	ADP
ma-254	51	17	k\(g	k\(g	NOUN
ma-254	51	18	)	)	PUNCT
ma-254	51	19	thesubset	thesubset	NOUN
ma-254	51	20	of	of	ADP
ma-254	51	21	k(g	k(g	PROPN
ma-254	51	22	)	)	PUNCT
ma-254	51	23	consisting	consist	VERB
ma-254	51	24	of	of	ADP
ma-254	51	25	k	k	ADJ
ma-254	51	26	-	-	ADJ
ma-254	51	27	bi	bi	ADJ
ma-254	51	28	-	-	ADJ
ma-254	51	29	invariant	invariant	ADJ
ma-254	51	30	functions	function	NOUN
ma-254	51	31	.	.	PUNCT
ma-254	52	1	now	now	ADV
ma-254	52	2	,	,	PUNCT
ma-254	52	3	assume	assume	VERB
ma-254	52	4	that	that	SCONJ
ma-254	52	5	the	the	DET
ma-254	52	6	hypergroup	hypergroup	NOUN
ma-254	52	7	g	g	PROPN
ma-254	52	8	isprovided	isprovide	VERB
ma-254	52	9	with	with	ADP
ma-254	52	10	a	a	DET
ma-254	52	11	left	left	ADJ
ma-254	52	12	haar	haar	NOUN
ma-254	52	13	measure	measure	NOUN
ma-254	52	14	and	and	CCONJ
ma-254	52	15	that	that	SCONJ
ma-254	52	16	k	k	PROPN
ma-254	52	17	is	be	AUX
ma-254	52	18	equipped	equip	VERB
ma-254	52	19	with	with	ADP
ma-254	52	20	a	a	DET
ma-254	52	21	normalized	normalize	VERB
ma-254	52	22	haar	haar	NOUN
ma-254	52	23	measure	measure	NOUN
ma-254	52	24	.	.	PUNCT
ma-254	53	1	for	for	ADP
ma-254	53	2	f	f	PROPN
ma-254	53	3	∈	∈	PROPN
ma-254	53	4	k(g	k(g	PROPN
ma-254	53	5	)	)	PUNCT
ma-254	53	6	,	,	PUNCT
ma-254	53	7	put	put	VERB
ma-254	53	8	f	f	PROPN
ma-254	53	9	\(x	\(x	NOUN
ma-254	53	10	)	)	PUNCT
ma-254	54	1	=	=	SYM
ma-254	54	2	∫	∫	PROPN
ma-254	55	1	k	k	PROPN
ma-254	55	2	∫	∫	PROPN
ma-254	55	3	k	k	PROPN
ma-254	55	4	f	f	PROPN
ma-254	55	5	(	(	PUNCT
ma-254	55	6	k1	k1	NOUN
ma-254	55	7	∗	∗	X
ma-254	55	8	x	x	PROPN
ma-254	55	9	∗	∗	NOUN
ma-254	55	10	k2)dk1dk2	k2)dk1dk2	PROPN
ma-254	55	11	.	.	PUNCT
ma-254	56	1	for	for	ADP
ma-254	56	2	a	a	DET
ma-254	56	3	measure	measure	NOUN
ma-254	56	4	µ	µ	PRON
ma-254	56	5	∈	∈	PROPN
ma-254	56	6	m(g	m(g	PROPN
ma-254	56	7	)	)	PUNCT
ma-254	56	8	,	,	PUNCT
ma-254	56	9	set	set	VERB
ma-254	56	10	µ\(f	µ\(f	X
ma-254	56	11	)	)	PUNCT
ma-254	57	1	=	=	SYM
ma-254	57	2	µ(f	µ(f	PROPN
ma-254	57	3	\	\	PROPN
ma-254	57	4	)	)	PUNCT
ma-254	57	5	,	,	PUNCT
ma-254	57	6	f	f	PROPN
ma-254	57	7	∈	∈	PROPN
ma-254	57	8	k(g	k(g	PROPN
ma-254	57	9	)	)	PUNCT
ma-254	57	10	.	.	PUNCT
ma-254	58	1	the	the	DET
ma-254	58	2	measure	measure	NOUN
ma-254	58	3	µ	µ	NOUN
ma-254	58	4	is	be	AUX
ma-254	58	5	called	call	VERB
ma-254	58	6	k	k	ADJ
ma-254	58	7	-	-	ADJ
ma-254	58	8	bi	bi	ADJ
ma-254	58	9	-	-	ADJ
ma-254	58	10	invariant	invariant	ADJ
ma-254	58	11	if	if	SCONJ
ma-254	58	12	µ\	µ\	NUM
ma-254	58	13	=	=	PUNCT
ma-254	58	14	µ.	µ.	NOUN
ma-254	58	15	denote	denote	NOUN
ma-254	58	16	by	by	ADP
ma-254	58	17	m\	m\	ADJ
ma-254	58	18	c(g	c(g	PROPN
ma-254	58	19	)	)	PUNCT
ma-254	58	20	the	the	DET
ma-254	58	21	set	set	NOUN
ma-254	58	22	of	of	ADP
ma-254	58	23	complex	complex	ADJ
ma-254	58	24	radon	radon	NOUN
ma-254	58	25	measures	measure	NOUN
ma-254	58	26	with	with	ADP
ma-254	58	27	compact	compact	ADJ
ma-254	58	28	support	support	NOUN
ma-254	58	29	that	that	PRON
ma-254	58	30	are	be	AUX
ma-254	58	31	also	also	ADV
ma-254	58	32	k	k	ADJ
ma-254	58	33	-	-	ADJ
ma-254	58	34	bi	bi	ADJ
ma-254	58	35	-	-	ADJ
ma-254	58	36	invariant	invariant	ADJ
ma-254	58	37	.	.	PUNCT
ma-254	59	1	for	for	ADP
ma-254	59	2	µ	µ	NUM
ma-254	59	3	,	,	PUNCT
ma-254	59	4	ν	ν	PROPN
ma-254	59	5	∈	∈	PROPN
ma-254	59	6	m(g	m(g	PROPN
ma-254	59	7	)	)	PUNCT
ma-254	59	8	,	,	PUNCT
ma-254	59	9	we	we	PRON
ma-254	59	10	define	define	VERB
ma-254	59	11	µ	µ	PRON
ma-254	59	12	∗	∗	NOUN
ma-254	59	13	ν	ν	NOUN
ma-254	59	14	by	by	ADP
ma-254	59	15	µ	µ	NOUN
ma-254	59	16	∗	∗	NOUN
ma-254	59	17	ν(f	ν(f	PROPN
ma-254	59	18	)	)	PUNCT
ma-254	60	1	=	=	PUNCT
ma-254	61	1	∫∫	∫∫	ADV
ma-254	61	2	g	g	NOUN
ma-254	61	3	f	f	X
ma-254	61	4	(	(	PUNCT
ma-254	61	5	x	x	NOUN
ma-254	61	6	∗	∗	NOUN
ma-254	61	7	y)dµ(x)dν(y	y)dµ(x)dν(y	PROPN
ma-254	61	8	)	)	PUNCT
ma-254	61	9	,	,	PUNCT
ma-254	61	10	f	f	PROPN
ma-254	61	11	∈	∈	PROPN
ma-254	61	12	c(g	c(g	PROPN
ma-254	61	13	)	)	PUNCT
ma-254	61	14	.	.	PUNCT
ma-254	62	1	also	also	ADV
ma-254	62	2	,	,	PUNCT
ma-254	62	3	for	for	ADP
ma-254	62	4	f	f	PROPN
ma-254	62	5	,	,	PUNCT
ma-254	62	6	g	g	PROPN
ma-254	62	7	∈	∈	PROPN
ma-254	62	8	k(g	k(g	PROPN
ma-254	62	9	)	)	PUNCT
ma-254	62	10	,	,	PUNCT
ma-254	62	11	the	the	DET
ma-254	62	12	convolution	convolution	NOUN
ma-254	62	13	product	product	NOUN
ma-254	62	14	of	of	ADP
ma-254	62	15	f	f	PROPN
ma-254	62	16	and	and	CCONJ
ma-254	62	17	g	g	PROPN
ma-254	62	18	is	be	AUX
ma-254	62	19	the	the	DET
ma-254	62	20	function	function	NOUN
ma-254	62	21	f	f	PROPN
ma-254	62	22	∗	∗	VERB
ma-254	62	23	g	g	PROPN
ma-254	62	24	defined	define	VERB
ma-254	62	25	by	by	ADP
ma-254	62	26	(	(	PUNCT
ma-254	62	27	f	f	PROPN
ma-254	62	28	∗	∗	PROPN
ma-254	62	29	g)(x	g)(x	PROPN
ma-254	62	30	)	)	PUNCT
ma-254	63	1	=	=	SYM
ma-254	64	1	∫	∫	PROPN
ma-254	64	2	g	g	PROPN
ma-254	64	3	f	f	PROPN
ma-254	64	4	(	(	PUNCT
ma-254	64	5	y)g(y	y)g(y	PROPN
ma-254	64	6	�	�	PROPN
ma-254	64	7	∗	∗	VERB
ma-254	64	8	x)dy	x)dy	PROPN
ma-254	65	1	=	=	SYM
ma-254	66	1	∫	∫	PROPN
ma-254	67	1	g	g	PROPN
ma-254	67	2	f	f	PROPN
ma-254	67	3	(	(	PUNCT
ma-254	67	4	x	x	PROPN
ma-254	67	5	∗	∗	PROPN
ma-254	67	6	y)g(y	y)g(y	NOUN
ma-254	67	7	�	�	PROPN
ma-254	67	8	)dy	)dy	PROPN
ma-254	67	9	.	.	PUNCT
ma-254	68	1	provided	provide	VERB
ma-254	68	2	with	with	ADP
ma-254	68	3	this	this	DET
ma-254	68	4	convolution	convolution	NOUN
ma-254	68	5	product	product	NOUN
ma-254	68	6	,	,	PUNCT
ma-254	68	7	k(g	k(g	PROPN
ma-254	68	8	)	)	PUNCT
ma-254	68	9	is	be	AUX
ma-254	68	10	an	an	DET
ma-254	68	11	algebra	algebra	NOUN
ma-254	68	12	and	and	CCONJ
ma-254	68	13	k\(g	k\(g	NOUN
ma-254	68	14	)	)	PUNCT
ma-254	68	15	is	be	AUX
ma-254	68	16	a	a	DET
ma-254	68	17	subalgebra	subalgebra	NOUN
ma-254	68	18	of	of	ADP
ma-254	68	19	k(g	k(g	PROPN
ma-254	68	20	)	)	PUNCT
ma-254	68	21	.	.	PUNCT
ma-254	69	1	definition	definition	NOUN
ma-254	69	2	2.3	2.3	NUM
ma-254	69	3	.	.	PUNCT
ma-254	70	1	let	let	VERB
ma-254	70	2	g	g	PRON
ma-254	70	3	be	be	AUX
ma-254	70	4	a	a	DET
ma-254	70	5	hypergroup	hypergroup	NOUN
ma-254	70	6	and	and	CCONJ
ma-254	70	7	let	let	VERB
ma-254	70	8	k	k	PRON
ma-254	70	9	be	be	AUX
ma-254	70	10	a	a	DET
ma-254	70	11	compact	compact	ADJ
ma-254	70	12	subhypergroup	subhypergroup	NOUN
ma-254	70	13	of	of	ADP
ma-254	70	14	g.	g.	PROPN
ma-254	70	15	the	the	DET
ma-254	70	16	pair	pair	NOUN
ma-254	70	17	(	(	PUNCT
ma-254	70	18	g	g	NOUN
ma-254	70	19	,	,	PUNCT
ma-254	70	20	k	k	NOUN
ma-254	70	21	)	)	PUNCT
ma-254	70	22	is	be	AUX
ma-254	70	23	called	call	VERB
ma-254	70	24	a	a	DET
ma-254	70	25	gelfand	gelfand	ADJ
ma-254	70	26	pair	pair	NOUN
ma-254	70	27	if	if	SCONJ
ma-254	70	28	the	the	DET
ma-254	70	29	space	space	NOUN
ma-254	70	30	(	(	PUNCT
ma-254	70	31	m\	m\	ADJ
ma-254	70	32	c(g	c(g	PROPN
ma-254	70	33	)	)	PUNCT
ma-254	70	34	,	,	PUNCT
ma-254	70	35	∗	∗	NOUN
ma-254	70	36	)	)	PUNCT
ma-254	70	37	is	be	AUX
ma-254	70	38	commutative	commutative	ADJ
ma-254	70	39	.	.	PUNCT
ma-254	71	1	we	we	PRON
ma-254	71	2	may	may	AUX
ma-254	71	3	refer	refer	VERB
ma-254	71	4	to	to	ADP
ma-254	71	5	this	this	DET
ma-254	71	6	gelfand	gelfand	ADJ
ma-254	71	7	pair	pair	NOUN
ma-254	71	8	as	as	ADP
ma-254	71	9	a	a	DET
ma-254	71	10	hypergroup	hypergroup	NOUN
ma-254	71	11	gelfand	gelfand	PROPN
ma-254	71	12	pair	pair	NOUN
ma-254	71	13	.	.	PUNCT
ma-254	72	1	if	if	SCONJ
ma-254	72	2	(	(	PUNCT
ma-254	72	3	g	g	NOUN
ma-254	72	4	,	,	PUNCT
ma-254	72	5	k	k	NOUN
ma-254	72	6	)	)	PUNCT
ma-254	72	7	is	be	AUX
ma-254	72	8	a	a	DET
ma-254	72	9	hypergroupgelfand	hypergroupgelfand	NOUN
ma-254	72	10	pair	pair	NOUN
ma-254	72	11	and	and	CCONJ
ma-254	72	12	if	if	SCONJ
ma-254	72	13	g	g	PROPN
ma-254	72	14	has	have	VERB
ma-254	72	15	a	a	DET
ma-254	72	16	haar	haar	NOUN
ma-254	72	17	measure	measure	NOUN
ma-254	72	18	then	then	ADV
ma-254	72	19	g	g	PROPN
ma-254	72	20	is	be	AUX
ma-254	72	21	unimodular	unimodular	ADJ
ma-254	72	22	[	[	X
ma-254	72	23	6].in	6].in	NUM
ma-254	72	24	the	the	DET
ma-254	72	25	rest	rest	NOUN
ma-254	72	26	of	of	ADP
ma-254	72	27	the	the	DET
ma-254	72	28	paper	paper	NOUN
ma-254	72	29	,	,	PUNCT
ma-254	72	30	(	(	PUNCT
ma-254	72	31	g	g	NOUN
ma-254	72	32	,	,	PUNCT
ma-254	72	33	k	k	NOUN
ma-254	72	34	)	)	PUNCT
ma-254	72	35	is	be	AUX
ma-254	72	36	assumed	assume	VERB
ma-254	72	37	to	to	PART
ma-254	72	38	be	be	AUX
ma-254	72	39	a	a	DET
ma-254	72	40	hypergroup	hypergroup	NOUN
ma-254	72	41	gelfand	gelfand	PROPN
ma-254	72	42	pair	pair	NOUN
ma-254	72	43	.	.	PUNCT
ma-254	73	1	we	we	PRON
ma-254	73	2	denote	denote	VERB
ma-254	73	3	by	by	ADP
ma-254	73	4	ĝ\the	ĝ\the	DET
ma-254	73	5	set	set	NOUN
ma-254	73	6	of	of	ADP
ma-254	73	7	bounded	bounded	ADJ
ma-254	73	8	continuous	continuous	ADJ
ma-254	73	9	functions	function	NOUN
ma-254	73	10	φ	φ	NOUN
ma-254	73	11	:	:	PUNCT
ma-254	73	12	g	g	PROPN
ma-254	73	13	−→	−→	NOUN
ma-254	73	14	c	c	PROPN
ma-254	73	15	such	such	ADJ
ma-254	73	16	that(1	that(1	NOUN
ma-254	73	17	)	)	PUNCT
ma-254	73	18	φ	φ	PROPN
ma-254	73	19	is	be	AUX
ma-254	73	20	k	k	ADJ
ma-254	73	21	-	-	ADJ
ma-254	73	22	bi	bi	ADJ
ma-254	73	23	-	-	ADJ
ma-254	73	24	invariant,(2	invariant,(2	NOUN
ma-254	73	25	)	)	PUNCT
ma-254	73	26	φ(e	φ(e	NUM
ma-254	73	27	)	)	PUNCT
ma-254	73	28	=	=	SYM
ma-254	73	29	1,(3	1,(3	X
ma-254	73	30	)	)	PUNCT
ma-254	73	31	∀x	∀x	NUM
ma-254	73	32	,	,	PUNCT
ma-254	73	33	y	y	PROPN
ma-254	73	34	∈	∈	PROPN
ma-254	73	35	g	g	PROPN
ma-254	73	36	,	,	PUNCT
ma-254	73	37	∫	∫	PROPN
ma-254	74	1	k	k	PROPN
ma-254	74	2	φ(x	φ(x	PROPN
ma-254	74	3	∗	∗	PROPN
ma-254	74	4	k	k	PROPN
ma-254	74	5	∗	∗	NOUN
ma-254	74	6	y)dk	y)dk	PROPN
ma-254	74	7	=	=	SYM
ma-254	74	8	φ(x)φ(y),(4	φ(x)φ(y),(4	PROPN
ma-254	74	9	)	)	PUNCT
ma-254	74	10	∀x	∀x	VERB
ma-254	74	11	∈	∈	PROPN
ma-254	74	12	g	g	NOUN
ma-254	74	13	,	,	PUNCT
ma-254	74	14	φ(x	φ(x	PROPN
ma-254	74	15	�	�	X
ma-254	74	16	)	)	PUNCT
ma-254	74	17	=	=	SYM
ma-254	74	18	φ(x	φ(x	NOUN
ma-254	74	19	)	)	PUNCT
ma-254	74	20	,	,	PUNCT
ma-254	74	21	where	where	SCONJ
ma-254	74	22	φ(x	φ(x	NOUN
ma-254	74	23	)	)	PUNCT
ma-254	74	24	is	be	AUX
ma-254	74	25	the	the	DET
ma-254	74	26	complex	complex	ADJ
ma-254	74	27	conjugate	conjugate	NOUN
ma-254	74	28	of	of	ADP
ma-254	74	29	φ(x	φ(x	NOUN
ma-254	74	30	)	)	PUNCT
ma-254	74	31	.	.	PUNCT
ma-254	75	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	75	2	eur	eur	PROPN
ma-254	75	3	.	.	PUNCT
ma-254	76	1	j.	j.	PROPN
ma-254	76	2	math	math	PROPN
ma-254	76	3	.	.	PUNCT
ma-254	77	1	anal	anal	PROPN
ma-254	77	2	.	.	PUNCT
ma-254	78	1	10.28924	10.28924	NUM
ma-254	78	2	/	/	SYM
ma-254	78	3	ada	ada	PROPN
ma-254	78	4	/	/	SYM
ma-254	78	5	ma.5.3	ma.5.3	PROPN
ma-254	78	6	4	4	NUM
ma-254	78	7	the	the	DET
ma-254	78	8	set	set	NOUN
ma-254	78	9	ĝ\	ĝ\	PROPN
ma-254	78	10	is	be	AUX
ma-254	78	11	called	call	VERB
ma-254	78	12	the	the	DET
ma-254	78	13	dual	dual	ADJ
ma-254	78	14	set	set	NOUN
ma-254	78	15	of	of	ADP
ma-254	78	16	the	the	DET
ma-254	78	17	hypergroup	hypergroup	NOUN
ma-254	78	18	g	g	NOUN
ma-254	78	19	[	[	X
ma-254	78	20	5	5	NUM
ma-254	78	21	]	]	PUNCT
ma-254	78	22	.	.	PUNCT
ma-254	79	1	when	when	SCONJ
ma-254	79	2	equipped	equip	VERB
ma-254	79	3	with	with	ADP
ma-254	79	4	the	the	DET
ma-254	79	5	topology	topology	NOUN
ma-254	79	6	ofuniform	ofuniform	NOUN
ma-254	79	7	convergence	convergence	NOUN
ma-254	79	8	on	on	ADP
ma-254	79	9	compact	compact	ADJ
ma-254	79	10	sets	set	NOUN
ma-254	79	11	,	,	PUNCT
ma-254	79	12	the	the	DET
ma-254	79	13	space	space	NOUN
ma-254	79	14	ĝ\	ĝ\	PROPN
ma-254	79	15	is	be	AUX
ma-254	79	16	a	a	DET
ma-254	79	17	locally	locally	ADV
ma-254	79	18	compact	compact	ADJ
ma-254	79	19	hausdorff	hausdorff	NOUN
ma-254	79	20	space	space	NOUN
ma-254	79	21	.	.	PUNCT
ma-254	80	1	definition	definition	NOUN
ma-254	80	2	2.4	2.4	NUM
ma-254	80	3	(	(	PUNCT
ma-254	80	4	[	[	X
ma-254	80	5	5	5	NUM
ma-254	80	6	]	]	PUNCT
ma-254	80	7	)	)	PUNCT
ma-254	80	8	.	.	PUNCT
ma-254	81	1	let	let	AUX
ma-254	81	2	(	(	PUNCT
ma-254	81	3	g	g	NOUN
ma-254	81	4	,	,	PUNCT
ma-254	81	5	k	k	NOUN
ma-254	81	6	)	)	PUNCT
ma-254	81	7	be	be	VERB
ma-254	81	8	a	a	DET
ma-254	81	9	hypergroup	hypergroup	NOUN
ma-254	81	10	gelfand	gelfand	PROPN
ma-254	81	11	pair	pair	NOUN
ma-254	81	12	.	.	PUNCT
ma-254	82	1	let	let	VERB
ma-254	82	2	f	f	PROPN
ma-254	82	3	∈	∈	PROPN
ma-254	82	4	k\(g	k\(g	PROPN
ma-254	82	5	)	)	PUNCT
ma-254	82	6	.	.	PUNCT
ma-254	83	1	the	the	DET
ma-254	83	2	fourier	fourier	NOUN
ma-254	83	3	transform	transform	NOUN
ma-254	83	4	of	of	ADP
ma-254	83	5	f	f	PROPN
ma-254	83	6	is	be	AUX
ma-254	83	7	the	the	DET
ma-254	83	8	map	map	NOUN
ma-254	83	9	f̂	f̂	NUM
ma-254	83	10	:	:	PUNCT
ma-254	83	11	ĝ\	ĝ\	PROPN
ma-254	83	12	−→	−→	NOUN
ma-254	83	13	c	c	NOUN
ma-254	83	14	defined	define	VERB
ma-254	83	15	by	by	ADP
ma-254	83	16	f̂	f̂	PROPN
ma-254	83	17	(	(	PUNCT
ma-254	83	18	φ	φ	NOUN
ma-254	83	19	)	)	PUNCT
ma-254	84	1	=	=	SYM
ma-254	84	2	∫	∫	PROPN
ma-254	84	3	g	g	PROPN
ma-254	84	4	φ(x	φ(x	PROPN
ma-254	84	5	�	�	NOUN
ma-254	84	6	)f	)f	NOUN
ma-254	84	7	(	(	PUNCT
ma-254	84	8	x)dx	x)dx	PROPN
ma-254	84	9	.	.	PUNCT
ma-254	85	1	by	by	ADP
ma-254	85	2	a	a	DET
ma-254	85	3	classical	classical	ADJ
ma-254	85	4	argument	argument	NOUN
ma-254	85	5	,	,	PUNCT
ma-254	85	6	the	the	DET
ma-254	85	7	inverse	inverse	NOUN
ma-254	85	8	fourier	fourier	NOUN
ma-254	85	9	transform	transform	NOUN
ma-254	85	10	is	be	AUX
ma-254	85	11	given	give	VERB
ma-254	85	12	by	by	ADP
ma-254	85	13	f	f	PROPN
ma-254	85	14	(	(	PUNCT
ma-254	85	15	x	x	NOUN
ma-254	85	16	)	)	PUNCT
ma-254	85	17	=	=	SYM
ma-254	86	1	∫	∫	PROPN
ma-254	86	2	ĝ\	ĝ\	PROPN
ma-254	86	3	φ(x)f̂	φ(x)f̂	PROPN
ma-254	86	4	(	(	PUNCT
ma-254	86	5	φ)dπ(φ	φ)dπ(φ	NOUN
ma-254	86	6	)	)	PUNCT
ma-254	86	7	where	where	SCONJ
ma-254	86	8	the	the	DET
ma-254	86	9	existence	existence	NOUN
ma-254	86	10	of	of	ADP
ma-254	86	11	the	the	DET
ma-254	86	12	measure	measure	NOUN
ma-254	86	13	π	π	NOUN
ma-254	86	14	is	be	AUX
ma-254	86	15	ensured	ensure	VERB
ma-254	86	16	by	by	ADP
ma-254	86	17	the	the	DET
ma-254	86	18	following	follow	VERB
ma-254	86	19	theorem	theorem	NOUN
ma-254	86	20	(	(	PUNCT
ma-254	86	21	theorem	theorem	VERB
ma-254	86	22	2.5	2.5	NUM
ma-254	86	23	)	)	PUNCT
ma-254	86	24	.	.	PUNCT
ma-254	87	1	theorem	theorem	VERB
ma-254	87	2	2.5	2.5	NUM
ma-254	87	3	(	(	PUNCT
ma-254	87	4	[	[	X
ma-254	87	5	5	5	NUM
ma-254	87	6	]	]	PUNCT
ma-254	87	7	)	)	PUNCT
ma-254	87	8	.	.	PUNCT
ma-254	88	1	let	let	AUX
ma-254	88	2	(	(	PUNCT
ma-254	88	3	g	g	NOUN
ma-254	88	4	,	,	PUNCT
ma-254	88	5	k	k	NOUN
ma-254	88	6	)	)	PUNCT
ma-254	88	7	be	be	VERB
ma-254	88	8	a	a	DET
ma-254	88	9	hypergroup	hypergroup	NOUN
ma-254	88	10	gelfand	gelfand	PROPN
ma-254	88	11	pair	pair	NOUN
ma-254	88	12	.	.	PUNCT
ma-254	89	1	there	there	PRON
ma-254	89	2	exists	exist	VERB
ma-254	89	3	a	a	DET
ma-254	89	4	unique	unique	ADJ
ma-254	89	5	nonnegative	nonnegative	ADJ
ma-254	89	6	measure	measure	NOUN
ma-254	89	7	π	π	PROPN
ma-254	89	8	on	on	ADP
ma-254	89	9	ĝ\	ĝ\	PROPN
ma-254	89	10	such	such	ADJ
ma-254	89	11	that∫	that∫	NOUN
ma-254	89	12	g	g	PROPN
ma-254	89	13	|f	|f	PROPN
ma-254	90	1	(	(	PUNCT
ma-254	90	2	x)|2dx	x)|2dx	PROPN
ma-254	90	3	=	=	SYM
ma-254	90	4	∫	∫	PROPN
ma-254	90	5	ĝ\	ĝ\	PROPN
ma-254	90	6	|f̂	|f̂	ADV
ma-254	90	7	(	(	PUNCT
ma-254	90	8	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	90	9	)	)	PUNCT
ma-254	90	10	,	,	PUNCT
ma-254	90	11	∀f	∀f	PROPN
ma-254	90	12	∈	∈	PROPN
ma-254	90	13	l1(g	l1(g	PROPN
ma-254	90	14	)	)	PUNCT
ma-254	90	15	∩	∩	NOUN
ma-254	90	16	l2(g	l2(g	VERB
ma-254	90	17	)	)	PUNCT
ma-254	90	18	.	.	PUNCT
ma-254	91	1	hereafter	hereafter	PROPN
ma-254	91	2	are	be	AUX
ma-254	91	3	the	the	DET
ma-254	91	4	analogue	analogue	NOUN
ma-254	91	5	of	of	ADP
ma-254	91	6	the	the	DET
ma-254	91	7	hausdorff	hausdorff	NOUN
ma-254	91	8	-	-	PUNCT
ma-254	91	9	young	young	ADJ
ma-254	91	10	inequality	inequality	NOUN
ma-254	91	11	and	and	CCONJ
ma-254	91	12	its	its	PRON
ma-254	91	13	inverse	inverse	NOUN
ma-254	91	14	inequality	inequality	NOUN
ma-254	91	15	.	.	PUNCT
ma-254	92	1	theorem	theorem	VERB
ma-254	92	2	2.6	2.6	NUM
ma-254	92	3	.	.	PUNCT
ma-254	93	1	[	[	X
ma-254	93	2	7	7	X
ma-254	93	3	]	]	PUNCT
ma-254	93	4	let	let	VERB
ma-254	93	5	p	p	PRON
ma-254	93	6	,	,	PUNCT
ma-254	93	7	q	q	ADJ
ma-254	93	8	be	be	AUX
ma-254	93	9	such	such	ADJ
ma-254	93	10	that	that	SCONJ
ma-254	93	11	1	1	NUM
ma-254	93	12	≤	≤	NOUN
ma-254	93	13	p	p	NOUN
ma-254	93	14	≤	≤	ADJ
ma-254	93	15	2	2	NUM
ma-254	93	16	and	and	CCONJ
ma-254	93	17	1	1	NUM
ma-254	94	1	p	p	NOUN
ma-254	94	2	+	+	NOUN
ma-254	94	3	1	1	NUM
ma-254	94	4	p′	p′	NOUN
ma-254	94	5	=	=	SYM
ma-254	94	6	1	1	X
ma-254	94	7	.	.	PUNCT
ma-254	95	1	then	then	ADV
ma-254	95	2	,	,	PUNCT
ma-254	95	3	the	the	DET
ma-254	95	4	following	follow	VERB
ma-254	95	5	inequalities	inequality	NOUN
ma-254	95	6	hold.(1	hold.(1	PROPN
ma-254	95	7	)	)	PUNCT
ma-254	95	8	‖f̂	‖f̂	NUM
ma-254	95	9	‖p′	‖p′	NOUN
ma-254	95	10	≤	≤	NOUN
ma-254	95	11	‖f	‖f	ADP
ma-254	96	1	‖p	‖p	PROPN
ma-254	96	2	,	,	PUNCT
ma-254	96	3	for	for	ADP
ma-254	96	4	all	all	DET
ma-254	96	5	f	f	PROPN
ma-254	96	6	∈	∈	PROPN
ma-254	96	7	lp(g).(2	lp(g).(2	ADJ
ma-254	96	8	)	)	PUNCT
ma-254	96	9	‖f	‖f	PUNCT
ma-254	97	1	‖p′	‖p′	NOUN
ma-254	97	2	≤	≤	NUM
ma-254	97	3	‖f̂	‖f̂	NUM
ma-254	97	4	‖p	‖p	PROPN
ma-254	97	5	,	,	PUNCT
ma-254	97	6	for	for	ADP
ma-254	97	7	all	all	DET
ma-254	97	8	f	f	PROPN
ma-254	97	9	∈	∈	PROPN
ma-254	97	10	lp′(g	lp′(g	PROPN
ma-254	97	11	)	)	PUNCT
ma-254	97	12	.	.	PUNCT
ma-254	98	1	3	3	X
ma-254	98	2	.	.	X
ma-254	98	3	sobolev	sobolev	NOUN
ma-254	98	4	spaces	space	NOUN
ma-254	98	5	and	and	CCONJ
ma-254	98	6	embedding	embed	VERB
ma-254	98	7	results	result	NOUN
ma-254	98	8	definition	definition	NOUN
ma-254	98	9	3.1	3.1	NUM
ma-254	98	10	.	.	PUNCT
ma-254	99	1	[	[	X
ma-254	99	2	2	2	NUM
ma-254	99	3	]	]	X
ma-254	99	4	let	let	VERB
ma-254	99	5	(	(	PUNCT
ma-254	99	6	g	g	NOUN
ma-254	99	7	,	,	PUNCT
ma-254	99	8	k	k	NOUN
ma-254	99	9	)	)	PUNCT
ma-254	99	10	be	be	VERB
ma-254	99	11	a	a	DET
ma-254	99	12	hypergroup	hypergroup	NOUN
ma-254	99	13	gelfand	gelfand	PROPN
ma-254	99	14	pair	pair	NOUN
ma-254	99	15	.	.	PUNCT
ma-254	100	1	let	let	VERB
ma-254	100	2	γ	γ	NOUN
ma-254	100	3	:	:	PUNCT
ma-254	100	4	ĝ\	ĝ\	PROPN
ma-254	100	5	−→	−→	NOUN
ma-254	100	6	r+	r+	PUNCT
ma-254	100	7	be	be	AUX
ma-254	100	8	a	a	DET
ma-254	100	9	positive	positive	ADJ
ma-254	100	10	measurable	measurable	ADJ
ma-254	100	11	function	function	NOUN
ma-254	100	12	and	and	CCONJ
ma-254	100	13	let	let	VERB
ma-254	100	14	s	s	PRON
ma-254	100	15	∈	∈	PROPN
ma-254	100	16	(	(	PUNCT
ma-254	100	17	0,+∞	0,+∞	NUM
ma-254	100	18	)	)	PUNCT
ma-254	100	19	.	.	PUNCT
ma-254	101	1	the	the	DET
ma-254	101	2	set	set	ADJ
ma-254	101	3	hs,\γ	hs,\γ	PROPN
ma-254	101	4	(	(	PUNCT
ma-254	101	5	g	g	NOUN
ma-254	101	6	)	)	PUNCT
ma-254	101	7	=	=	NOUN
ma-254	101	8	{	{	PUNCT
ma-254	101	9	f	f	PROPN
ma-254	101	10	∈	∈	PROPN
ma-254	101	11	l2,\(g	l2,\(g	PROPN
ma-254	101	12	)	)	PUNCT
ma-254	101	13	:	:	PUNCT
ma-254	102	1	∫	∫	PROPN
ma-254	102	2	ĝ\	ĝ\	PROPN
ma-254	102	3	(	(	PUNCT
ma-254	102	4	1	1	NUM
ma-254	102	5	+	+	CCONJ
ma-254	102	6	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	102	7	|f̂	|f̂	X
ma-254	102	8	(	(	PUNCT
ma-254	102	9	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	102	10	)	)	PUNCT
ma-254	103	1	<	<	X
ma-254	103	2	∞	∞	PROPN
ma-254	103	3	}	}	PUNCT
ma-254	103	4	provided	provide	VERB
ma-254	103	5	with	with	ADP
ma-254	103	6	the	the	DET
ma-254	103	7	norm	norm	NOUN
ma-254	103	8	‖f	‖f	PRON
ma-254	103	9	‖	‖	PROPN
ma-254	103	10	hs,\γ	hs,\γ	PROPN
ma-254	103	11	=	=	SYM
ma-254	103	12	(	(	PUNCT
ma-254	103	13	∫	∫	PROPN
ma-254	103	14	ĝ\	ĝ\	PROPN
ma-254	103	15	(	(	PUNCT
ma-254	103	16	1	1	NUM
ma-254	103	17	+	+	CCONJ
ma-254	103	18	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	103	19	|f̂	|f̂	X
ma-254	103	20	(	(	PUNCT
ma-254	103	21	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	103	22	)	)	PUNCT
ma-254	103	23	)	)	PUNCT
ma-254	103	24	1	1	NUM
ma-254	103	25	2	2	NUM
ma-254	103	26	will	will	AUX
ma-254	103	27	be	be	AUX
ma-254	103	28	called	call	VERB
ma-254	103	29	a	a	DET
ma-254	103	30	sobolev	sobolev	ADJ
ma-254	103	31	space	space	NOUN
ma-254	103	32	.	.	PUNCT
ma-254	104	1	in	in	ADP
ma-254	104	2	the	the	DET
ma-254	104	3	sequel	sequel	NOUN
ma-254	104	4	,	,	PUNCT
ma-254	104	5	the	the	DET
ma-254	104	6	symbol	symbol	NOUN
ma-254	104	7	↪	↪	PROPN
ma-254	104	8	→	→	SYM
ma-254	104	9	denotes	denote	VERB
ma-254	104	10	the	the	DET
ma-254	104	11	continuous	continuous	ADJ
ma-254	104	12	embedding	embedding	NOUN
ma-254	104	13	.	.	PUNCT
ma-254	105	1	theorem	theorem	ADJ
ma-254	105	2	3.2	3.2	NUM
ma-254	105	3	.	.	PUNCT
ma-254	106	1	let	let	AUX
ma-254	106	2	(	(	PUNCT
ma-254	106	3	g	g	NOUN
ma-254	106	4	,	,	PUNCT
ma-254	106	5	k	k	NOUN
ma-254	106	6	)	)	PUNCT
ma-254	106	7	be	be	VERB
ma-254	106	8	a	a	DET
ma-254	106	9	hypergroup	hypergroup	NOUN
ma-254	106	10	gelfand	gelfand	PROPN
ma-254	106	11	pair	pair	NOUN
ma-254	106	12	.	.	PUNCT
ma-254	107	1	let	let	VERB
ma-254	107	2	α	α	PRON
ma-254	107	3	>	>	X
ma-254	107	4	s	s	PROPN
ma-254	107	5	>	>	X
ma-254	107	6	0	0	PUNCT
ma-254	108	1	and	and	CCONJ
ma-254	108	2	let	let	VERB
ma-254	108	3	p	p	NOUN
ma-254	108	4	=	=	PUNCT
ma-254	108	5	2α	2α	X
ma-254	108	6	α+	α+	X
ma-254	108	7	s	s	X
ma-254	108	8	.	.	PUNCT
ma-254	109	1	let	let	VERB
ma-254	109	2	p′	p′	NOUN
ma-254	109	3	be	be	AUX
ma-254	109	4	such	such	ADJ
ma-254	109	5	that	that	SCONJ
ma-254	109	6	1	1	NUM
ma-254	109	7	p	p	NOUN
ma-254	109	8	+	+	NOUN
ma-254	109	9	1	1	NUM
ma-254	109	10	p′	p′	NOUN
ma-254	109	11	=	=	SYM
ma-254	109	12	1	1	X
ma-254	109	13	.	.	PUNCT
ma-254	110	1	if	if	SCONJ
ma-254	110	2	(	(	PUNCT
ma-254	110	3	1	1	NUM
ma-254	110	4	+	+	NUM
ma-254	110	5	γ2)−1	γ2)−1	X
ma-254	110	6	∈	∈	NOUN
ma-254	110	7	lα(ĝ\	lα(ĝ\	PUNCT
ma-254	110	8	)	)	PUNCT
ma-254	110	9	,	,	PUNCT
ma-254	110	10	then	then	ADV
ma-254	110	11	hs,\γ	hs,\γ	PROPN
ma-254	110	12	(	(	PUNCT
ma-254	110	13	g	g	NOUN
ma-254	110	14	)	)	PUNCT
ma-254	110	15	↪	↪	PROPN
ma-254	110	16	→	→	SYM
ma-254	110	17	lp	lp	ADJ
ma-254	110	18	′,\(g	′,\(g	PROPN
ma-254	110	19	)	)	PUNCT
ma-254	110	20	.	.	PUNCT
ma-254	111	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	111	2	eur	eur	PROPN
ma-254	111	3	.	.	PUNCT
ma-254	112	1	j.	j.	PROPN
ma-254	112	2	math	math	PROPN
ma-254	112	3	.	.	PUNCT
ma-254	113	1	anal	anal	PROPN
ma-254	113	2	.	.	PUNCT
ma-254	114	1	10.28924	10.28924	NUM
ma-254	114	2	/	/	SYM
ma-254	114	3	ada	ada	PROPN
ma-254	114	4	/	/	SYM
ma-254	114	5	ma.5.3	ma.5.3	PROPN
ma-254	114	6	5	5	NUM
ma-254	114	7	proof	proof	NOUN
ma-254	114	8	.	.	PUNCT
ma-254	115	1	the	the	DET
ma-254	115	2	conditions	condition	NOUN
ma-254	115	3	about	about	ADP
ma-254	115	4	α	α	PROPN
ma-254	115	5	and	and	CCONJ
ma-254	115	6	s	s	AUX
ma-254	115	7	imply	imply	NOUN
ma-254	115	8	1	1	NUM
ma-254	115	9	<	<	X
ma-254	115	10	p	p	X
ma-254	115	11	<	<	X
ma-254	115	12	2	2	NUM
ma-254	115	13	.	.	PUNCT
ma-254	115	14	then	then	ADV
ma-254	115	15	,	,	PUNCT
ma-254	115	16	by	by	ADP
ma-254	115	17	the	the	DET
ma-254	115	18	inverse	inverse	NOUN
ma-254	115	19	hausdorff	hausdorff	NOUN
ma-254	115	20	-	-	PUNCT
ma-254	115	21	younginequality	younginequality	NOUN
ma-254	115	22	in	in	ADP
ma-254	115	23	theorem	theorem	NOUN
ma-254	115	24	2.6	2.6	NUM
ma-254	115	25	,	,	PUNCT
ma-254	115	26	we	we	PRON
ma-254	115	27	have	have	VERB
ma-254	115	28	‖f	‖f	PRON
ma-254	115	29	‖p′	‖p′	NOUN
ma-254	115	30	≤	≤	NUM
ma-254	115	31	‖f̂	‖f̂	NUM
ma-254	115	32	‖p	‖p	PROPN
ma-254	115	33	.	.	PUNCT
ma-254	116	1	‖f̂	‖f̂	X
ma-254	116	2	‖pp	‖pp	NUM
ma-254	116	3	=	=	SYM
ma-254	116	4	∫	∫	PROPN
ma-254	117	1	ĝ\	ĝ\	PROPN
ma-254	117	2	|f̂	|f̂	ADV
ma-254	117	3	(	(	PUNCT
ma-254	117	4	φ)|pdπ(φ	φ)|pdπ(φ	NUM
ma-254	117	5	)	)	PUNCT
ma-254	117	6	=	=	SYM
ma-254	118	1	∫	∫	PROPN
ma-254	118	2	ĝ\	ĝ\	PROPN
ma-254	118	3	|f̂	|f̂	ADV
ma-254	118	4	(	(	PUNCT
ma-254	118	5	φ)|p	φ)|p	NOUN
ma-254	118	6	·	·	PUNCT
ma-254	118	7	(	(	PUNCT
ma-254	118	8	1	1	NUM
ma-254	118	9	+	+	CCONJ
ma-254	118	10	γ(φ)2	γ(φ)2	PROPN
ma-254	118	11	)	)	PUNCT
ma-254	118	12	sp	sp	ADP
ma-254	118	13	2	2	NUM
ma-254	118	14	(	(	PUNCT
ma-254	118	15	1	1	NUM
ma-254	118	16	+	+	CCONJ
ma-254	118	17	γ(φ)2	γ(φ)2	PROPN
ma-254	118	18	)	)	PUNCT
ma-254	118	19	sp	sp	ADP
ma-254	118	20	2	2	NUM
ma-254	118	21	dπ(φ	dπ(φ	NUM
ma-254	118	22	)	)	PUNCT
ma-254	118	23	=	=	SYM
ma-254	119	1	∫	∫	PROPN
ma-254	119	2	ĝ\	ĝ\	PROPN
ma-254	119	3	|f̂	|f̂	ADV
ma-254	119	4	(	(	PUNCT
ma-254	119	5	φ)|	φ)|	VERB
ma-254	119	6	2p	2p	NUM
ma-254	119	7	2	2	NUM
ma-254	119	8	(	(	PUNCT
ma-254	119	9	1	1	NUM
ma-254	119	10	+	+	CCONJ
ma-254	119	11	γ(φ)2	γ(φ)2	PROPN
ma-254	119	12	)	)	PUNCT
ma-254	119	13	sp	sp	ADP
ma-254	119	14	2	2	NUM
ma-254	119	15	(	(	PUNCT
ma-254	119	16	1	1	NUM
ma-254	119	17	+	+	CCONJ
ma-254	119	18	γ(φ)2	γ(φ)2	PROPN
ma-254	119	19	)	)	PUNCT
ma-254	119	20	−	−	PROPN
ma-254	119	21	sp(2−p	sp(2−p	PROPN
ma-254	119	22	)	)	PUNCT
ma-254	119	23	2(2−p	2(2−p	NUM
ma-254	119	24	)	)	PUNCT
ma-254	119	25	dπ(φ	dπ(φ	NUM
ma-254	119	26	)	)	PUNCT
ma-254	119	27	.	.	PUNCT
ma-254	120	1	since	since	SCONJ
ma-254	120	2	p	p	PROPN
ma-254	120	3	2	2	NUM
ma-254	120	4	+	+	NUM
ma-254	120	5	2−	2−	NUM
ma-254	120	6	p	p	NOUN
ma-254	120	7	2	2	NUM
ma-254	120	8	=	=	SYM
ma-254	120	9	1	1	NUM
ma-254	120	10	,	,	PUNCT
ma-254	120	11	then	then	ADV
ma-254	120	12	by	by	ADP
ma-254	120	13	the	the	DET
ma-254	120	14	hölder	hölder	PROPN
ma-254	120	15	’s	’s	PART
ma-254	120	16	inequality	inequality	NOUN
ma-254	120	17	,	,	PUNCT
ma-254	120	18	we	we	PRON
ma-254	120	19	have	have	VERB
ma-254	120	20	‖f̂	‖f̂	NUM
ma-254	120	21	‖pp	‖pp	NUM
ma-254	120	22	≤	≤	NUM
ma-254	121	1	(	(	PUNCT
ma-254	121	2	∫	∫	PROPN
ma-254	121	3	ĝ\	ĝ\	PROPN
ma-254	121	4	(	(	PUNCT
ma-254	121	5	1	1	NUM
ma-254	121	6	+	+	CCONJ
ma-254	121	7	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	121	8	|f̂	|f̂	X
ma-254	121	9	(	(	PUNCT
ma-254	121	10	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	121	11	)	)	PUNCT
ma-254	121	12	)	)	PUNCT
ma-254	122	1	p	p	NOUN
ma-254	122	2	2	2	NUM
ma-254	122	3	(	(	PUNCT
ma-254	122	4	∫	∫	PROPN
ma-254	122	5	ĝ\	ĝ\	PROPN
ma-254	122	6	(	(	PUNCT
ma-254	122	7	1	1	NUM
ma-254	122	8	+	+	NUM
ma-254	122	9	γ(φ)2)−	γ(φ)2)−	NUM
ma-254	122	10	sp	sp	ADP
ma-254	122	11	2−p	2−p	NUM
ma-254	122	12	dπ(φ	dπ(φ	NUM
ma-254	122	13	)	)	PUNCT
ma-254	122	14	)	)	PUNCT
ma-254	123	1	2−p	2−p	NUM
ma-254	123	2	2	2	NUM
ma-254	123	3	‖f̂	‖f̂	NUM
ma-254	123	4	‖p	‖p	NOUN
ma-254	123	5	≤	≤	NOUN
ma-254	123	6	(	(	PUNCT
ma-254	124	1	∫	∫	PROPN
ma-254	124	2	ĝ\	ĝ\	PROPN
ma-254	124	3	(	(	PUNCT
ma-254	124	4	1	1	NUM
ma-254	124	5	+	+	CCONJ
ma-254	124	6	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	124	7	|f̂	|f̂	X
ma-254	124	8	(	(	PUNCT
ma-254	124	9	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	124	10	)	)	PUNCT
ma-254	124	11	)	)	PUNCT
ma-254	124	12	1	1	NUM
ma-254	124	13	2	2	NUM
ma-254	124	14	(	(	PUNCT
ma-254	124	15	∫	∫	PROPN
ma-254	124	16	ĝ\	ĝ\	PROPN
ma-254	124	17	(	(	PUNCT
ma-254	124	18	1	1	NUM
ma-254	124	19	+	+	NUM
ma-254	124	20	γ(φ)2)−	γ(φ)2)−	NUM
ma-254	124	21	sp	sp	ADP
ma-254	124	22	2−p	2−p	NUM
ma-254	124	23	dπ(φ	dπ(φ	NUM
ma-254	124	24	)	)	PUNCT
ma-254	124	25	)	)	PUNCT
ma-254	125	1	2−p	2−p	NUM
ma-254	125	2	2p	2p	NOUN
ma-254	125	3	≤	≤	NOUN
ma-254	125	4	‖f	‖f	ADP
ma-254	126	1	‖	‖	PROPN
ma-254	126	2	hs,\γ	hs,\γ	PROPN
ma-254	126	3	(	(	PUNCT
ma-254	126	4	∫	∫	PROPN
ma-254	126	5	ĝ\	ĝ\	PROPN
ma-254	126	6	(	(	PUNCT
ma-254	126	7	1	1	NUM
ma-254	126	8	+	+	NUM
ma-254	126	9	γ(φ)2)−	γ(φ)2)−	NUM
ma-254	126	10	sp	sp	ADP
ma-254	126	11	2−p	2−p	NUM
ma-254	126	12	dπ(φ	dπ(φ	NUM
ma-254	126	13	)	)	PUNCT
ma-254	126	14	)	)	PUNCT
ma-254	127	1	2−p	2−p	NUM
ma-254	127	2	2p	2p	NOUN
ma-254	127	3	≤	≤	NOUN
ma-254	127	4	‖f	‖f	ADP
ma-254	127	5	‖	‖	PROPN
ma-254	127	6	hs,\γ	hs,\γ	PROPN
ma-254	127	7	‖(1	‖(1	PRON
ma-254	128	1	+	+	CCONJ
ma-254	128	2	γ2)−1‖	γ2)−1‖	PROPN
ma-254	128	3	s	s	PROPN
ma-254	128	4	2	2	NUM
ma-254	128	5	α	α	NOUN
ma-254	128	6	since	since	SCONJ
ma-254	128	7	α	α	PROPN
ma-254	128	8	=	=	PUNCT
ma-254	128	9	sp	sp	ADP
ma-254	128	10	2−	2−	NUM
ma-254	128	11	p	p	NOUN
ma-254	128	12	.	.	PUNCT
ma-254	129	1	finally	finally	ADV
ma-254	129	2	,	,	PUNCT
ma-254	129	3	‖f	‖f	ADP
ma-254	129	4	‖p′	‖p′	NOUN
ma-254	129	5	≤	≤	NUM
ma-254	129	6	‖f̂	‖f̂	PUNCT
ma-254	129	7	‖p	‖p	NOUN
ma-254	129	8	≤	≤	NOUN
ma-254	129	9	‖f	‖f	ADP
ma-254	129	10	‖hs,\γ	‖hs,\γ	NOUN
ma-254	130	1	‖(1	‖(1	NUM
ma-254	131	1	+	+	NUM
ma-254	131	2	γ2)−1‖	γ2)−1‖	PROPN
ma-254	131	3	s	s	PROPN
ma-254	131	4	2	2	NUM
ma-254	131	5	α	α	NOUN
ma-254	131	6	.	.	PUNCT
ma-254	132	1	thus	thus	ADV
ma-254	132	2	,	,	PUNCT
ma-254	132	3	hs,\γ	hs,\γ	PROPN
ma-254	132	4	(	(	PUNCT
ma-254	132	5	g	g	NOUN
ma-254	132	6	)	)	PUNCT
ma-254	132	7	↪	↪	PROPN
ma-254	132	8	→	→	SYM
ma-254	132	9	lp	lp	ADJ
ma-254	132	10	′,\(g	′,\(g	PROPN
ma-254	132	11	)	)	PUNCT
ma-254	132	12	.	.	PUNCT
ma-254	133	1	�	�	PROPN
ma-254	133	2	lemma	lemma	PROPN
ma-254	133	3	3.3	3.3	NUM
ma-254	133	4	.	.	PUNCT
ma-254	134	1	let	let	AUX
ma-254	134	2	(	(	PUNCT
ma-254	134	3	g	g	NOUN
ma-254	134	4	,	,	PUNCT
ma-254	134	5	k	k	NOUN
ma-254	134	6	)	)	PUNCT
ma-254	134	7	be	be	VERB
ma-254	134	8	a	a	DET
ma-254	134	9	hypergroup	hypergroup	NOUN
ma-254	134	10	gelfand	gelfand	PROPN
ma-254	134	11	pair	pair	NOUN
ma-254	134	12	.	.	PUNCT
ma-254	135	1	if	if	SCONJ
ma-254	135	2	φ	φ	PROPN
ma-254	135	3	∈	∈	PROPN
ma-254	135	4	ĝ\	ĝ\	PROPN
ma-254	135	5	,	,	PUNCT
ma-254	135	6	then	then	ADV
ma-254	135	7	∀g	∀g	PROPN
ma-254	135	8	∈	∈	PROPN
ma-254	135	9	k\(g	k\(g	PROPN
ma-254	135	10	)	)	PUNCT
ma-254	135	11	,	,	PUNCT
ma-254	135	12	g	g	PROPN
ma-254	135	13	∗φ	∗φ	PROPN
ma-254	135	14	=	=	SYM
ma-254	135	15	ĝ(φ)φ	ĝ(φ)φ	PROPN
ma-254	135	16	.	.	PUNCT
ma-254	135	17	proof	proof	NOUN
ma-254	135	18	.	.	PUNCT
ma-254	136	1	let	let	VERB
ma-254	136	2	f	f	NOUN
ma-254	136	3	,	,	PUNCT
ma-254	136	4	g	g	PROPN
ma-254	136	5	∈	∈	PROPN
ma-254	136	6	k\(g	k\(g	PROPN
ma-254	136	7	)	)	PUNCT
ma-254	136	8	.	.	PUNCT
ma-254	137	1	consider	consider	VERB
ma-254	137	2	φ(g	φ(g	NOUN
ma-254	137	3	)	)	PUNCT
ma-254	137	4	=	=	PUNCT
ma-254	137	5	ĝ(φ	ĝ(φ	NOUN
ma-254	137	6	)	)	PUNCT
ma-254	137	7	.	.	PUNCT
ma-254	138	1	set	set	VERB
ma-254	138	2	a	a	DET
ma-254	138	3	=	=	X
ma-254	138	4	∫	∫	PROPN
ma-254	138	5	g	g	PROPN
ma-254	138	6	f	f	PROPN
ma-254	138	7	(	(	PUNCT
ma-254	138	8	x)φ(g)φ(x	x)φ(g)φ(x	PROPN
ma-254	138	9	�	�	NOUN
ma-254	138	10	)dx	)dx	ADJ
ma-254	138	11	.	.	PUNCT
ma-254	139	1	we	we	PRON
ma-254	139	2	have	have	VERB
ma-254	139	3	a	a	DET
ma-254	139	4	=	=	SYM
ma-254	139	5	φ(f	φ(f	PROPN
ma-254	139	6	)	)	PUNCT
ma-254	139	7	φ(g	φ(g	PROPN
ma-254	139	8	)	)	PUNCT
ma-254	139	9	=	=	SYM
ma-254	139	10	φ(f	φ(f	PROPN
ma-254	139	11	∗	∗	NOUN
ma-254	139	12	g	g	NOUN
ma-254	139	13	)	)	PUNCT
ma-254	139	14	(	(	PUNCT
ma-254	139	15	the	the	DET
ma-254	139	16	convolution	convolution	NOUN
ma-254	139	17	theorem	theorem	VERB
ma-254	139	18	)	)	PUNCT
ma-254	139	19	=	=	SYM
ma-254	140	1	∫	∫	PROPN
ma-254	140	2	g	g	PROPN
ma-254	140	3	f	f	PROPN
ma-254	140	4	∗	∗	PROPN
ma-254	140	5	g(x)φ(x	g(x)φ(x	PROPN
ma-254	140	6	�	�	PROPN
ma-254	140	7	)dx	)dx	ADJ
ma-254	140	8	=	=	SYM
ma-254	140	9	∫	∫	PROPN
ma-254	140	10	g	g	PROPN
ma-254	140	11	φ(x	φ(x	PROPN
ma-254	140	12	�	�	PROPN
ma-254	140	13	)	)	PUNCT
ma-254	140	14	(	(	PUNCT
ma-254	140	15	∫	∫	PROPN
ma-254	140	16	g	g	PROPN
ma-254	140	17	f	f	PROPN
ma-254	140	18	(	(	PUNCT
ma-254	140	19	x	x	PROPN
ma-254	140	20	∗	∗	PROPN
ma-254	140	21	y)g(y	y)g(y	NOUN
ma-254	140	22	�	�	PROPN
ma-254	140	23	)dy	)dy	PUNCT
ma-254	140	24	)	)	PUNCT
ma-254	141	1	dx	dx	PROPN
ma-254	142	1	=	=	SYM
ma-254	142	2	∫	∫	PROPN
ma-254	142	3	g	g	PROPN
ma-254	142	4	g(y	g(y	PROPN
ma-254	142	5	�	�	PROPN
ma-254	142	6	)	)	PUNCT
ma-254	142	7	(	(	PUNCT
ma-254	142	8	∫	∫	PROPN
ma-254	142	9	g	g	PROPN
ma-254	142	10	f	f	PROPN
ma-254	142	11	(	(	PUNCT
ma-254	142	12	x	x	PROPN
ma-254	142	13	∗	∗	PROPN
ma-254	142	14	y)φ(x	y)φ(x	NOUN
ma-254	142	15	�	�	PROPN
ma-254	142	16	)dx	)dx	ADJ
ma-254	142	17	)	)	PUNCT
ma-254	143	1	dy	dy	NOUN
ma-254	143	2	(	(	PUNCT
ma-254	143	3	the	the	DET
ma-254	143	4	fubini	fubini	NOUN
ma-254	143	5	’s	’s	PART
ma-254	143	6	theorem	theorem	ADJ
ma-254	143	7	)	)	PUNCT
ma-254	143	8	=	=	SYM
ma-254	143	9	∫	∫	PROPN
ma-254	143	10	g	g	PROPN
ma-254	143	11	g(y	g(y	PROPN
ma-254	143	12	�	�	PROPN
ma-254	143	13	)	)	PUNCT
ma-254	143	14	(	(	PUNCT
ma-254	143	15	∫	∫	PROPN
ma-254	143	16	g	g	PROPN
ma-254	143	17	f	f	PROPN
ma-254	143	18	(	(	PUNCT
ma-254	143	19	x)φ(y	x)φ(y	PROPN
ma-254	143	20	∗	∗	PROPN
ma-254	143	21	x	x	NOUN
ma-254	143	22	�	�	NOUN
ma-254	143	23	)dx	)dx	ADJ
ma-254	143	24	)	)	PUNCT
ma-254	144	1	dy	dy	NOUN
ma-254	144	2	=	=	SYM
ma-254	145	1	∫	∫	PROPN
ma-254	145	2	g	g	PROPN
ma-254	145	3	f	f	PROPN
ma-254	145	4	(	(	PUNCT
ma-254	145	5	x	x	X
ma-254	145	6	)	)	PUNCT
ma-254	145	7	(	(	PUNCT
ma-254	145	8	∫	∫	PROPN
ma-254	145	9	g	g	PROPN
ma-254	145	10	g(y	g(y	PROPN
ma-254	145	11	�	�	PROPN
ma-254	145	12	)φ(y	)φ(y	ADJ
ma-254	145	13	∗	∗	X
ma-254	145	14	x	x	NOUN
ma-254	145	15	�	�	PROPN
ma-254	145	16	)dy	)dy	PUNCT
ma-254	145	17	)	)	PUNCT
ma-254	146	1	dx	dx	PROPN
ma-254	146	2	(	(	PUNCT
ma-254	146	3	again	again	ADV
ma-254	146	4	the	the	DET
ma-254	146	5	fubini	fubini	NOUN
ma-254	146	6	’s	’s	PART
ma-254	146	7	theorem	theorem	ADJ
ma-254	146	8	)	)	PUNCT
ma-254	146	9	=	=	SYM
ma-254	147	1	∫	∫	PROPN
ma-254	147	2	g	g	PROPN
ma-254	147	3	f	f	PROPN
ma-254	147	4	(	(	PUNCT
ma-254	147	5	x	x	X
ma-254	147	6	)	)	PUNCT
ma-254	147	7	(	(	PUNCT
ma-254	147	8	∫	∫	PROPN
ma-254	147	9	g	g	PROPN
ma-254	147	10	g(y)φ(y	g(y)φ(y	PROPN
ma-254	147	11	�	�	PROPN
ma-254	147	12	∗	∗	X
ma-254	147	13	x	x	NOUN
ma-254	147	14	�	�	NOUN
ma-254	147	15	)dy	)dy	PUNCT
ma-254	147	16	)	)	PUNCT
ma-254	148	1	dx	dx	PROPN
ma-254	148	2	(	(	PUNCT
ma-254	148	3	change	change	NOUN
ma-254	148	4	of	of	ADP
ma-254	148	5	variable	variable	ADJ
ma-254	148	6	y	y	PROPN
ma-254	148	7	→	→	SYM
ma-254	148	8	y	y	PROPN
ma-254	148	9	�	�	PROPN
ma-254	148	10	)	)	PUNCT
ma-254	148	11	=	=	SYM
ma-254	149	1	∫	∫	PROPN
ma-254	149	2	g	g	PROPN
ma-254	149	3	f	f	PROPN
ma-254	149	4	(	(	PUNCT
ma-254	149	5	x)(g	x)(g	PROPN
ma-254	149	6	∗	∗	NOUN
ma-254	149	7	φ)(x	φ)(x	NUM
ma-254	149	8	�	�	NOUN
ma-254	149	9	)dx	)dx	ADJ
ma-254	149	10	.	.	PUNCT
ma-254	150	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	150	2	eur	eur	PROPN
ma-254	150	3	.	.	PUNCT
ma-254	151	1	j.	j.	PROPN
ma-254	151	2	math	math	PROPN
ma-254	151	3	.	.	PUNCT
ma-254	152	1	anal	anal	PROPN
ma-254	152	2	.	.	PUNCT
ma-254	153	1	10.28924	10.28924	NUM
ma-254	153	2	/	/	SYM
ma-254	153	3	ada	ada	PROPN
ma-254	153	4	/	/	SYM
ma-254	153	5	ma.5.3	ma.5.3	PROPN
ma-254	153	6	6	6	NUM
ma-254	153	7	since	since	SCONJ
ma-254	153	8	∫	∫	PROPN
ma-254	153	9	g	g	PROPN
ma-254	153	10	f	f	PROPN
ma-254	153	11	(	(	PUNCT
ma-254	153	12	x)φ(g)φ(x	x)φ(g)φ(x	PROPN
ma-254	153	13	�	�	NOUN
ma-254	153	14	)dx	)dx	ADJ
ma-254	154	1	=	=	SYM
ma-254	154	2	∫	∫	PROPN
ma-254	154	3	g	g	PROPN
ma-254	154	4	f	f	PROPN
ma-254	154	5	(	(	PUNCT
ma-254	154	6	x)(g	x)(g	PROPN
ma-254	154	7	∗	∗	NOUN
ma-254	154	8	φ)(x	φ)(x	NUM
ma-254	154	9	�	�	NOUN
ma-254	154	10	)dx	)dx	ADJ
ma-254	154	11	for	for	ADP
ma-254	154	12	all	all	DET
ma-254	154	13	f	f	PROPN
ma-254	154	14	∈	∈	PROPN
ma-254	154	15	k\(g	k\(g	PROPN
ma-254	154	16	)	)	PUNCT
ma-254	154	17	,	,	PUNCT
ma-254	154	18	then	then	ADV
ma-254	154	19	φ(g)φ(x	φ(g)φ(x	PROPN
ma-254	154	20	�	�	PROPN
ma-254	154	21	)	)	PUNCT
ma-254	154	22	=	=	PUNCT
ma-254	155	1	(	(	PUNCT
ma-254	155	2	g	g	NOUN
ma-254	155	3	∗	∗	PROPN
ma-254	155	4	φ)(x	φ)(x	NUM
ma-254	155	5	�	�	PROPN
ma-254	155	6	)	)	PUNCT
ma-254	155	7	.	.	PUNCT
ma-254	156	1	therefore	therefore	ADV
ma-254	156	2	,	,	PUNCT
ma-254	156	3	g	g	PROPN
ma-254	156	4	∗	∗	X
ma-254	156	5	φ	φ	PROPN
ma-254	156	6	=	=	SYM
ma-254	156	7	φ(g)φ	φ(g)φ	PROPN
ma-254	156	8	=	=	SYM
ma-254	156	9	ĝ(φ)φ	ĝ(φ)φ	PROPN
ma-254	156	10	.	.	PROPN
ma-254	156	11	�	�	PROPN
ma-254	156	12	theorem	theorem	VERB
ma-254	156	13	3.4	3.4	NUM
ma-254	156	14	.	.	PUNCT
ma-254	157	1	let	let	AUX
ma-254	157	2	(	(	PUNCT
ma-254	157	3	g	g	NOUN
ma-254	157	4	,	,	PUNCT
ma-254	157	5	k	k	NOUN
ma-254	157	6	)	)	PUNCT
ma-254	157	7	be	be	VERB
ma-254	157	8	a	a	DET
ma-254	157	9	hypergroup	hypergroup	NOUN
ma-254	157	10	gelfand	gelfand	PROPN
ma-254	157	11	pair	pair	NOUN
ma-254	157	12	.	.	PUNCT
ma-254	158	1	let	let	VERB
ma-254	158	2	f	f	PROPN
ma-254	158	3	∈	∈	PROPN
ma-254	158	4	hs,\γ	hs,\γ	PROPN
ma-254	158	5	(	(	PUNCT
ma-254	158	6	g	g	NOUN
ma-254	158	7	)	)	PUNCT
ma-254	158	8	.	.	PUNCT
ma-254	159	1	if	if	SCONJ
ma-254	159	2	y	y	PROPN
ma-254	159	3	∈	∈	PROPN
ma-254	159	4	g	g	PROPN
ma-254	159	5	,	,	PUNCT
ma-254	159	6	then∫	then∫	NOUN
ma-254	159	7	g	g	PROPN
ma-254	159	8	|f	|f	PROPN
ma-254	159	9	(	(	PUNCT
ma-254	159	10	x	x	PROPN
ma-254	159	11	∗	∗	PROPN
ma-254	159	12	y	y	PROPN
ma-254	159	13	�	�	PROPN
ma-254	159	14	)−	)−	PUNCT
ma-254	159	15	f	f	PROPN
ma-254	159	16	(	(	PUNCT
ma-254	159	17	x)|2dx	x)|2dx	PROPN
ma-254	159	18	≤	≤	PROPN
ma-254	159	19	(	(	PUNCT
ma-254	159	20	sup	sup	NOUN
ma-254	159	21	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	159	22	|φ(y)−	|φ(y)−	PROPN
ma-254	159	23	1|2	1|2	PROPN
ma-254	159	24	(	(	PUNCT
ma-254	159	25	1	1	NUM
ma-254	159	26	+	+	X
ma-254	159	27	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	159	28	)	)	PUNCT
ma-254	159	29	·	·	PUNCT
ma-254	159	30	‖f	‖f	ADP
ma-254	159	31	‖2	‖2	NOUN
ma-254	159	32	hs,\γ	hs,\γ	NOUN
ma-254	159	33	.	.	PUNCT
ma-254	160	1	proof	proof	NOUN
ma-254	160	2	.	.	PUNCT
ma-254	161	1	fix	fix	VERB
ma-254	161	2	y	y	PROPN
ma-254	161	3	∈	∈	PROPN
ma-254	161	4	g.	g.	NOUN
ma-254	161	5	let	let	VERB
ma-254	161	6	f	f	PROPN
ma-254	161	7	∈	∈	PROPN
ma-254	161	8	k\(g	k\(g	PROPN
ma-254	161	9	)	)	PUNCT
ma-254	161	10	.	.	PUNCT
ma-254	162	1	set	set	VERB
ma-254	162	2	fy	fy	PROPN
ma-254	162	3	(	(	PUNCT
ma-254	162	4	x	x	NOUN
ma-254	162	5	)	)	PUNCT
ma-254	162	6	=	=	SYM
ma-254	162	7	f	f	X
ma-254	162	8	(	(	PUNCT
ma-254	162	9	x	x	PROPN
ma-254	162	10	∗	∗	PROPN
ma-254	162	11	y	y	PROPN
ma-254	162	12	�	�	PROPN
ma-254	162	13	)	)	PUNCT
ma-254	162	14	,	,	PUNCT
ma-254	162	15	x	x	PUNCT
ma-254	162	16	∈	∈	NOUN
ma-254	162	17	g.	g.	NOUN
ma-254	162	18	we	we	PRON
ma-254	162	19	have	have	VERB
ma-254	162	20	,	,	PUNCT
ma-254	162	21	f̂y	f̂y	X
ma-254	162	22	(	(	PUNCT
ma-254	162	23	φ	φ	NOUN
ma-254	162	24	)	)	PUNCT
ma-254	162	25	=	=	SYM
ma-254	163	1	∫	∫	PROPN
ma-254	163	2	g	g	PROPN
ma-254	163	3	φ(x	φ(x	PROPN
ma-254	163	4	�	�	NOUN
ma-254	163	5	)f	)f	NOUN
ma-254	163	6	(	(	PUNCT
ma-254	163	7	x	x	PROPN
ma-254	163	8	∗	∗	PROPN
ma-254	163	9	y	y	PROPN
ma-254	163	10	�	�	PROPN
ma-254	163	11	)dx	)dx	ADJ
ma-254	164	1	=	=	SYM
ma-254	164	2	∫	∫	PROPN
ma-254	164	3	g	g	PROPN
ma-254	164	4	φ(y	φ(y	PROPN
ma-254	164	5	�	�	PROPN
ma-254	164	6	∗	∗	X
ma-254	164	7	x	x	NOUN
ma-254	164	8	�	�	NOUN
ma-254	164	9	)f	)f	PUNCT
ma-254	164	10	(	(	PUNCT
ma-254	164	11	x)dx	x)dx	PROPN
ma-254	164	12	(	(	PUNCT
ma-254	164	13	change	change	NOUN
ma-254	164	14	of	of	ADP
ma-254	164	15	variable	variable	NOUN
ma-254	164	16	x	x	PUNCT
ma-254	164	17	→	→	SYM
ma-254	164	18	x	x	SYM
ma-254	164	19	∗	∗	PROPN
ma-254	164	20	y	y	PROPN
ma-254	164	21	�	�	PROPN
ma-254	164	22	)	)	PUNCT
ma-254	164	23	=	=	SYM
ma-254	165	1	∫	∫	PROPN
ma-254	165	2	g	g	PROPN
ma-254	165	3	φ(y	φ(y	PROPN
ma-254	165	4	�	�	PROPN
ma-254	165	5	∗	∗	NOUN
ma-254	165	6	x)f	x)f	X
ma-254	165	7	(	(	PUNCT
ma-254	165	8	x	x	X
ma-254	165	9	�	�	X
ma-254	165	10	)dx	)dx	ADJ
ma-254	165	11	(	(	PUNCT
ma-254	165	12	change	change	NOUN
ma-254	165	13	of	of	ADP
ma-254	165	14	variable	variable	NOUN
ma-254	165	15	x	x	INTJ
ma-254	165	16	→	→	SYM
ma-254	165	17	x	x	SYM
ma-254	165	18	�	�	PROPN
ma-254	165	19	)	)	PUNCT
ma-254	165	20	=	=	PUNCT
ma-254	165	21	(	(	PUNCT
ma-254	165	22	φ	φ	PROPN
ma-254	165	23	∗	∗	PROPN
ma-254	165	24	f	f	PROPN
ma-254	165	25	)	)	PUNCT
ma-254	165	26	(	(	PUNCT
ma-254	165	27	y	y	PROPN
ma-254	165	28	�	�	PROPN
ma-254	165	29	)	)	PUNCT
ma-254	165	30	=	=	PUNCT
ma-254	166	1	(	(	PUNCT
ma-254	166	2	f	f	PROPN
ma-254	166	3	∗	∗	PROPN
ma-254	166	4	φ)(y	φ)(y	PROPN
ma-254	166	5	�	�	PROPN
ma-254	166	6	)	)	PUNCT
ma-254	166	7	=	=	SYM
ma-254	166	8	f̂	f̂	X
ma-254	166	9	(	(	PUNCT
ma-254	166	10	φ)φ(y	φ)φ(y	PROPN
ma-254	166	11	�	�	X
ma-254	166	12	)(lemma	)(lemma	NOUN
ma-254	166	13	3.3).∫	3.3).∫	NUM
ma-254	166	14	g	g	X
ma-254	166	15	|fy	|fy	X
ma-254	166	16	(	(	PUNCT
ma-254	166	17	x)−	x)−	PROPN
ma-254	166	18	f	f	PROPN
ma-254	166	19	(	(	PUNCT
ma-254	166	20	x)|2dx	x)|2dx	PROPN
ma-254	166	21	=	=	SYM
ma-254	166	22	∫	∫	PROPN
ma-254	166	23	ĝ\	ĝ\	PROPN
ma-254	166	24	|f̂y	|f̂y	PROPN
ma-254	166	25	(	(	PUNCT
ma-254	166	26	φ)−	φ)−	PROPN
ma-254	166	27	f̂	f̂	PROPN
ma-254	166	28	(	(	PUNCT
ma-254	166	29	φ)|2dπ(φ)(theorem	φ)|2dπ(φ)(theorem	X
ma-254	166	30	2.5	2.5	NUM
ma-254	166	31	)	)	PUNCT
ma-254	166	32	=	=	SYM
ma-254	167	1	∫	∫	PROPN
ma-254	168	1	ĝ\	ĝ\	PROPN
ma-254	168	2	|f̂	|f̂	PROPN
ma-254	168	3	(	(	PUNCT
ma-254	168	4	φ)φ(y	φ)φ(y	PROPN
ma-254	168	5	�	�	PROPN
ma-254	168	6	)−	)−	SYM
ma-254	168	7	f̂	f̂	PROPN
ma-254	168	8	(	(	PUNCT
ma-254	168	9	φ)|2dπ(φ	φ)|2dπ(φ	NUM
ma-254	168	10	)	)	PUNCT
ma-254	168	11	=	=	SYM
ma-254	169	1	∫	∫	PROPN
ma-254	170	1	ĝ\	ĝ\	PROPN
ma-254	170	2	|f̂	|f̂	ADV
ma-254	170	3	(	(	PUNCT
ma-254	170	4	φ)(φ(y	φ)(φ(y	PROPN
ma-254	170	5	�	�	PROPN
ma-254	170	6	)−	)−	PUNCT
ma-254	170	7	1)|2dπ(φ	1)|2dπ(φ	NUM
ma-254	170	8	)	)	PUNCT
ma-254	170	9	=	=	SYM
ma-254	171	1	∫	∫	PROPN
ma-254	171	2	ĝ\	ĝ\	PROPN
ma-254	171	3	|f̂	|f̂	PROPN
ma-254	171	4	(	(	PUNCT
ma-254	171	5	φ)|2|φ(y	φ)|2|φ(y	PROPN
ma-254	171	6	�	�	PROPN
ma-254	171	7	)−	)−	PUNCT
ma-254	171	8	1|2dπ(φ	1|2dπ(φ	NUM
ma-254	171	9	)	)	PUNCT
ma-254	172	1	=	=	SYM
ma-254	172	2	∫	∫	PROPN
ma-254	173	1	ĝ\	ĝ\	PROPN
ma-254	173	2	|f̂	|f̂	ADV
ma-254	173	3	(	(	PUNCT
ma-254	173	4	φ)|2|φ(y)−	φ)|2|φ(y)−	PROPN
ma-254	173	5	1|2	1|2	NUM
ma-254	173	6	(	(	PUNCT
ma-254	173	7	1	1	NUM
ma-254	173	8	+	+	CCONJ
ma-254	173	9	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	173	10	(	(	PUNCT
ma-254	173	11	1	1	NUM
ma-254	173	12	+	+	CCONJ
ma-254	173	13	γ(φ)2)s	γ(φ)2)s	ADJ
ma-254	173	14	dπ(φ	dπ(φ	NUM
ma-254	173	15	)	)	PUNCT
ma-254	173	16	≤	≤	NUM
ma-254	173	17	(	(	PUNCT
ma-254	173	18	sup	sup	NOUN
ma-254	173	19	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	173	20	|φ(y)−	|φ(y)−	PROPN
ma-254	173	21	1|2	1|2	PROPN
ma-254	173	22	(	(	PUNCT
ma-254	173	23	1	1	NUM
ma-254	173	24	+	+	X
ma-254	173	25	γ(φ)2)s	γ(φ)2)s	NOUN
ma-254	173	26	)	)	PUNCT
ma-254	173	27	·	·	PUNCT
ma-254	173	28	‖f	‖f	ADP
ma-254	173	29	‖2	‖2	NOUN
ma-254	173	30	hs,\γ	hs,\γ	PROPN
ma-254	173	31	.	.	PUNCT
ma-254	174	1	since	since	SCONJ
ma-254	174	2	k\(g	k\(g	PROPN
ma-254	174	3	)	)	PUNCT
ma-254	174	4	is	be	AUX
ma-254	174	5	dense	dense	ADJ
ma-254	174	6	in	in	ADP
ma-254	174	7	hs,\γ	hs,\γ	PROPN
ma-254	174	8	(	(	PUNCT
ma-254	174	9	g	g	NOUN
ma-254	174	10	)	)	PUNCT
ma-254	174	11	,	,	PUNCT
ma-254	174	12	the	the	DET
ma-254	174	13	result	result	NOUN
ma-254	174	14	holds	hold	VERB
ma-254	174	15	for	for	ADP
ma-254	174	16	all	all	DET
ma-254	174	17	f	f	PROPN
ma-254	174	18	∈	∈	PROPN
ma-254	174	19	hs,\γ	hs,\γ	PROPN
ma-254	174	20	(	(	PUNCT
ma-254	174	21	g	g	NOUN
ma-254	174	22	)	)	PUNCT
ma-254	174	23	.	.	PUNCT
ma-254	175	1	�	�	PROPN
ma-254	175	2	theorem	theorem	VERB
ma-254	175	3	3.5	3.5	NUM
ma-254	175	4	.	.	PUNCT
ma-254	176	1	let	let	AUX
ma-254	176	2	(	(	PUNCT
ma-254	176	3	g	g	NOUN
ma-254	176	4	,	,	PUNCT
ma-254	176	5	k	k	NOUN
ma-254	176	6	)	)	PUNCT
ma-254	176	7	be	be	VERB
ma-254	176	8	a	a	DET
ma-254	176	9	hypergroup	hypergroup	NOUN
ma-254	176	10	gelfand	gelfand	PROPN
ma-254	176	11	pair	pair	NOUN
ma-254	176	12	.	.	PUNCT
ma-254	177	1	if	if	SCONJ
ma-254	177	2	f	f	PROPN
ma-254	177	3	∈	∈	PROPN
ma-254	177	4	hs,\γ	hs,\γ	PROPN
ma-254	177	5	(	(	PUNCT
ma-254	177	6	g	g	NOUN
ma-254	177	7	)	)	PUNCT
ma-254	177	8	,	,	PUNCT
ma-254	177	9	then	then	ADV
ma-254	177	10	there	there	PRON
ma-254	177	11	exists	exist	VERB
ma-254	177	12	η	η	PROPN
ma-254	177	13	∈	∈	PROPN
ma-254	177	14	k\(g	k\(g	PROPN
ma-254	177	15	)	)	PUNCT
ma-254	177	16	such	such	ADJ
ma-254	177	17	that	that	SCONJ
ma-254	177	18	‖f	‖f	ADP
ma-254	177	19	∗	∗	X
ma-254	177	20	η	η	PROPN
ma-254	177	21	−	−	PROPN
ma-254	177	22	f	f	PROPN
ma-254	177	23	‖2	‖2	NOUN
ma-254	177	24	≤	≤	NUM
ma-254	177	25	sup	sup	NOUN
ma-254	177	26	y∈supp(η	y∈supp(η	PROPN
ma-254	177	27	)	)	PUNCT
ma-254	177	28	sup	sup	PROPN
ma-254	177	29	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	177	30	|φ(y)−	|φ(y)−	PROPN
ma-254	177	31	1|	1|	NUM
ma-254	177	32	(	(	PUNCT
ma-254	177	33	1	1	NUM
ma-254	177	34	+	+	CCONJ
ma-254	177	35	γ(φ)2	γ(φ)2	PROPN
ma-254	177	36	)	)	PUNCT
ma-254	177	37	s	s	PART
ma-254	177	38	2	2	NUM
ma-254	177	39	·	·	PUNCT
ma-254	177	40	‖f	‖f	ADP
ma-254	178	1	‖	‖	PROPN
ma-254	178	2	hs,\γ	hs,\γ	PROPN
ma-254	178	3	.	.	PUNCT
ma-254	179	1	proof	proof	NOUN
ma-254	179	2	.	.	PUNCT
ma-254	180	1	since	since	SCONJ
ma-254	180	2	g	g	PROPN
ma-254	180	3	is	be	AUX
ma-254	180	4	a	a	DET
ma-254	180	5	locally	locally	ADV
ma-254	180	6	compact	compact	ADJ
ma-254	180	7	compact	compact	ADJ
ma-254	180	8	hausdorff	hausdorff	NOUN
ma-254	180	9	space	space	NOUN
ma-254	180	10	,	,	PUNCT
ma-254	180	11	then	then	ADV
ma-254	180	12	it	it	PRON
ma-254	180	13	is	be	AUX
ma-254	180	14	a	a	DET
ma-254	180	15	tychonoff	tychonoff	NOUN
ma-254	180	16	space	space	NOUN
ma-254	180	17	.	.	PUNCT
ma-254	181	1	therefore	therefore	ADV
ma-254	181	2	,	,	PUNCT
ma-254	181	3	there	there	PRON
ma-254	181	4	exists	exist	VERB
ma-254	181	5	η	η	PROPN
ma-254	181	6	∈	∈	PROPN
ma-254	181	7	k\(g	k\(g	PROPN
ma-254	181	8	)	)	PUNCT
ma-254	181	9	such	such	ADJ
ma-254	181	10	that	that	SCONJ
ma-254	181	11	η(e	η(e	PROPN
ma-254	181	12	)	)	PUNCT
ma-254	181	13	6=	6=	ADP
ma-254	181	14	0	0	NUM
ma-254	181	15	,	,	PUNCT
ma-254	181	16	η	η	PROPN
ma-254	181	17	≥	≥	X
ma-254	181	18	0	0	NUM
ma-254	181	19	and	and	CCONJ
ma-254	181	20	∫	∫	PROPN
ma-254	181	21	g	g	PROPN
ma-254	181	22	η(x)dx	η(x)dx	PART
ma-254	181	23	=	=	NOUN
ma-254	181	24	1	1	X
ma-254	181	25	.	.	PUNCT
ma-254	182	1	then	then	ADV
ma-254	182	2	,	,	PUNCT
ma-254	182	3	we	we	PRON
ma-254	182	4	have	have	VERB
ma-254	182	5	‖f	‖f	ADP
ma-254	182	6	∗	∗	X
ma-254	182	7	η	η	PROPN
ma-254	183	1	−	−	PROPN
ma-254	183	2	f	f	X
ma-254	183	3	‖2	‖2	NOUN
ma-254	183	4	=	=	SYM
ma-254	183	5	(	(	PUNCT
ma-254	183	6	∫	∫	PROPN
ma-254	183	7	g	g	PROPN
ma-254	183	8	|f	|f	PROPN
ma-254	183	9	∗	∗	PROPN
ma-254	183	10	η(x)−	η(x)−	PROPN
ma-254	183	11	f	f	PROPN
ma-254	183	12	(	(	PUNCT
ma-254	183	13	x)|2dx	x)|2dx	PROPN
ma-254	183	14	)	)	PUNCT
ma-254	183	15	1	1	NUM
ma-254	183	16	2	2	NUM
ma-254	183	17	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	183	18	eur	eur	PROPN
ma-254	183	19	.	.	PUNCT
ma-254	184	1	j.	j.	PROPN
ma-254	184	2	math	math	PROPN
ma-254	184	3	.	.	PUNCT
ma-254	185	1	anal	anal	PROPN
ma-254	185	2	.	.	PUNCT
ma-254	186	1	10.28924	10.28924	NUM
ma-254	186	2	/	/	SYM
ma-254	186	3	ada	ada	PROPN
ma-254	186	4	/	/	SYM
ma-254	186	5	ma.5.3	ma.5.3	PROPN
ma-254	186	6	7	7	NUM
ma-254	186	7	=	=	SYM
ma-254	186	8	(	(	PUNCT
ma-254	186	9	∫	∫	PROPN
ma-254	186	10	g	g	PROPN
ma-254	186	11	∣∣∣∣∫	∣∣∣∣∫	PROPN
ma-254	186	12	g	g	PROPN
ma-254	187	1	f	f	PROPN
ma-254	187	2	(	(	PUNCT
ma-254	187	3	x	x	PROPN
ma-254	187	4	∗	∗	PROPN
ma-254	187	5	y	y	PROPN
ma-254	187	6	�	�	PROPN
ma-254	187	7	)η(y)dy	)η(y)dy	PUNCT
ma-254	187	8	−	−	PROPN
ma-254	187	9	f	f	PROPN
ma-254	187	10	(	(	PUNCT
ma-254	187	11	x	x	NOUN
ma-254	187	12	)	)	PUNCT
ma-254	187	13	∣∣∣∣2	∣∣∣∣2	NOUN
ma-254	187	14	dx	dx	PROPN
ma-254	187	15	)	)	PUNCT
ma-254	187	16	1	1	NUM
ma-254	187	17	2	2	NUM
ma-254	187	18	=	=	SYM
ma-254	187	19	(	(	PUNCT
ma-254	187	20	∫	∫	PROPN
ma-254	187	21	g	g	PROPN
ma-254	187	22	∣∣∣∣∫	∣∣∣∣∫	PROPN
ma-254	187	23	g	g	PROPN
ma-254	187	24	f	f	PROPN
ma-254	187	25	(	(	PUNCT
ma-254	187	26	x	x	PROPN
ma-254	187	27	∗	∗	PROPN
ma-254	187	28	y	y	PROPN
ma-254	187	29	�	�	PROPN
ma-254	187	30	)η(y)dy	)η(y)dy	PUNCT
ma-254	187	31	−	−	PROPN
ma-254	187	32	f	f	PROPN
ma-254	187	33	(	(	PUNCT
ma-254	187	34	x	x	X
ma-254	187	35	)	)	PUNCT
ma-254	187	36	∫	∫	PROPN
ma-254	188	1	g	g	PROPN
ma-254	188	2	η(y)dy	η(y)dy	PROPN
ma-254	188	3	∣∣∣∣2	∣∣∣∣2	NOUN
ma-254	188	4	dx	dx	PROPN
ma-254	188	5	)	)	PUNCT
ma-254	188	6	1	1	NUM
ma-254	188	7	2	2	NUM
ma-254	188	8	=	=	SYM
ma-254	188	9	(	(	PUNCT
ma-254	188	10	∫	∫	PROPN
ma-254	188	11	g	g	PROPN
ma-254	188	12	∣∣∣∣∫	∣∣∣∣∫	PROPN
ma-254	188	13	g	g	PROPN
ma-254	188	14	(	(	PUNCT
ma-254	188	15	f	f	PROPN
ma-254	188	16	(	(	PUNCT
ma-254	188	17	x	x	PROPN
ma-254	188	18	∗	∗	PROPN
ma-254	188	19	y	y	PROPN
ma-254	188	20	�	�	PROPN
ma-254	188	21	)−	)−	PUNCT
ma-254	188	22	f	f	PROPN
ma-254	188	23	(	(	PUNCT
ma-254	188	24	x))η(y)dy	x))η(y)dy	PROPN
ma-254	188	25	∣∣∣∣2	∣∣∣∣2	PROPN
ma-254	188	26	dx	dx	PROPN
ma-254	188	27	)	)	PUNCT
ma-254	188	28	1	1	NUM
ma-254	188	29	2	2	NUM
ma-254	188	30	≤	≤	NUM
ma-254	188	31	∫	∫	PROPN
ma-254	188	32	g	g	PROPN
ma-254	188	33	(	(	PUNCT
ma-254	188	34	∫	∫	PROPN
ma-254	188	35	g	g	PROPN
ma-254	188	36	|f	|f	PROPN
ma-254	188	37	(	(	PUNCT
ma-254	188	38	x	x	PROPN
ma-254	188	39	∗	∗	PROPN
ma-254	188	40	y	y	PROPN
ma-254	188	41	�	�	PROPN
ma-254	188	42	)−	)−	PUNCT
ma-254	188	43	f	f	PROPN
ma-254	188	44	(	(	PUNCT
ma-254	188	45	x)|2|η(y)|2dx	x)|2|η(y)|2dx	X
ma-254	188	46	)	)	PUNCT
ma-254	188	47	1	1	NUM
ma-254	188	48	2	2	NUM
ma-254	188	49	dy	dy	NOUN
ma-254	188	50	≤	≤	NUM
ma-254	188	51	∫	∫	PROPN
ma-254	188	52	g	g	PROPN
ma-254	188	53	|η(y)|	|η(y)|	PROPN
ma-254	188	54	(	(	PUNCT
ma-254	188	55	∫	∫	PROPN
ma-254	188	56	g	g	PROPN
ma-254	188	57	|f	|f	PROPN
ma-254	188	58	(	(	PUNCT
ma-254	188	59	x	x	PROPN
ma-254	188	60	∗	∗	PROPN
ma-254	188	61	y	y	PROPN
ma-254	188	62	�	�	PROPN
ma-254	188	63	)−	)−	PUNCT
ma-254	188	64	f	f	PROPN
ma-254	188	65	(	(	PUNCT
ma-254	188	66	x)|2dx	x)|2dx	PROPN
ma-254	188	67	)	)	PUNCT
ma-254	188	68	1	1	NUM
ma-254	188	69	2	2	NUM
ma-254	188	70	dy	dy	NOUN
ma-254	188	71	≤	≤	NUM
ma-254	188	72	sup	sup	NOUN
ma-254	188	73	y∈supp(η	y∈supp(η	PROPN
ma-254	188	74	)	)	PUNCT
ma-254	188	75	sup	sup	PROPN
ma-254	188	76	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	188	77	|φ(y)−	|φ(y)−	PROPN
ma-254	188	78	1|	1|	NUM
ma-254	188	79	(	(	PUNCT
ma-254	188	80	1	1	NUM
ma-254	188	81	+	+	CCONJ
ma-254	188	82	γ(φ)2	γ(φ)2	PROPN
ma-254	188	83	)	)	PUNCT
ma-254	188	84	s	s	PART
ma-254	188	85	2	2	NUM
ma-254	188	86	·	·	PUNCT
ma-254	188	87	‖f	‖f	ADP
ma-254	188	88	‖	‖	PROPN
ma-254	188	89	hs,\γ	hs,\γ	PROPN
ma-254	188	90	(	(	PUNCT
ma-254	188	91	use	use	NOUN
ma-254	188	92	theorem	theorem	VERB
ma-254	188	93	3.4	3.4	NUM
ma-254	188	94	)	)	PUNCT
ma-254	188	95	.	.	PUNCT
ma-254	189	1	�	�	PROPN
ma-254	189	2	in	in	ADP
ma-254	189	3	the	the	DET
ma-254	189	4	rest	rest	NOUN
ma-254	189	5	of	of	ADP
ma-254	189	6	the	the	DET
ma-254	189	7	paper	paper	NOUN
ma-254	189	8	,	,	PUNCT
ma-254	189	9	we	we	PRON
ma-254	189	10	assume	assume	VERB
ma-254	189	11	that	that	SCONJ
ma-254	189	12	g	g	PROPN
ma-254	189	13	is	be	AUX
ma-254	189	14	compact	compact	ADJ
ma-254	189	15	.	.	PUNCT
ma-254	190	1	theorem	theorem	VERB
ma-254	190	2	3.6	3.6	NUM
ma-254	190	3	.	.	PUNCT
ma-254	191	1	let	let	VERB
ma-254	191	2	g	g	PRON
ma-254	191	3	be	be	AUX
ma-254	191	4	a	a	DET
ma-254	191	5	compact	compact	ADJ
ma-254	191	6	hypergroup	hypergroup	NOUN
ma-254	191	7	.	.	PUNCT
ma-254	192	1	let	let	AUX
ma-254	192	2	(	(	PUNCT
ma-254	192	3	g	g	NOUN
ma-254	192	4	,	,	PUNCT
ma-254	192	5	k	k	NOUN
ma-254	192	6	)	)	PUNCT
ma-254	192	7	be	be	VERB
ma-254	192	8	a	a	DET
ma-254	192	9	hypergroup	hypergroup	NOUN
ma-254	192	10	gelfand	gelfand	PROPN
ma-254	192	11	pair	pair	NOUN
ma-254	192	12	.	.	PUNCT
ma-254	193	1	let	let	VERB
ma-254	193	2	p	p	PRON
ma-254	193	3	,	,	PUNCT
ma-254	193	4	q	q	NOUN
ma-254	193	5	∈	∈	PROPN
ma-254	193	6	(	(	PUNCT
ma-254	193	7	1,∞	1,∞	NUM
ma-254	193	8	)	)	PUNCT
ma-254	193	9	.	.	PUNCT
ma-254	194	1	if	if	SCONJ
ma-254	194	2	a	a	DET
ma-254	194	3	sequence	sequence	NOUN
ma-254	194	4	(	(	PUNCT
ma-254	194	5	fn	fn	NOUN
ma-254	194	6	)	)	PUNCT
ma-254	194	7	⊂	⊂	PROPN
ma-254	194	8	lp,\(g	lp,\(g	PROPN
ma-254	194	9	)	)	PUNCT
ma-254	194	10	converges	converge	VERB
ma-254	194	11	weakly	weakly	ADJ
ma-254	194	12	to	to	ADP
ma-254	194	13	a	a	DET
ma-254	194	14	function	function	NOUN
ma-254	194	15	f	f	NOUN
ma-254	194	16	,	,	PUNCT
ma-254	194	17	then	then	ADV
ma-254	194	18	for	for	ADP
ma-254	194	19	every	every	DET
ma-254	194	20	η	η	PROPN
ma-254	194	21	∈	∈	PROPN
ma-254	194	22	k\(g	k\(g	PROPN
ma-254	194	23	)	)	PUNCT
ma-254	194	24	the	the	DET
ma-254	194	25	sequence	sequence	NOUN
ma-254	194	26	(	(	PUNCT
ma-254	194	27	fn	fn	PROPN
ma-254	194	28	∗	∗	X
ma-254	194	29	η	η	PROPN
ma-254	194	30	)	)	PUNCT
ma-254	194	31	converges	converge	VERB
ma-254	194	32	strongly	strongly	ADV
ma-254	194	33	to	to	ADP
ma-254	194	34	f	f	PROPN
ma-254	194	35	∗	∗	X
ma-254	194	36	η	η	PROPN
ma-254	194	37	in	in	ADP
ma-254	194	38	lq,\(g	lq,\(g	PROPN
ma-254	194	39	)	)	PUNCT
ma-254	194	40	.	.	PUNCT
ma-254	195	1	proof	proof	NOUN
ma-254	195	2	.	.	PUNCT
ma-254	196	1	since	since	SCONJ
ma-254	196	2	the	the	DET
ma-254	196	3	sequence	sequence	NOUN
ma-254	196	4	(	(	PUNCT
ma-254	196	5	fn	fn	NOUN
ma-254	196	6	)	)	PUNCT
ma-254	196	7	converges	converge	VERB
ma-254	196	8	weakly	weakly	ADJ
ma-254	196	9	to	to	ADP
ma-254	196	10	f	f	PROPN
ma-254	196	11	,	,	PUNCT
ma-254	196	12	then	then	ADV
ma-254	196	13	by	by	ADP
ma-254	196	14	[	[	X
ma-254	196	15	4	4	NUM
ma-254	196	16	,	,	PUNCT
ma-254	196	17	proposition	proposition	NOUN
ma-254	196	18	3.5	3.5	NUM
ma-254	196	19	]	]	PUNCT
ma-254	196	20	there	there	PRON
ma-254	196	21	exists	exist	VERB
ma-254	196	22	apositive	apositive	ADJ
ma-254	196	23	real	real	NOUN
ma-254	196	24	m	m	VERB
ma-254	196	25	such	such	ADJ
ma-254	196	26	that	that	SCONJ
ma-254	196	27	‖fn‖p	‖fn‖p	PROPN
ma-254	196	28	≤	≤	PROPN
ma-254	196	29	m	m	VERB
ma-254	196	30	and	and	CCONJ
ma-254	196	31	‖f	‖f	ADJ
ma-254	196	32	‖p	‖p	PROPN
ma-254	196	33	≤	≤	NUM
ma-254	196	34	m.	m.	NOUN
ma-254	196	35	we	we	PRON
ma-254	196	36	have	have	VERB
ma-254	196	37	|fn	|fn	NUM
ma-254	196	38	∗	∗	NOUN
ma-254	196	39	η(x)|	η(x)|	NOUN
ma-254	196	40	=	=	SYM
ma-254	196	41	∣∣∣∣∫	∣∣∣∣∫	NOUN
ma-254	196	42	g	g	PROPN
ma-254	196	43	fn(y)η(y	fn(y)η(y	PROPN
ma-254	196	44	�	�	PROPN
ma-254	196	45	∗	∗	NOUN
ma-254	196	46	x)dy	x)dy	PROPN
ma-254	196	47	∣∣∣∣	∣∣∣∣	PROPN
ma-254	196	48	≤	≤	NUM
ma-254	197	1	∫	∫	PROPN
ma-254	197	2	g	g	PROPN
ma-254	197	3	|fn(y)η(y	|fn(y)η(y	PROPN
ma-254	197	4	�	�	PROPN
ma-254	197	5	∗	∗	NOUN
ma-254	197	6	x)|	x)|	PROPN
ma-254	197	7	dy	dy	NOUN
ma-254	197	8	≤	≤	PUNCT
ma-254	198	1	‖fn‖p	‖fn‖p	PROPN
ma-254	198	2	(	(	PUNCT
ma-254	198	3	∫	∫	PROPN
ma-254	198	4	g	g	PROPN
ma-254	198	5	|η(y	|η(y	PROPN
ma-254	198	6	�	�	PROPN
ma-254	198	7	∗	∗	NOUN
ma-254	198	8	x)|p′dy	x)|p′dy	PROPN
ma-254	198	9	)	)	PUNCT
ma-254	198	10	1	1	NUM
ma-254	198	11	p′	p′	NOUN
ma-254	198	12	≤	≤	NOUN
ma-254	198	13	m‖η‖p′	m‖η‖p′	NUM
ma-254	198	14	where	where	SCONJ
ma-254	198	15	p′	p′	NOUN
ma-254	198	16	is	be	AUX
ma-254	198	17	such	such	ADJ
ma-254	199	1	that	that	SCONJ
ma-254	199	2	1	1	NUM
ma-254	199	3	p	p	NOUN
ma-254	199	4	+	+	NOUN
ma-254	199	5	1	1	NUM
ma-254	199	6	p′	p′	NOUN
ma-254	199	7	=	=	SYM
ma-254	199	8	1	1	X
ma-254	199	9	.	.	PUNCT
ma-254	200	1	since	since	SCONJ
ma-254	200	2	g	g	PROPN
ma-254	200	3	is	be	AUX
ma-254	200	4	compact	compact	ADJ
ma-254	200	5	,	,	PUNCT
ma-254	200	6	the	the	DET
ma-254	200	7	constant	constant	ADJ
ma-254	200	8	function	function	NOUN
ma-254	200	9	x	x	PUNCT
ma-254	200	10	7−→	7−→	NOUN
ma-254	200	11	m‖η‖p′	m‖η‖p′	NUM
ma-254	200	12	isintegrable	isintegrable	ADJ
ma-254	200	13	.	.	PUNCT
ma-254	201	1	therefore	therefore	ADV
ma-254	201	2	,	,	PUNCT
ma-254	201	3	by	by	ADP
ma-254	201	4	the	the	DET
ma-254	201	5	dominated	dominate	VERB
ma-254	201	6	convergence	convergence	NOUN
ma-254	201	7	theorem	theorem	VERB
ma-254	201	8	,	,	PUNCT
ma-254	201	9	we	we	PRON
ma-254	201	10	have	have	VERB
ma-254	201	11	fn	fn	NOUN
ma-254	201	12	∗	∗	NOUN
ma-254	201	13	η(x	η(x	X
ma-254	201	14	)	)	PUNCT
ma-254	201	15	=	=	SYM
ma-254	202	1	∫	∫	PROPN
ma-254	202	2	g	g	PROPN
ma-254	202	3	fn(y)η(y	fn(y)η(y	PROPN
ma-254	202	4	�	�	PROPN
ma-254	202	5	∗	∗	NOUN
ma-254	202	6	x)dy	x)dy	PROPN
ma-254	202	7	n→∞−−−→	n→∞−−−→	PROPN
ma-254	202	8	∫	∫	PROPN
ma-254	202	9	g	g	PROPN
ma-254	202	10	f	f	PROPN
ma-254	202	11	(	(	PUNCT
ma-254	202	12	y)η(y	y)η(y	PROPN
ma-254	202	13	�	�	PROPN
ma-254	202	14	∗	∗	VERB
ma-254	202	15	x)dy	x)dy	PROPN
ma-254	203	1	=	=	PUNCT
ma-254	204	1	f	f	PROPN
ma-254	205	1	∗	∗	NOUN
ma-254	205	2	η(x	η(x	PROPN
ma-254	205	3	)	)	PUNCT
ma-254	205	4	.	.	PUNCT
ma-254	206	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	206	2	eur	eur	PROPN
ma-254	206	3	.	.	PUNCT
ma-254	207	1	j.	j.	PROPN
ma-254	207	2	math	math	PROPN
ma-254	207	3	.	.	PUNCT
ma-254	208	1	anal	anal	PROPN
ma-254	208	2	.	.	PUNCT
ma-254	209	1	10.28924	10.28924	NUM
ma-254	209	2	/	/	SYM
ma-254	209	3	ada	ada	PROPN
ma-254	209	4	/	/	SYM
ma-254	209	5	ma.5.3	ma.5.3	PROPN
ma-254	209	6	8then	8then	PROPN
ma-254	209	7	,	,	PUNCT
ma-254	209	8	|fn	|fn	PUNCT
ma-254	209	9	∗	∗	NOUN
ma-254	209	10	η(x)−	η(x)−	PROPN
ma-254	209	11	f	f	PROPN
ma-254	209	12	∗	∗	NOUN
ma-254	209	13	η(x)|	η(x)|	PROPN
ma-254	209	14	=	=	SYM
ma-254	209	15	∣∣∣∣∫	∣∣∣∣∫	NOUN
ma-254	209	16	g	g	PROPN
ma-254	209	17	fn(y)η(y	fn(y)η(y	PROPN
ma-254	209	18	�	�	PROPN
ma-254	209	19	∗	∗	NOUN
ma-254	209	20	x)dy	x)dy	PROPN
ma-254	210	1	−	−	PROPN
ma-254	210	2	∫	∫	PROPN
ma-254	210	3	g	g	PROPN
ma-254	210	4	f	f	PROPN
ma-254	210	5	(	(	PUNCT
ma-254	210	6	y)η(y	y)η(y	PROPN
ma-254	210	7	�	�	PROPN
ma-254	210	8	∗	∗	VERB
ma-254	210	9	x)dy	x)dy	PROPN
ma-254	210	10	∣∣∣∣	∣∣∣∣	PROPN
ma-254	210	11	=	=	SYM
ma-254	210	12	∣∣∣∣∫	∣∣∣∣∫	NOUN
ma-254	210	13	g	g	NOUN
ma-254	210	14	(	(	PUNCT
ma-254	210	15	fn(y)−	fn(y)−	PROPN
ma-254	210	16	f	f	PROPN
ma-254	210	17	(	(	PUNCT
ma-254	210	18	y))η(y	y))η(y	PROPN
ma-254	210	19	�	�	PROPN
ma-254	210	20	∗	∗	VERB
ma-254	210	21	x)dy	x)dy	PROPN
ma-254	210	22	∣∣∣∣	∣∣∣∣	PROPN
ma-254	210	23	≤	≤	NOUN
ma-254	211	1	‖fn	‖fn	PROPN
ma-254	211	2	−	−	PROPN
ma-254	211	3	f	f	PROPN
ma-254	211	4	‖p	‖p	PROPN
ma-254	211	5	(	(	PUNCT
ma-254	211	6	∫	∫	PROPN
ma-254	211	7	g	g	PROPN
ma-254	211	8	|η(y	|η(y	PROPN
ma-254	211	9	�	�	PROPN
ma-254	211	10	∗	∗	NOUN
ma-254	211	11	x)|p′dy	x)|p′dy	PROPN
ma-254	211	12	)	)	PUNCT
ma-254	211	13	1	1	NUM
ma-254	211	14	p′	p′	NOUN
ma-254	211	15	≤	≤	NOUN
ma-254	211	16	2	2	NUM
ma-254	211	17	m	m	NOUN
ma-254	211	18	(	(	PUNCT
ma-254	211	19	∫	∫	PROPN
ma-254	211	20	g	g	PROPN
ma-254	211	21	|η(z)|p′d(δy	|η(z)|p′d(δy	NOUN
ma-254	211	22	�	�	PROPN
ma-254	211	23	∗	∗	NOUN
ma-254	211	24	δx)(z	δx)(z	PROPN
ma-254	211	25	)	)	PUNCT
ma-254	211	26	)	)	PUNCT
ma-254	211	27	1	1	NUM
ma-254	211	28	p′	p′	NOUN
ma-254	211	29	≤	≤	NOUN
ma-254	211	30	2m‖η‖p′	2m‖η‖p′	NUM
ma-254	211	31	.again	.again	NOUN
ma-254	211	32	,	,	PUNCT
ma-254	211	33	by	by	ADP
ma-254	211	34	the	the	DET
ma-254	211	35	dominated	dominate	VERB
ma-254	211	36	convergence	convergence	NOUN
ma-254	211	37	theorem	theorem	VERB
ma-254	211	38	,	,	PUNCT
ma-254	211	39	we	we	PRON
ma-254	211	40	obtain	obtain	VERB
ma-254	211	41	lim	lim	PROPN
ma-254	211	42	n→∞	n→∞	X
ma-254	211	43	‖fn	‖fn	PROPN
ma-254	211	44	∗	∗	X
ma-254	211	45	η	η	PROPN
ma-254	211	46	−	−	PROPN
ma-254	211	47	f	f	PROPN
ma-254	211	48	∗	∗	NOUN
ma-254	211	49	η‖q	η‖q	NOUN
ma-254	211	50	=	=	SYM
ma-254	211	51	0	0	X
ma-254	211	52	.	.	X
ma-254	212	1	�	�	PROPN
ma-254	212	2	hereafter	hereafter	PROPN
ma-254	212	3	is	be	AUX
ma-254	212	4	the	the	DET
ma-254	212	5	analogue	analogue	NOUN
ma-254	212	6	of	of	ADP
ma-254	212	7	the	the	DET
ma-254	212	8	rellich	rellich	NOUN
ma-254	212	9	-	-	PUNCT
ma-254	212	10	kondrachov	kondrachov	NOUN
ma-254	212	11	theorem	theorem	NOUN
ma-254	212	12	for	for	ADP
ma-254	212	13	hypergroup	hypergroup	NOUN
ma-254	212	14	gelfand	gelfand	ADJ
ma-254	212	15	pairs	pair	NOUN
ma-254	212	16	.	.	PUNCT
ma-254	213	1	theorem	theorem	VERB
ma-254	213	2	3.7	3.7	NUM
ma-254	213	3	.	.	PUNCT
ma-254	214	1	assume	assume	VERB
ma-254	214	2	that	that	SCONJ
ma-254	214	3	g	g	PROPN
ma-254	214	4	is	be	AUX
ma-254	214	5	compact	compact	ADJ
ma-254	214	6	.	.	PUNCT
ma-254	215	1	let	let	AUX
ma-254	215	2	(	(	PUNCT
ma-254	215	3	g	g	NOUN
ma-254	215	4	,	,	PUNCT
ma-254	215	5	k	k	NOUN
ma-254	215	6	)	)	PUNCT
ma-254	215	7	be	be	VERB
ma-254	215	8	a	a	DET
ma-254	215	9	hypergroup	hypergroup	NOUN
ma-254	215	10	gelfand	gelfand	PROPN
ma-254	215	11	pair	pair	NOUN
ma-254	215	12	.	.	PUNCT
ma-254	216	1	let	let	VERB
ma-254	216	2	α	α	PRON
ma-254	216	3	>	>	X
ma-254	216	4	s	s	PROPN
ma-254	216	5	>	>	X
ma-254	216	6	0	0	X
ma-254	216	7	.	.	PUNCT
ma-254	217	1	let	let	VERB
ma-254	217	2	p	p	NOUN
ma-254	217	3	:	:	PUNCT
ma-254	217	4	=	=	SYM
ma-254	217	5	2α	2α	X
ma-254	217	6	α+s	α+s	NUM
ma-254	217	7	and	and	CCONJ
ma-254	217	8	let	let	VERB
ma-254	217	9	p′	p′	NOUN
ma-254	217	10	be	be	AUX
ma-254	217	11	such	such	ADJ
ma-254	217	12	that	that	SCONJ
ma-254	217	13	1	1	NUM
ma-254	217	14	p	p	NOUN
ma-254	217	15	+	+	NOUN
ma-254	217	16	1	1	NUM
ma-254	217	17	p′	p′	NOUN
ma-254	217	18	=	=	SYM
ma-254	217	19	1	1	X
ma-254	217	20	.	.	PUNCT
ma-254	218	1	if	if	SCONJ
ma-254	218	2	(	(	PUNCT
ma-254	218	3	1	1	NUM
ma-254	218	4	+	+	NUM
ma-254	218	5	γ2)−1	γ2)−1	X
ma-254	218	6	∈	∈	NOUN
ma-254	218	7	lα(ĝ\	lα(ĝ\	PUNCT
ma-254	218	8	)	)	PUNCT
ma-254	218	9	and	and	CCONJ
ma-254	218	10	lim	lim	PROPN
ma-254	218	11	y→e	y→e	PROPN
ma-254	218	12	(	(	PUNCT
ma-254	218	13	sup	sup	PROPN
ma-254	218	14	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	218	15	|φ(y)−	|φ(y)−	PROPN
ma-254	218	16	1|	1|	NUM
ma-254	218	17	(	(	PUNCT
ma-254	218	18	1	1	NUM
ma-254	218	19	+	+	CCONJ
ma-254	218	20	γ(φ)2	γ(φ)2	PROPN
ma-254	218	21	)	)	PUNCT
ma-254	218	22	s	s	PART
ma-254	218	23	2	2	NUM
ma-254	218	24	)	)	PUNCT
ma-254	218	25	=	=	SYM
ma-254	218	26	0	0	NUM
ma-254	218	27	,	,	PUNCT
ma-254	218	28	then	then	ADV
ma-254	218	29	hs,\γ	hs,\γ	PROPN
ma-254	218	30	(	(	PUNCT
ma-254	218	31	g	g	NOUN
ma-254	218	32	)	)	PUNCT
ma-254	218	33	embeds	embed	VERB
ma-254	218	34	compactly	compactly	ADV
ma-254	218	35	in	in	ADP
ma-254	218	36	lq,\(g	lq,\(g	PROPN
ma-254	218	37	)	)	PUNCT
ma-254	218	38	for	for	ADP
ma-254	218	39	every	every	DET
ma-254	218	40	q	q	X
ma-254	218	41	∈	∈	PROPN
ma-254	218	42	[	[	X
ma-254	218	43	1	1	NUM
ma-254	218	44	,	,	PUNCT
ma-254	218	45	p′	p′	NOUN
ma-254	218	46	]	]	PUNCT
ma-254	218	47	.	.	PUNCT
ma-254	219	1	proof	proof	NOUN
ma-254	219	2	.	.	PUNCT
ma-254	220	1	in	in	ADP
ma-254	220	2	theorem	theorem	NOUN
ma-254	220	3	3.2	3.2	NUM
ma-254	220	4	,	,	PUNCT
ma-254	220	5	we	we	PRON
ma-254	220	6	obtained	obtain	VERB
ma-254	220	7	that	that	DET
ma-254	220	8	hs,\γ	hs,\γ	PROPN
ma-254	220	9	(	(	PUNCT
ma-254	220	10	g	g	NOUN
ma-254	220	11	)	)	PUNCT
ma-254	220	12	↪	↪	PROPN
ma-254	220	13	→	→	SYM
ma-254	220	14	lp	lp	ADJ
ma-254	220	15	′,\(g	′,\(g	PROPN
ma-254	220	16	)	)	PUNCT
ma-254	220	17	;	;	PUNCT
ma-254	220	18	since	since	SCONJ
ma-254	220	19	g	g	NOUN
ma-254	220	20	is	be	AUX
ma-254	220	21	compact	compact	ADJ
ma-254	220	22	and	and	CCONJ
ma-254	220	23	p′	p′	NOUN
ma-254	220	24	>	>	X
ma-254	220	25	q	q	X
ma-254	220	26	,	,	PUNCT
ma-254	220	27	then	then	ADV
ma-254	220	28	lp	lp	PROPN
ma-254	220	29	′,\(g	′,\(g	PROPN
ma-254	220	30	)	)	PUNCT
ma-254	220	31	↪	↪	PROPN
ma-254	220	32	→	→	SYM
ma-254	220	33	lq,\(g	lq,\(g	PROPN
ma-254	220	34	)	)	PUNCT
ma-254	220	35	.	.	PUNCT
ma-254	221	1	therefore	therefore	ADV
ma-254	221	2	,	,	PUNCT
ma-254	221	3	we	we	PRON
ma-254	221	4	have	have	VERB
ma-254	221	5	that	that	DET
ma-254	221	6	hs,\γ	hs,\γ	PROPN
ma-254	221	7	(	(	PUNCT
ma-254	221	8	g	g	NOUN
ma-254	221	9	)	)	PUNCT
ma-254	221	10	↪	↪	PROPN
ma-254	221	11	→	→	SYM
ma-254	221	12	lq,\(g	lq,\(g	PROPN
ma-254	221	13	)	)	PUNCT
ma-254	221	14	.	.	PUNCT
ma-254	222	1	now	now	ADV
ma-254	222	2	,	,	PUNCT
ma-254	222	3	let	let	VERB
ma-254	222	4	(	(	PUNCT
ma-254	222	5	fn	fn	NOUN
ma-254	222	6	)	)	PUNCT
ma-254	222	7	be	be	AUX
ma-254	222	8	a	a	DET
ma-254	222	9	boundedsequence	boundedsequence	NOUN
ma-254	222	10	in	in	ADP
ma-254	222	11	hs,\γ	hs,\γ	PROPN
ma-254	222	12	(	(	PUNCT
ma-254	222	13	g	g	NOUN
ma-254	222	14	)	)	PUNCT
ma-254	222	15	.	.	PUNCT
ma-254	223	1	then	then	ADV
ma-254	223	2	,	,	PUNCT
ma-254	223	3	(	(	PUNCT
ma-254	223	4	fn	fn	NOUN
ma-254	223	5	)	)	PUNCT
ma-254	223	6	is	be	AUX
ma-254	223	7	a	a	DET
ma-254	223	8	bounded	bounded	ADJ
ma-254	223	9	sequence	sequence	NOUN
ma-254	223	10	in	in	ADP
ma-254	223	11	lp′,\(g	lp′,\(g	PROPN
ma-254	223	12	)	)	PUNCT
ma-254	223	13	.	.	PUNCT
ma-254	224	1	there	there	PRON
ma-254	224	2	exists	exist	VERB
ma-254	224	3	m	m	VERB
ma-254	224	4	>	>	X
ma-254	224	5	0	0	NUM
ma-254	224	6	such	such	ADJ
ma-254	224	7	that	that	SCONJ
ma-254	224	8	∀n	∀n	NUM
ma-254	224	9	∈	∈	PROPN
ma-254	224	10	n	n	CCONJ
ma-254	224	11	,	,	PUNCT
ma-254	224	12	‖fn‖p′	‖fn‖p′	PROPN
ma-254	224	13	6	6	NUM
ma-254	224	14	m.for	m.for	ADP
ma-254	224	15	g	g	PROPN
ma-254	224	16	∈	∈	PROPN
ma-254	224	17	lp,\(g	lp,\(g	PROPN
ma-254	224	18	)	)	PUNCT
ma-254	224	19	,	,	PUNCT
ma-254	224	20	we	we	PRON
ma-254	224	21	have	have	VERB
ma-254	224	22	|〈fn	|〈fn	NOUN
ma-254	224	23	,	,	PUNCT
ma-254	224	24	g〉|	g〉|	X
ma-254	224	25	6	6	NUM
ma-254	224	26	‖fn‖p′‖g‖p	‖fn‖p′‖g‖p	NUM
ma-254	224	27	6	6	NUM
ma-254	224	28	m‖g‖p.therefore	m‖g‖p.therefore	ADV
ma-254	224	29	,	,	PUNCT
ma-254	224	30	(	(	PUNCT
ma-254	224	31	fn	fn	NOUN
ma-254	224	32	)	)	PUNCT
ma-254	224	33	is	be	AUX
ma-254	224	34	weakly	weakly	ADV
ma-254	224	35	bounded	bound	VERB
ma-254	224	36	.	.	PUNCT
ma-254	225	1	it	it	PRON
ma-254	225	2	admits	admit	VERB
ma-254	225	3	a	a	DET
ma-254	225	4	subsequence	subsequence	NOUN
ma-254	225	5	(	(	PUNCT
ma-254	225	6	hn	hn	PROPN
ma-254	225	7	)	)	PUNCT
ma-254	225	8	which	which	PRON
ma-254	225	9	converges	converge	VERB
ma-254	225	10	weakly	weakly	ADV
ma-254	225	11	to	to	ADP
ma-254	225	12	h	h	PROPN
ma-254	225	13	∈	∈	PROPN
ma-254	225	14	lp′,\(g	lp′,\(g	PROPN
ma-254	225	15	)	)	PUNCT
ma-254	225	16	.	.	PUNCT
ma-254	226	1	take	take	VERB
ma-254	226	2	ε	ε	PROPN
ma-254	226	3	>	>	PUNCT
ma-254	226	4	0	0	PUNCT
ma-254	226	5	and	and	CCONJ
ma-254	226	6	η	η	PROPN
ma-254	226	7	∈	∈	PROPN
ma-254	226	8	k\(g	k\(g	PROPN
ma-254	226	9	)	)	PUNCT
ma-254	226	10	such	such	ADJ
ma-254	226	11	that	that	SCONJ
ma-254	226	12	‖h	‖h	PROPN
ma-254	226	13	∗	∗	PROPN
ma-254	226	14	η	η	PROPN
ma-254	226	15	−	−	PROPN
ma-254	226	16	h‖2	h‖2	NOUN
ma-254	226	17	<	<	X
ma-254	226	18	ε.by	ε.by	PROPN
ma-254	226	19	theorem	theorem	VERB
ma-254	226	20	3.5	3.5	NUM
ma-254	226	21	and	and	CCONJ
ma-254	226	22	theorem	theorem	VERB
ma-254	226	23	3.6	3.6	NUM
ma-254	226	24	,	,	PUNCT
ma-254	226	25	we	we	PRON
ma-254	226	26	have	have	VERB
ma-254	226	27	‖hn	‖hn	NOUN
ma-254	226	28	−	−	PROPN
ma-254	226	29	h‖2	h‖2	NOUN
ma-254	226	30	≤	≤	NUM
ma-254	226	31	‖hn	‖hn	NUM
ma-254	226	32	−	−	PROPN
ma-254	227	1	hn	hn	PROPN
ma-254	227	2	∗	∗	NOUN
ma-254	227	3	η‖2	η‖2	PROPN
ma-254	227	4	+	+	CCONJ
ma-254	227	5	‖hn	‖hn	X
ma-254	227	6	∗	∗	NOUN
ma-254	227	7	η	η	PROPN
ma-254	227	8	−	−	PROPN
ma-254	227	9	h	h	PROPN
ma-254	227	10	∗	∗	NOUN
ma-254	227	11	η‖2	η‖2	PROPN
ma-254	228	1	+	+	CCONJ
ma-254	228	2	‖h	‖h	PROPN
ma-254	228	3	∗	∗	PROPN
ma-254	228	4	η	η	PROPN
ma-254	228	5	−	−	PROPN
ma-254	228	6	h‖2	h‖2	NOUN
ma-254	228	7	≤	≤	NUM
ma-254	228	8	sup	sup	NOUN
ma-254	228	9	y∈supp(η	y∈supp(η	PROPN
ma-254	228	10	)	)	PUNCT
ma-254	228	11	(	(	PUNCT
ma-254	228	12	sup	sup	NOUN
ma-254	228	13	φ∈ĝ\	φ∈ĝ\	PROPN
ma-254	228	14	|φ(y)−	|φ(y)−	PROPN
ma-254	228	15	1|	1|	NUM
ma-254	228	16	(	(	PUNCT
ma-254	228	17	1	1	NUM
ma-254	228	18	+	+	CCONJ
ma-254	228	19	γ(φ)2	γ(φ)2	PROPN
ma-254	228	20	)	)	PUNCT
ma-254	228	21	s	s	PART
ma-254	228	22	2	2	NUM
ma-254	228	23	)	)	PUNCT
ma-254	228	24	·	·	PUNCT
ma-254	228	25	‖hn‖hs,\γ	‖hn‖hs,\γ	VERB
ma-254	228	26	+	+	CCONJ
ma-254	228	27	‖hn	‖hn	PROPN
ma-254	228	28	∗	∗	NOUN
ma-254	228	29	η	η	PROPN
ma-254	228	30	−	−	PROPN
ma-254	228	31	h	h	PROPN
ma-254	228	32	∗	∗	NOUN
ma-254	228	33	η‖2	η‖2	PROPN
ma-254	229	1	+	+	CCONJ
ma-254	229	2	ε	ε	PROPN
ma-254	229	3	≤	≤	NUM
ma-254	229	4	2ε+	2ε+	NUM
ma-254	229	5	‖hn	‖hn	PROPN
ma-254	229	6	∗	∗	X
ma-254	229	7	η	η	PROPN
ma-254	229	8	−	−	PROPN
ma-254	229	9	h	h	PROPN
ma-254	229	10	∗	∗	NOUN
ma-254	229	11	η‖2	η‖2	PROPN
ma-254	229	12	.	.	PUNCT
ma-254	230	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	230	2	eur	eur	PROPN
ma-254	230	3	.	.	PUNCT
ma-254	231	1	j.	j.	PROPN
ma-254	231	2	math	math	PROPN
ma-254	231	3	.	.	PUNCT
ma-254	232	1	anal	anal	PROPN
ma-254	232	2	.	.	PUNCT
ma-254	233	1	10.28924	10.28924	NUM
ma-254	233	2	/	/	SYM
ma-254	233	3	ada	ada	PROPN
ma-254	233	4	/	/	SYM
ma-254	233	5	ma.5.3	ma.5.3	PROPN
ma-254	233	6	9as	9as	NOUN
ma-254	233	7	the	the	DET
ma-254	233	8	above	above	ADJ
ma-254	233	9	inequality	inequality	NOUN
ma-254	233	10	is	be	AUX
ma-254	233	11	realized	realize	VERB
ma-254	233	12	for	for	ADP
ma-254	233	13	an	an	DET
ma-254	233	14	arbitrary	arbitrary	ADJ
ma-254	233	15	ε	ε	NOUN
ma-254	233	16	,	,	PUNCT
ma-254	233	17	then	then	ADV
ma-254	233	18	‖hn	‖hn	NUM
ma-254	233	19	−	−	PROPN
ma-254	233	20	h‖2	h‖2	NOUN
ma-254	233	21	≤	≤	NUM
ma-254	233	22	‖hn	‖hn	PROPN
ma-254	233	23	∗	∗	NOUN
ma-254	233	24	η	η	PROPN
ma-254	233	25	−	−	PROPN
ma-254	233	26	h	h	PROPN
ma-254	233	27	∗	∗	NOUN
ma-254	233	28	η‖2	η‖2	PROPN
ma-254	233	29	.	.	PUNCT
ma-254	234	1	therefore	therefore	ADV
ma-254	234	2	,	,	PUNCT
ma-254	234	3	lim	lim	PROPN
ma-254	234	4	n→∞	n→∞	X
ma-254	234	5	‖hn	‖hn	PROPN
ma-254	234	6	−	−	NOUN
ma-254	234	7	h‖2	h‖2	NOUN
ma-254	234	8	=	=	SYM
ma-254	234	9	lim	lim	PROPN
ma-254	234	10	n→∞	n→∞	X
ma-254	234	11	‖hn	‖hn	PROPN
ma-254	234	12	∗	∗	NOUN
ma-254	234	13	η	η	PROPN
ma-254	234	14	−	−	PROPN
ma-254	234	15	h	h	PROPN
ma-254	234	16	∗	∗	NOUN
ma-254	234	17	η‖2	η‖2	PROPN
ma-254	234	18	=	=	PUNCT
ma-254	234	19	0	0	NUM
ma-254	234	20	.	.	PUNCT
ma-254	234	21	thus	thus	ADV
ma-254	234	22	,	,	PUNCT
ma-254	234	23	(	(	PUNCT
ma-254	234	24	hn	hn	NOUN
ma-254	234	25	)	)	PUNCT
ma-254	234	26	converges	converge	VERB
ma-254	234	27	to	to	ADP
ma-254	234	28	h	h	PROPN
ma-254	234	29	in	in	ADP
ma-254	234	30	l2,\(g	l2,\(g	PROPN
ma-254	234	31	)	)	PUNCT
ma-254	234	32	.	.	PUNCT
ma-254	235	1	since	since	SCONJ
ma-254	235	2	g	g	PROPN
ma-254	235	3	is	be	AUX
ma-254	235	4	compact	compact	ADJ
ma-254	235	5	,	,	PUNCT
ma-254	235	6	we	we	PRON
ma-254	235	7	apply	apply	VERB
ma-254	235	8	the	the	DET
ma-254	235	9	vitali	vitali	PROPN
ma-254	235	10	’s	’s	PART
ma-254	235	11	convergence	convergence	NOUN
ma-254	235	12	theoremto	theoremto	ADP
ma-254	235	13	conclude	conclude	NOUN
ma-254	235	14	that	that	SCONJ
ma-254	235	15	(	(	PUNCT
ma-254	235	16	hn	hn	NOUN
ma-254	235	17	)	)	PUNCT
ma-254	235	18	converges	converge	VERB
ma-254	235	19	to	to	ADP
ma-254	235	20	h	h	PROPN
ma-254	235	21	in	in	ADP
ma-254	235	22	lq,\(g	lq,\(g	PROPN
ma-254	235	23	)	)	PUNCT
ma-254	235	24	.	.	PUNCT
ma-254	236	1	�	�	PROPN
ma-254	236	2	references	reference	NOUN
ma-254	236	3	[	[	X
ma-254	236	4	1	1	NUM
ma-254	236	5	]	]	PUNCT
ma-254	236	6	r.	r.	PROPN
ma-254	236	7	a.	a.	PROPN
ma-254	236	8	adams	adams	PROPN
ma-254	236	9	,	,	PUNCT
ma-254	236	10	sobolev	sobolev	NOUN
ma-254	236	11	spaces	space	NOUN
ma-254	236	12	,	,	PUNCT
ma-254	236	13	academic	academic	ADJ
ma-254	236	14	press	press	NOUN
ma-254	236	15	,	,	PUNCT
ma-254	236	16	new	new	PROPN
ma-254	236	17	york	york	PROPN
ma-254	236	18	,	,	PUNCT
ma-254	236	19	1975.[2	1975.[2	NUM
ma-254	236	20	]	]	X
ma-254	236	21	k.	k.	PROPN
ma-254	236	22	t.	t.	PROPN
ma-254	236	23	bataka	bataka	PROPN
ma-254	236	24	,	,	PUNCT
ma-254	236	25	e.	e.	PROPN
ma-254	236	26	m.	m.	PROPN
ma-254	236	27	egwe	egwe	PROPN
ma-254	236	28	and	and	CCONJ
ma-254	236	29	y.	y.	PROPN
ma-254	236	30	mensah	mensah	PROPN
ma-254	236	31	,	,	PUNCT
ma-254	236	32	sobolev	sobolev	NOUN
ma-254	236	33	spaces	space	VERB
ma-254	236	34	on	on	ADP
ma-254	236	35	hypergroup	hypergroup	PROPN
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ma-254	236	38	,	,	PUNCT
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ma-254	236	43	.	.	PUNCT
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ma-254	237	2	.	.	PROPN
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ma-254	237	7	)	)	PUNCT
ma-254	237	8	,	,	PUNCT
ma-254	237	9	57–69	57–69	NUM
ma-254	237	10	,	,	PUNCT
ma-254	237	11	https://doi.org/10.17654/097208712505.[3	https://doi.org/10.17654/097208712505.[3	PROPN
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ma-254	237	13	w.	w.	PROPN
ma-254	237	14	r.	r.	PROPN
ma-254	237	15	bloom	bloom	PROPN
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ma-254	237	17	h.	h.	PROPN
ma-254	237	18	heyer	heyer	PROPN
ma-254	237	19	,	,	PUNCT
ma-254	237	20	harmonic	harmonic	VERB
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ma-254	237	23	probability	probability	NOUN
ma-254	237	24	measures	measure	NOUN
ma-254	237	25	on	on	ADP
ma-254	237	26	hypergroups	hypergroup	NOUN
ma-254	237	27	,	,	PUNCT
ma-254	237	28	de	de	X
ma-254	237	29	gruyter	gruyter	NOUN
ma-254	237	30	studies	study	NOUN
ma-254	237	31	inmathematics	inmathematic	NOUN
ma-254	237	32	20	20	NUM
ma-254	237	33	,	,	PUNCT
ma-254	237	34	berlin	berlin	PROPN
ma-254	237	35	,	,	PUNCT
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ma-254	237	42	spaces	space	NOUN
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ma-254	237	47	,	,	PUNCT
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ma-254	237	49	,	,	PUNCT
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ma-254	237	56	i.	i.	PROPN
ma-254	237	57	toure	toure	PROPN
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ma-254	237	59	k.	k.	PROPN
ma-254	237	60	kangni	kangni	PROPN
ma-254	237	61	,	,	PUNCT
ma-254	237	62	a	a	DET
ma-254	237	63	plancherel	plancherel	NOUN
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ma-254	237	65	on	on	ADP
ma-254	237	66	a	a	DET
ma-254	237	67	noncommutative	noncommutative	ADJ
ma-254	237	68	hypergroup	hypergroup	NOUN
ma-254	237	69	,	,	PUNCT
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ma-254	238	3	.	.	PUNCT
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ma-254	239	2	.	.	PROPN
ma-254	239	3	,	,	PUNCT
ma-254	239	4	20(2022	20(2022	PROPN
ma-254	239	5	)	)	PUNCT
ma-254	239	6	,	,	PUNCT
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ma-254	239	8	,	,	PUNCT
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ma-254	239	11	k.	k.	PROPN
ma-254	240	1	g.	g.	PROPN
ma-254	240	2	brou	brou	PROPN
ma-254	240	3	and	and	CCONJ
ma-254	240	4	k.	k.	PROPN
ma-254	240	5	kangni	kangni	PROPN
ma-254	240	6	,	,	PUNCT
ma-254	240	7	on	on	ADP
ma-254	240	8	gelfand	gelfand	ADJ
ma-254	240	9	pair	pair	NOUN
ma-254	240	10	over	over	ADP
ma-254	240	11	hypergroups	hypergroup	NOUN
ma-254	240	12	,	,	PUNCT
ma-254	240	13	far	far	PROPN
ma-254	240	14	east	east	PROPN
ma-254	240	15	j.	j.	PROPN
ma-254	240	16	math	math	PROPN
ma-254	240	17	.	.	PUNCT
ma-254	241	1	sci	sci	PROPN
ma-254	241	2	.	.	PROPN
ma-254	241	3	,	,	PUNCT
ma-254	241	4	132(1	132(1	NUM
ma-254	241	5	)	)	PUNCT
ma-254	241	6	(	(	PUNCT
ma-254	241	7	2021	2021	NUM
ma-254	241	8	)	)	PUNCT
ma-254	241	9	63	63	NUM
ma-254	241	10	-	-	SYM
ma-254	241	11	76	76	NUM
ma-254	241	12	,	,	PUNCT
ma-254	241	13	http	http	CCONJ
ma-254	241	14	:	:	PUNCT
ma-254	241	15	//dx.doi.org/10.17654	//dx.doi.org/10.17654	NUM
ma-254	241	16	/	/	SYM
ma-254	241	17	ms132010063.[7	ms132010063.[7	PROPN
ma-254	241	18	]	]	PUNCT
ma-254	241	19	k.	k.	PROPN
ma-254	241	20	g.	g.	PROPN
ma-254	241	21	brou	brou	PROPN
ma-254	241	22	,	,	PUNCT
ma-254	241	23	p.	p.	NOUN
ma-254	241	24	coulibaly	coulibaly	NOUN
ma-254	241	25	and	and	CCONJ
ma-254	241	26	k.	k.	PROPN
ma-254	241	27	kangni	kangni	PROPN
ma-254	241	28	,	,	PUNCT
ma-254	241	29	uncertainly	uncertainly	ADV
ma-254	241	30	principles	principle	VERB
ma-254	241	31	for	for	ADP
ma-254	241	32	a	a	DET
ma-254	241	33	non	non	ADJ
ma-254	241	34	commutative	commutative	PROPN
ma-254	241	35	hypergroup	hypergroup	PROPN
ma-254	241	36	,	,	PUNCT
ma-254	241	37	adv	adv	PROPN
ma-254	241	38	.	.	PUNCT
ma-254	242	1	in	in	ADP
ma-254	242	2	math.sci	math.sci	X
ma-254	242	3	.	.	PUNCT
ma-254	243	1	j.	j.	PROPN
ma-254	243	2	,	,	PUNCT
ma-254	243	3	12	12	NUM
ma-254	243	4	(	(	PUNCT
ma-254	243	5	2	2	NUM
ma-254	243	6	)	)	PUNCT
ma-254	243	7	,	,	PUNCT
ma-254	243	8	(	(	PUNCT
ma-254	243	9	2023	2023	NUM
ma-254	243	10	)	)	PUNCT
ma-254	243	11	381	381	NUM
ma-254	243	12	-	-	SYM
ma-254	243	13	392	392	NUM
ma-254	243	14	,	,	PUNCT
ma-254	243	15	https://doi.org/10.37418/amsj.12.2.6.[8	https://doi.org/10.37418/amsj.12.2.6.[8	PROPN
ma-254	243	16	]	]	PUNCT
ma-254	243	17	s.	s.	PROPN
ma-254	243	18	chua	chua	PROPN
ma-254	243	19	,	,	PUNCT
ma-254	243	20	s.	s.	PROPN
ma-254	243	21	rodney	rodney	PROPN
ma-254	243	22	and	and	CCONJ
ma-254	243	23	r.	r.	PROPN
ma-254	243	24	wheeden	wheeden	PROPN
ma-254	243	25	,	,	PUNCT
ma-254	243	26	a	a	DET
ma-254	243	27	compact	compact	ADJ
ma-254	243	28	embedding	embed	VERB
ma-254	243	29	theorem	theorem	NOUN
ma-254	243	30	for	for	ADP
ma-254	243	31	generalized	generalized	ADJ
ma-254	243	32	sobolev	sobolev	NOUN
ma-254	243	33	spaces	space	NOUN
ma-254	243	34	,	,	PUNCT
ma-254	243	35	pacific	pacific	PROPN
ma-254	243	36	j.math	j.math	PROPN
ma-254	243	37	.	.	PROPN
ma-254	243	38	,	,	PUNCT
ma-254	243	39	265(1	265(1	NUM
ma-254	243	40	)	)	PUNCT
ma-254	243	41	,	,	PUNCT
ma-254	243	42	(	(	PUNCT
ma-254	243	43	2013	2013	NUM
ma-254	243	44	)	)	PUNCT
ma-254	243	45	17	17	NUM
ma-254	243	46	-	-	SYM
ma-254	243	47	57	57	NUM
ma-254	243	48	,	,	PUNCT
ma-254	243	49	10.2140	10.2140	NUM
ma-254	243	50	/	/	SYM
ma-254	243	51	pjm.2013.265.17.[9	pjm.2013.265.17.[9	NOUN
ma-254	243	52	]	]	PUNCT
ma-254	243	53	d.	d.	PROPN
ma-254	243	54	e.	e.	PROPN
ma-254	243	55	edmunds	edmunds	PROPN
ma-254	243	56	and	and	CCONJ
ma-254	243	57	w.	w.	PROPN
ma-254	243	58	d.	d.	PROPN
ma-254	243	59	evans	evans	PROPN
ma-254	243	60	,	,	PUNCT
ma-254	243	61	spectral	spectral	ADJ
ma-254	243	62	theory	theory	NOUN
ma-254	243	63	and	and	CCONJ
ma-254	243	64	differential	differential	ADJ
ma-254	243	65	operators	operator	NOUN
ma-254	243	66	,	,	PUNCT
ma-254	243	67	oxford	oxford	PROPN
ma-254	243	68	mathematical	mathematical	PROPN
ma-254	243	69	monograph	monograph	NOUN
ma-254	243	70	,	,	PUNCT
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ma-254	243	72	,	,	PUNCT
ma-254	243	73	oxford	oxford	PROPN
ma-254	243	74	science	science	NOUN
ma-254	243	75	publications	publication	NOUN
ma-254	243	76	,	,	PUNCT
ma-254	243	77	oxford	oxford	PROPN
ma-254	243	78	university	university	PROPN
ma-254	243	79	press	press	NOUN
ma-254	243	80	,	,	PUNCT
ma-254	243	81	2018.[10	2018.[10	NUM
ma-254	243	82	]	]	PUNCT
ma-254	243	83	p.	p.	NOUN
ma-254	243	84	górka	górka	NOUN
ma-254	243	85	,	,	PUNCT
ma-254	243	86	t.	t.	PROPN
ma-254	243	87	kostrzewa	kostrzewa	PROPN
ma-254	243	88	and	and	CCONJ
ma-254	243	89	e.	e.	PROPN
ma-254	243	90	g.	g.	PROPN
ma-254	243	91	reyes	reyes	PROPN
ma-254	243	92	,	,	PUNCT
ma-254	243	93	sobolev	sobolev	NOUN
ma-254	243	94	spaces	space	VERB
ma-254	243	95	on	on	ADP
ma-254	243	96	locally	locally	ADV
ma-254	243	97	compact	compact	ADJ
ma-254	243	98	abelian	abelian	ADJ
ma-254	243	99	groups	group	NOUN
ma-254	243	100	:	:	PUNCT
ma-254	243	101	compact	compact	ADJ
ma-254	243	102	embeddingsand	embeddingsand	NOUN
ma-254	243	103	local	local	ADJ
ma-254	243	104	spaces	space	NOUN
ma-254	243	105	,	,	PUNCT
ma-254	243	106	journal	journal	NOUN
ma-254	243	107	of	of	ADP
ma-254	243	108	function	function	NOUN
ma-254	243	109	spaces	space	NOUN
ma-254	243	110	,	,	PUNCT
ma-254	243	111	(	(	PUNCT
ma-254	243	112	2014	2014	NUM
ma-254	243	113	)	)	PUNCT
ma-254	243	114	,	,	PUNCT
ma-254	243	115	article	article	NOUN
ma-254	243	116	i	i	PROPN
ma-254	243	117	d	d	PROPN
ma-254	243	118	404738	404738	NUM
ma-254	243	119	,	,	PUNCT
ma-254	243	120	6	6	NUM
ma-254	243	121	pages	page	NOUN
ma-254	243	122	,	,	PUNCT
ma-254	243	123	http://dx.doi.org/10.1155/	http://dx.doi.org/10.1155/	PROPN
ma-254	243	124	2014/404738.[11	2014/404738.[11	NUM
ma-254	243	125	]	]	X
ma-254	243	126	p.	p.	NOUN
ma-254	243	127	górka	górka	NOUN
ma-254	243	128	,	,	PUNCT
ma-254	243	129	t.	t.	PROPN
ma-254	243	130	kostrzewa	kostrzewa	PROPN
ma-254	243	131	and	and	CCONJ
ma-254	243	132	e.	e.	PROPN
ma-254	243	133	g.	g.	PROPN
ma-254	243	134	reyes	reyes	PROPN
ma-254	243	135	,	,	PUNCT
ma-254	243	136	sobolev	sobolev	NOUN
ma-254	243	137	spaces	space	VERB
ma-254	243	138	on	on	ADP
ma-254	243	139	locally	locally	ADV
ma-254	243	140	compact	compact	ADJ
ma-254	243	141	abelian	abelian	ADJ
ma-254	243	142	groups	group	NOUN
ma-254	243	143	and	and	CCONJ
ma-254	243	144	the	the	DET
ma-254	243	145	bosonic	bosonic	PROPN
ma-254	243	146	stringequation	stringequation	NOUN
ma-254	243	147	,	,	PUNCT
ma-254	243	148	j.	j.	PROPN
ma-254	243	149	aust	aust	PROPN
ma-254	243	150	.	.	PUNCT
ma-254	244	1	math	math	PROPN
ma-254	244	2	.	.	PUNCT
ma-254	245	1	soc	soc	PROPN
ma-254	245	2	.	.	PUNCT
ma-254	245	3	,	,	PUNCT
ma-254	245	4	98	98	NUM
ma-254	245	5	(	(	PUNCT
ma-254	245	6	2015	2015	NUM
ma-254	245	7	)	)	PUNCT
ma-254	245	8	,	,	PUNCT
ma-254	245	9	39	39	NUM
ma-254	245	10	-	-	SYM
ma-254	245	11	53	53	NUM
ma-254	245	12	,	,	PUNCT
ma-254	245	13	10.1017	10.1017	NUM
ma-254	245	14	/	/	SYM
ma-254	245	15	s1446788714000433.[12	s1446788714000433.[12	PROPN
ma-254	245	16	]	]	X
ma-254	245	17	p.	p.	PROPN
ma-254	245	18	hajlasz	hajlasz	PROPN
ma-254	245	19	,	,	PUNCT
ma-254	245	20	sobolev	sobolev	NOUN
ma-254	245	21	spaces	space	VERB
ma-254	245	22	on	on	ADP
ma-254	245	23	an	an	DET
ma-254	245	24	arbitrary	arbitrary	ADJ
ma-254	245	25	metric	metric	ADJ
ma-254	245	26	space	space	NOUN
ma-254	245	27	,	,	PUNCT
ma-254	245	28	potential	potential	ADJ
ma-254	245	29	anal	anal	NOUN
ma-254	245	30	.	.	PUNCT
ma-254	245	31	,	,	PUNCT
ma-254	245	32	5(4	5(4	NUM
ma-254	245	33	)	)	PUNCT
ma-254	245	34	(	(	PUNCT
ma-254	245	35	1996	1996	NUM
ma-254	245	36	)	)	PUNCT
ma-254	245	37	,	,	PUNCT
ma-254	245	38	403	403	NUM
ma-254	245	39	-	-	SYM
ma-254	245	40	415	415	NUM
ma-254	245	41	,	,	PUNCT
ma-254	245	42	https://doi.org/	https://doi.org/	VERB
ma-254	245	43	10.1007	10.1007	NUM
ma-254	245	44	/	/	SYM
ma-254	245	45	bf00275475.[13	bf00275475.[13	NOUN
ma-254	245	46	]	]	PUNCT
ma-254	245	47	p.	p.	NOUN
ma-254	246	1	hajlasz	hajlasz	PROPN
ma-254	247	1	and	and	CCONJ
ma-254	247	2	p.	p.	PROPN
ma-254	247	3	koskela	koskela	PROPN
ma-254	247	4	,	,	PUNCT
ma-254	247	5	sobolev	sobolev	NOUN
ma-254	247	6	met	meet	VERB
ma-254	247	7	poincaré	poincaré	PROPN
ma-254	247	8	,	,	PUNCT
ma-254	247	9	mem	mem	PROPN
ma-254	247	10	.	.	PUNCT
ma-254	248	1	amer	amer	PROPN
ma-254	248	2	.	.	PUNCT
ma-254	248	3	math	math	PROPN
ma-254	248	4	.	.	PUNCT
ma-254	249	1	soc	soc	PROPN
ma-254	249	2	.	.	PUNCT
ma-254	249	3	,	,	PUNCT
ma-254	249	4	145(688	145(688	NUM
ma-254	249	5	)	)	PUNCT
ma-254	249	6	(	(	PUNCT
ma-254	249	7	2000).[14	2000).[14	NUM
ma-254	249	8	]	]	PUNCT
ma-254	249	9	e.	e.	PROPN
ma-254	249	10	hebey	hebey	PROPN
ma-254	249	11	,	,	PUNCT
ma-254	249	12	sobolev	sobolev	NOUN
ma-254	249	13	spaces	space	VERB
ma-254	249	14	on	on	ADP
ma-254	249	15	riemannian	riemannian	ADJ
ma-254	249	16	manifolds	manifold	NOUN
ma-254	249	17	,	,	PUNCT
ma-254	249	18	lecture	lecture	NOUN
ma-254	249	19	notes	note	NOUN
ma-254	249	20	in	in	ADP
ma-254	249	21	mathematics	mathematic	NOUN
ma-254	249	22	,	,	PUNCT
ma-254	249	23	1635	1635	NUM
ma-254	249	24	,	,	PUNCT
ma-254	249	25	springer	springer	NOUN
ma-254	249	26	,	,	PUNCT
ma-254	249	27	berlin	berlin	PROPN
ma-254	249	28	,	,	PUNCT
ma-254	249	29	1996.[15	1996.[15	NUM
ma-254	249	30	]	]	X
ma-254	249	31	v.	v.	PROPN
ma-254	249	32	i.	i.	PROPN
ma-254	249	33	kondrachov	kondrachov	PROPN
ma-254	249	34	,	,	PUNCT
ma-254	249	35	on	on	ADP
ma-254	249	36	certain	certain	ADJ
ma-254	249	37	properties	property	NOUN
ma-254	249	38	of	of	ADP
ma-254	249	39	functions	function	NOUN
ma-254	249	40	in	in	ADP
ma-254	249	41	the	the	DET
ma-254	249	42	spaces	space	NOUN
ma-254	249	43	lp	lp	VERB
ma-254	249	44	,	,	PUNCT
ma-254	249	45	dokl	dokl	NOUN
ma-254	249	46	.	.	PUNCT
ma-254	250	1	akad	akad	PROPN
ma-254	250	2	.	.	PUNCT
ma-254	251	1	nauk	nauk	PROPN
ma-254	251	2	sssr	sssr	PROPN
ma-254	251	3	,	,	PUNCT
ma-254	251	4	48	48	NUM
ma-254	251	5	(	(	PUNCT
ma-254	251	6	8)	8)	NUM
ma-254	251	7	(	(	PUNCT
ma-254	251	8	1945	1945	NUM
ma-254	251	9	)	)	PUNCT
ma-254	251	10	563	563	NUM
ma-254	251	11	-	-	SYM
ma-254	251	12	566.[16	566.[16	PROPN
ma-254	251	13	]	]	PUNCT
ma-254	251	14	m.	m.	NOUN
ma-254	251	15	krukowski	krukowski	PROPN
ma-254	251	16	,	,	PUNCT
ma-254	251	17	sobolev	sobolev	NOUN
ma-254	251	18	spaces	space	VERB
ma-254	251	19	on	on	ADP
ma-254	251	20	gelfand	gelfand	ADJ
ma-254	251	21	pairs	pair	NOUN
ma-254	251	22	,	,	PUNCT
ma-254	251	23	(	(	PUNCT
ma-254	251	24	2020	2020	NUM
ma-254	251	25	)	)	PUNCT
ma-254	251	26	,	,	PUNCT
ma-254	251	27	https://arxiv.org/abs/2003.08519v1.[17	https://arxiv.org/abs/2003.08519v1.[17	ADJ
ma-254	251	28	]	]	PUNCT
ma-254	251	29	m.	m.	NOUN
ma-254	251	30	kumar	kumar	PROPN
ma-254	251	31	and	and	CCONJ
ma-254	251	32	n.	n.	PROPN
ma-254	251	33	s.	s.	PROPN
ma-254	251	34	kumar	kumar	PROPN
ma-254	251	35	,	,	PUNCT
ma-254	251	36	sobolev	sobolev	NOUN
ma-254	251	37	spaces	space	VERB
ma-254	251	38	on	on	ADP
ma-254	251	39	compact	compact	ADJ
ma-254	251	40	groups	group	NOUN
ma-254	251	41	,	,	PUNCT
ma-254	251	42	forum	forum	PROPN
ma-254	251	43	math	math	NOUN
ma-254	251	44	.	.	PUNCT
ma-254	252	1	35(4	35(4	NUM
ma-254	252	2	)	)	PUNCT
ma-254	252	3	(	(	PUNCT
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ma-254	252	5	)	)	PUNCT
ma-254	252	6	,	,	PUNCT
ma-254	252	7	901911	901911	NUM
ma-254	252	8	,	,	PUNCT
ma-254	252	9	https	https	NOUN
ma-254	252	10	:	:	PUNCT
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ma-254	252	15	0076.[18	0076.[18	NUM
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ma-254	252	24	a	a	DET
ma-254	252	25	generalized	generalized	ADJ
ma-254	252	26	spherical	spherical	ADJ
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ma-254	252	31	.	.	PUNCT
ma-254	252	32	math	math	PROPN
ma-254	252	33	.	.	PUNCT
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ma-254	254	5	(	(	PUNCT
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ma-254	254	7	-	-	SYM
ma-254	254	8	2955	2955	NUM
ma-254	254	9	,	,	PUNCT
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ma-254	254	11	]	]	PUNCT
ma-254	254	12	f.	f.	PROPN
ma-254	254	13	rellich	rellich	PROPN
ma-254	254	14	,	,	PUNCT
ma-254	254	15	ein	ein	PROPN
ma-254	254	16	satz	satz	PROPN
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ma-254	254	18	mittlere	mittlere	PROPN
ma-254	254	19	konvergenz	konvergenz	PROPN
ma-254	254	20	,	,	PUNCT
ma-254	254	21	nachr	nachr	PROPN
ma-254	254	22	.	.	PUNCT
ma-254	255	1	ges	ges	PROPN
ma-254	255	2	.	.	PROPN
ma-254	255	3	wiss	wiss	PROPN
ma-254	255	4	.	.	PUNCT
ma-254	256	1	göttingen	göttingen	PROPN
ma-254	256	2	,	,	PUNCT
ma-254	256	3	math.-phys	math.-phys	PROPN
ma-254	256	4	.	.	PUNCT
ma-254	256	5	kl	kl	PROPN
ma-254	256	6	.	.	PROPN
ma-254	256	7	,	,	PUNCT
ma-254	256	8	141	141	NUM
ma-254	256	9	,	,	PUNCT
ma-254	256	10	(	(	PUNCT
ma-254	256	11	1930	1930	NUM
ma-254	256	12	)	)	PUNCT
ma-254	256	13	30	30	NUM
ma-254	256	14	-	-	SYM
ma-254	256	15	35	35	NUM
ma-254	256	16	.	.	PUNCT
ma-254	257	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	257	2	https://doi.org/10.17654/097208712505	https://doi.org/10.17654/097208712505	PROPN
ma-254	257	3	https://doi.org/10.28924/2291-8639-20-2022-32	https://doi.org/10.28924/2291-8639-20-2022-32	PROPN
ma-254	257	4	http://dx.doi.org/10.17654/ms132010063	http://dx.doi.org/10.17654/ms132010063	ADV
ma-254	257	5	http://dx.doi.org/10.17654/ms132010063	http://dx.doi.org/10.17654/ms132010063	ADP
ma-254	257	6	https://doi.org/10.37418/amsj.12.2.6	https://doi.org/10.37418/amsj.12.2.6	PROPN
ma-254	257	7	10.2140	10.2140	NUM
ma-254	257	8	/	/	SYM
ma-254	257	9	pjm.2013.265.17	pjm.2013.265.17	NOUN
ma-254	257	10	http://dx.doi.org/10.1155/2014/404738	http://dx.doi.org/10.1155/2014/404738	NOUN
ma-254	257	11	http://dx.doi.org/10.1155/2014/404738	http://dx.doi.org/10.1155/2014/404738	NOUN
ma-254	257	12	10.1017	10.1017	NUM
ma-254	257	13	/	/	SYM
ma-254	257	14	s1446788714000433	s1446788714000433	PROPN
ma-254	258	1	https://doi.org/10.1007/bf00275475	https://doi.org/10.1007/bf00275475	NOUN
ma-254	259	1	https://doi.org/10.1007/bf00275475	https://doi.org/10.1007/bf00275475	X
ma-254	259	2	https://arxiv.org/abs/2003.08519v1	https://arxiv.org/abs/2003.08519v1	PUNCT
ma-254	259	3	https://doi.org/10.1515/forum-2022-0076	https://doi.org/10.1515/forum-2022-0076	VERB
ma-254	259	4	https://doi.org/10.1515/forum-2022-0076	https://doi.org/10.1515/forum-2022-0076	NOUN
ma-254	259	5	https://doi.org/10.37418/amsj.10.7.3	https://doi.org/10.37418/amsj.10.7.3	ADJ
ma-254	259	6	eur	eur	NOUN
ma-254	259	7	.	.	PUNCT
ma-254	260	1	j.	j.	PROPN
ma-254	260	2	math	math	PROPN
ma-254	260	3	.	.	PUNCT
ma-254	261	1	anal	anal	PROPN
ma-254	261	2	.	.	PUNCT
ma-254	262	1	10.28924	10.28924	NUM
ma-254	262	2	/	/	SYM
ma-254	262	3	ada	ada	PROPN
ma-254	262	4	/	/	SYM
ma-254	262	5	ma.5.3	ma.5.3	PROPN
ma-254	262	6	10	10	NUM
ma-254	263	1	[	[	SYM
ma-254	263	2	20	20	NUM
ma-254	263	3	]	]	PUNCT
ma-254	263	4	a.	a.	NOUN
ma-254	263	5	rozanova	rozanova	PROPN
ma-254	263	6	-	-	PUNCT
ma-254	263	7	pierrat	pierrat	PROPN
ma-254	263	8	,	,	PUNCT
ma-254	263	9	generalization	generalization	NOUN
ma-254	263	10	of	of	ADP
ma-254	263	11	rellich	rellich	NOUN
ma-254	263	12	-	-	PUNCT
ma-254	263	13	kondrachov	kondrachov	NOUN
ma-254	263	14	theorem	theorem	NOUN
ma-254	263	15	and	and	CCONJ
ma-254	263	16	trace	trace	NOUN
ma-254	263	17	compactness	compactness	NOUN
ma-254	263	18	for	for	ADP
ma-254	263	19	fractal	fractal	ADJ
ma-254	263	20	boundaries	boundary	NOUN
ma-254	263	21	,	,	PUNCT
ma-254	263	22	in	in	ADP
ma-254	263	23	:	:	PUNCT
ma-254	263	24	m.	m.	NOUN
ma-254	263	25	rosaria	rosaria	PROPN
ma-254	263	26	lancia	lancia	PROPN
ma-254	263	27	,	,	PUNCT
ma-254	263	28	a.	a.	PROPN
ma-254	263	29	rozanova	rozanova	PROPN
ma-254	263	30	-	-	PUNCT
ma-254	263	31	pierrat	pierrat	NOUN
ma-254	263	32	(	(	PUNCT
ma-254	263	33	eds	ed	NOUN
ma-254	263	34	.	.	PUNCT
ma-254	263	35	)	)	PUNCT
ma-254	263	36	,	,	PUNCT
ma-254	263	37	fractals	fractal	NOUN
ma-254	263	38	in	in	ADP
ma-254	263	39	engineering	engineering	NOUN
ma-254	263	40	:	:	PUNCT
ma-254	263	41	theoretical	theoretical	ADJ
ma-254	263	42	aspects	aspect	NOUN
ma-254	263	43	and	and	CCONJ
ma-254	263	44	numericalapproximations	numericalapproximation	NOUN
ma-254	263	45	,	,	PUNCT
ma-254	263	46	springer	springer	NOUN
ma-254	263	47	,	,	PUNCT
ma-254	263	48	(	(	PUNCT
ma-254	263	49	2021	2021	NUM
ma-254	263	50	)	)	PUNCT
ma-254	264	1	pp	pp	ADP
ma-254	264	2	.	.	PUNCT
ma-254	265	1	155	155	NUM
ma-254	265	2	-	-	SYM
ma-254	265	3	173	173	NUM
ma-254	265	4	.	.	PUNCT
ma-254	266	1	https://doi.org/10.28924/ada/ma.5.3	https://doi.org/10.28924/ada/ma.5.3	PROPN
ma-254	266	2	1	1	NUM
ma-254	266	3	.	.	PUNCT
ma-254	266	4	introduction	introduction	NOUN
ma-254	266	5	2	2	NUM
ma-254	266	6	.	.	PUNCT
ma-254	266	7	preliminaries	preliminary	NOUN
ma-254	266	8	3	3	NUM
ma-254	266	9	.	.	X
ma-254	266	10	sobolev	sobolev	NOUN
ma-254	266	11	spaces	space	NOUN
ma-254	266	12	and	and	CCONJ
ma-254	266	13	embedding	embed	VERB
ma-254	266	14	results	result	NOUN
ma-254	266	15	references	reference	NOUN