id	sid	eid	entity	type
ma-254	1	1	2025	CARDINAL
ma-254	2	1	j. math	PERSON
ma-254	4	1	5 (	CARDINAL
ma-254	4	2	2025	DATE
ma-254	5	1	3doi	CARDINAL
ma-254	5	2	10.28924	CARDINAL
ma-254	5	3	hypergroups ky	ORG
ma-254	5	4	bataka1,	GPE
ma-254	5	5	mensah1,2,∗	GPE
ma-254	5	6	1department	CARDINAL
ma-254	5	7	pob 1515 lomé 1,togo	ORG
ma-254	6	1	icmpa)-unesco	ORG
ma-254	6	2	benin	GPE
ma-254	9	1	1	CARDINAL
ma-254	10	1	1	CARDINAL
ma-254	10	2	4	CARDINAL
ma-254	10	3	asriemannian manifolds	ORG
ma-254	11	1	13	CARDINAL
ma-254	11	2	14	CARDINAL
ma-254	11	3	12	CARDINAL
ma-254	11	4	algebraic	PERSON
ma-254	11	5	abelian	NORP
ma-254	12	1	10	CARDINAL
ma-254	12	2	11	CARDINAL
ma-254	12	3	górka et al	PERSON
ma-254	12	4	abelian	NORP
ma-254	14	1	16	CARDINAL
ma-254	14	2	kumar	PERSON
ma-254	15	1	17	CARDINAL
ma-254	15	2	mensah	PERSON
ma-254	15	3	18	CARDINAL
ma-254	15	4	bataka et al	PERSON
ma-254	16	1	2].in	CARDINAL
ma-254	20	1	3 jul 2024	CARDINAL
ma-254	22	1	rellich-kondrachov	ORG
ma-254	23	1	j. math	PERSON
ma-254	25	1	10.28924	CARDINAL
ma-254	26	1	19	CARDINAL
ma-254	26	2	kondrachov	PERSON
ma-254	26	3	15	CARDINAL
ma-254	27	1	8	CARDINAL
ma-254	27	2	20	CARDINAL
ma-254	29	1	section 2	LAW
ma-254	30	1	2	CARDINAL
ma-254	30	2	3	CARDINAL
ma-254	30	3	5	DATE
ma-254	30	4	6	CARDINAL
ma-254	32	1	•	CARDINAL
ma-254	32	2	•	CARDINAL
ma-254	32	3	m(g	PERSON
ma-254	32	4	•	CARDINAL
ma-254	32	5	•	CARDINAL
ma-254	32	6	michael	PERSON
ma-254	33	1	2.1	CARDINAL
ma-254	34	1	7→	CARDINAL
ma-254	34	2	∀x	ORG
ma-254	34	3	supp(δx ∗ δy	PERSON
ma-254	34	4	c(g).(2	GPE
ma-254	35	1	∀x	ORG
ma-254	35	2	∈	PRODUCT
ma-254	36	1	3	CARDINAL
ma-254	38	1	4	CARDINAL
ma-254	38	2	∈	ORG
ma-254	39	1	2.2	CARDINAL
ma-254	40	1	nonempty	ORG
ma-254	41	1	j. math	PERSON
ma-254	43	1	10.28924	CARDINAL
ma-254	43	2	∀x	ORG
ma-254	43	3	y ∈ h	ORG
ma-254	44	1	⊂	GPE
ma-254	45	1	⋃	DATE
ma-254	45	2	k1,k2∈k supp(δk1 ∗ δx ∗	LAW
ma-254	48	1	z)d(δx ∗ δy	PERSON
ma-254	49	1	k-bi-invariant	PERSON
ma-254	51	1	k(g	GPE
ma-254	51	2	k(g	GPE
ma-254	53	1	f ∈ k(g	ORG
ma-254	53	2	\(x	NORP
ma-254	55	1	k ∫ k f	PERSON
ma-254	55	2	∗ k2)dk1dk2	ORG
ma-254	58	1	k-bi-invariant	ORG
ma-254	58	2	m\ c(g	ORG
ma-254	58	3	k-bi-invariant	ORG
ma-254	62	1	f ∗ g)(x	ORG
ma-254	68	1	k(g	GPE
ma-254	68	2	k(g	GPE
ma-254	69	1	2.3	CARDINAL
ma-254	72	1	6].in	CARDINAL
ma-254	73	1	φ	ORG
ma-254	73	2	k-bi-invariant,(2	ORG
ma-254	73	3	1,(3	CARDINAL
ma-254	74	1	∈	PRODUCT
ma-254	76	1	j. math	PERSON
ma-254	78	1	10.28924	CARDINAL
ma-254	78	2	5	CARDINAL
ma-254	80	1	2.4	CARDINAL
ma-254	80	2	5	CARDINAL
ma-254	83	1	f̂	CARDINAL
ma-254	86	1	2.5	CARDINAL
ma-254	87	1	2.5	CARDINAL
ma-254	87	2	5	CARDINAL
ma-254	90	1	x)|2dx = ∫ ĝ\ |f̂	PERSON
ma-254	92	1	2.6	CARDINAL
ma-254	93	1	1 ≤	MONEY
ma-254	93	2	1	CARDINAL
ma-254	94	1	1	CARDINAL
ma-254	96	1	∈	ORG
ma-254	98	1	3	CARDINAL
ma-254	98	2	3.1	CARDINAL
ma-254	99	1	2	CARDINAL
ma-254	102	1	1 + γ(φ)2)s |f̂	QUANTITY
ma-254	103	1	1 + γ(φ)2)s |f̂	QUANTITY
ma-254	103	2	1 2	CARDINAL
ma-254	105	1	3.2	CARDINAL
ma-254	108	1	2α α+	MONEY
ma-254	109	1	1	CARDINAL
ma-254	109	2	1	CARDINAL
ma-254	110	1	1 + γ2)−1	DATE
ma-254	110	2	∈	ORG
ma-254	112	1	j. math	PERSON
ma-254	114	1	10.28924	CARDINAL
ma-254	115	1	1	CARDINAL
ma-254	115	2	2	CARDINAL
ma-254	115	3	2.6	CARDINAL
ma-254	118	1	1 +	CARDINAL
ma-254	118	2	2	CARDINAL
ma-254	118	3	1 +	CARDINAL
ma-254	118	4	2 dπ(φ	DATE
ma-254	119	1	2p 2	CARDINAL
ma-254	119	2	1 +	CARDINAL
ma-254	119	3	2	CARDINAL
ma-254	119	4	1 +	CARDINAL
ma-254	119	5	2(2−p	DATE
ma-254	120	1	2 + 2−	MONEY
ma-254	120	2	2	CARDINAL
ma-254	120	3	1	CARDINAL
ma-254	121	1	1 + γ(φ)2)s |f̂	QUANTITY
ma-254	122	1	2	CARDINAL
ma-254	122	2	1 +	CARDINAL
ma-254	122	3	2−p dπ(φ	DATE
ma-254	123	1	2−p 2	CARDINAL
ma-254	124	1	1 + γ(φ)2)s |f̂	QUANTITY
ma-254	124	2	1 2	CARDINAL
ma-254	124	3	1 +	CARDINAL
ma-254	124	4	2−p dπ(φ	DATE
ma-254	125	1	2−p 2p	CARDINAL
ma-254	126	1	1 +	CARDINAL
ma-254	126	2	2−p dπ(φ	DATE
ma-254	127	1	2−p 2p	CARDINAL
ma-254	128	1	2	CARDINAL
ma-254	128	2	2− p	GPE
ma-254	131	1	2	CARDINAL
ma-254	133	1	3.3	CARDINAL
ma-254	135	1	φ ∈	PERSON
ma-254	135	2	∀g ∈	ORG
ma-254	138	1	x)φ(g)φ(x	ORG
ma-254	139	1	φ(f ∗ g	PERSON
ma-254	140	1	∗	CARDINAL
ma-254	143	1	g g(y�	PERSON
ma-254	143	2	x)φ(y ∗ x	PERSON
ma-254	149	1	x)(g	ORG
ma-254	149	2	φ)(x	GPE
ma-254	151	1	j. math	PERSON
ma-254	153	1	10.28924	CARDINAL
ma-254	153	2	x)φ(g)φ(x	ORG
ma-254	154	1	x)(g	ORG
ma-254	154	2	φ)(x	GPE
ma-254	155	1	φ)(x	GPE
ma-254	156	1	3.4	CARDINAL
ma-254	159	1	1|2	CARDINAL
ma-254	165	1	∗ x)f	DATE
ma-254	166	1	f̂	TIME
ma-254	166	2	x)|2dx = ∫ ĝ\ |f̂y	PERSON
ma-254	166	3	2.5	CARDINAL
ma-254	171	1	1|2dπ(φ	CARDINAL
ma-254	173	1	1 + γ(φ)2)s dπ(φ	QUANTITY
ma-254	173	2	1|2	CARDINAL
ma-254	175	1	3.5	CARDINAL
ma-254	177	1	η ∈ k\(g	PERSON
ma-254	177	2	∗ η	QUANTITY
ma-254	177	3	1|	CARDINAL
ma-254	177	4	2	CARDINAL
ma-254	181	1	η ∈ k\(g	PERSON
ma-254	181	2	6=	DATE
ma-254	181	3	η	GPE
ma-254	181	4	1	CARDINAL
ma-254	183	1	1 2	CARDINAL
ma-254	184	1	j. math	PERSON
ma-254	186	1	10.28924	CARDINAL
ma-254	187	1	1 2	CARDINAL
ma-254	188	1	1 2	CARDINAL
ma-254	188	2	x))η(y)dy ∣∣∣∣2 dx	ORG
ma-254	188	3	1 2 ≤	CARDINAL
ma-254	188	4	1 2 dy ≤	QUANTITY
ma-254	188	5	1 2 dy ≤	QUANTITY
ma-254	188	6	1|	CARDINAL
ma-254	188	7	2	CARDINAL
ma-254	188	8	3.4	CARDINAL
ma-254	190	1	3.6	CARDINAL
ma-254	193	1	∈	ORG
ma-254	193	2	1,∞	CARDINAL
ma-254	194	1	f ∗ η	ORG
ma-254	196	1	4	CARDINAL
ma-254	196	2	3.5	CARDINAL
ma-254	197	1	∗ x)| dy ≤	PRODUCT
ma-254	198	1	1	CARDINAL
ma-254	199	1	1	CARDINAL
ma-254	199	2	1	CARDINAL
ma-254	207	1	j. math	PERSON
ma-254	209	1	10.28924	CARDINAL
ma-254	210	1	y))η(y	ORG
ma-254	211	1	1	CARDINAL
ma-254	211	2	2	CARDINAL
ma-254	211	3	1	CARDINAL
ma-254	211	4	lim	ORG
ma-254	211	5	∗	CARDINAL
ma-254	211	6	0	CARDINAL
ma-254	213	1	3.7	CARDINAL
ma-254	216	1	0	CARDINAL
ma-254	217	1	2α	CARDINAL
ma-254	217	2	1	CARDINAL
ma-254	217	3	1	CARDINAL
ma-254	218	1	1 + γ2)−1	DATE
ma-254	218	2	∈	ORG
ma-254	218	3	lim y→e	PERSON
ma-254	218	4	1|	CARDINAL
ma-254	218	5	2	CARDINAL
ma-254	218	6	0	CARDINAL
ma-254	218	7	1	CARDINAL
ma-254	220	1	3.2	DATE
ma-254	224	1	0	CARDINAL
ma-254	224	2	∀n ∈ n	ORG
ma-254	224	3	6	CARDINAL
ma-254	224	4	g ∈ lp,\(g	PERSON
ma-254	224	5	6	CARDINAL
ma-254	224	6	6	CARDINAL
ma-254	226	1	η ∈ k\(g	PERSON
ma-254	226	2	3.5	CARDINAL
ma-254	226	3	3.6	CARDINAL
ma-254	226	4	− h‖2 ≤	ORG
ma-254	227	1	∗ η − h ∗ η‖2	ORG
ma-254	228	1	1|	CARDINAL
ma-254	228	2	2	CARDINAL
ma-254	228	3	∗ η − h ∗ η‖2	ORG
ma-254	229	1	∗	CARDINAL
ma-254	231	1	j. math	PERSON
ma-254	233	1	10.28924	CARDINAL
ma-254	233	2	− h‖2 ≤ ‖hn	ORG
ma-254	233	3	∗	CARDINAL
ma-254	234	1	lim	PERSON
ma-254	234	2	− h‖2 = lim	ORG
ma-254	234	3	n→∞	CARDINAL
ma-254	234	4	∗	CARDINAL
ma-254	234	5	0	CARDINAL
ma-254	235	1	vitali	PERSON
ma-254	236	1	1	CARDINAL
ma-254	236	2	r. a. adams	PERSON
ma-254	236	3	new york	GPE
ma-254	236	4	1975.[2	CARDINAL
ma-254	236	5	k. t. bataka	PERSON
ma-254	236	6	e. m. egwe	PERSON
ma-254	236	7	y. mensah	PERSON
ma-254	237	1	sci.	ORG
ma-254	237	2	2024	CARDINAL
ma-254	237	3	57–69	CARDINAL
ma-254	237	4	w. r.	PERSON
ma-254	237	5	h. heyer	PERSON
ma-254	237	6	hypergroups	GPE
ma-254	237	7	de gruyter	PERSON
ma-254	237	8	20	CARDINAL
ma-254	237	9	berlin	GPE
ma-254	237	10	1995.[4	CARDINAL
ma-254	237	11	h. brezis	PERSON
ma-254	237	12	k. g. brou	PERSON
ma-254	237	13	i. toure	PERSON
ma-254	237	14	k. kangni	PERSON
ma-254	237	15	noncommutative	NORP
ma-254	238	1	j. anal	PERSON
ma-254	239	1	20(2022	CARDINAL
ma-254	239	2	https://doi.org/10.28924/2291-8639-20-2022-32.[6	ORG
ma-254	240	1	k. kangni	PERSON
ma-254	240	2	hypergroups	GPE
ma-254	241	1	sci.	ORG
ma-254	241	2	132(1	CARDINAL
ma-254	241	3	2021	CARDINAL
ma-254	241	4	63	CARDINAL
ma-254	241	5	k. g. brou	PERSON
ma-254	241	6	k. kangni	PERSON
ma-254	242	1	math.sci	DATE
ma-254	243	1	j., 12 (	ORG
ma-254	243	2	2	CARDINAL
ma-254	243	3	2023	CARDINAL
ma-254	243	4	381	CARDINAL
ma-254	243	5	s. chua	PERSON
ma-254	243	6	s. rodney	PERSON
ma-254	243	7	r. wheeden	PERSON
ma-254	243	8	generalized sobolev spaces	ORG
ma-254	243	9	pacific	ORG
ma-254	243	10	265(1	CARDINAL
ma-254	243	11	2013	DATE
ma-254	243	12	17	CARDINAL
ma-254	243	13	10.2140	CARDINAL
ma-254	243	14	d. e. edmunds	PERSON
ma-254	243	15	w. d. evans	PERSON
ma-254	243	16	oxford	NORP
ma-254	243	17	2ndedition	LAW
ma-254	243	18	oxford science	ORG
ma-254	243	19	oxford university press	ORG
ma-254	243	20	t. kostrzewa	PERSON
ma-254	243	21	e. g. reyes	PERSON
ma-254	243	22	abelian	NORP
ma-254	243	23	2014	DATE
ma-254	243	24	article id 404738	LAW
ma-254	243	25	6	CARDINAL
ma-254	243	26	2014/404738.[11	CARDINAL
ma-254	243	27	t. kostrzewa	PERSON
ma-254	243	28	e. g. reyes	PERSON
ma-254	243	29	abelian	NORP
ma-254	243	30	j. aust	PERSON
ma-254	245	1	98	CARDINAL
ma-254	245	2	2015	CARDINAL
ma-254	245	3	39	CARDINAL
ma-254	245	4	5(4	CARDINAL
ma-254	245	5	1996	DATE
ma-254	245	6	403	CARDINAL
ma-254	245	7	10.1007	CARDINAL
ma-254	248	1	amer	PERSON
ma-254	249	1	145(688	CARDINAL
ma-254	249	2	2000).[14	CARDINAL
ma-254	249	3	riemannian manifolds	ORG
ma-254	249	4	1635	CARDINAL
ma-254	249	5	berlin	GPE
ma-254	249	6	1996.[15	GPE
ma-254	249	7	i. kondrachov	PERSON
ma-254	250	1	akad	PERSON
ma-254	251	1	nauk sssr	PERSON
ma-254	251	2	48	DATE
ma-254	251	3	563	CARDINAL
ma-254	251	4	m. krukowski	PERSON
ma-254	251	5	2020	DATE
ma-254	251	6	m. kumar	PERSON
ma-254	251	7	n. s. kumar	PERSON
ma-254	252	1	2023	CARDINAL
ma-254	252	2	901911	DATE
ma-254	252	3	y. mensah	PERSON
ma-254	253	1	sci	ORG
ma-254	254	1	j.	PERSON
ma-254	254	2	2021),2947-2955	CARDINAL
ma-254	254	3	https://doi.org/10.37418/amsj.10.7.3.[19] f. rellich	ORG
ma-254	254	4	ein satz über	ORG
ma-254	254	5	konvergenz	PERSON
ma-254	255	1	ges	ORG
ma-254	255	2	wiss	PERSON
ma-254	256	1	göttingen	PERSON
ma-254	256	2	math.-phys	PERSON
ma-254	256	3	kl.	PERSON
ma-254	256	4	141	DATE
ma-254	256	5	1930	DATE
ma-254	256	6	30	CARDINAL
ma-254	257	1	10.2140	CARDINAL
ma-254	257	2	10.1017	CARDINAL
ma-254	260	1	j. math	PERSON
ma-254	262	1	10.28924	CARDINAL
ma-254	263	1	20	CARDINAL
ma-254	263	2	a. rozanova-pierrat	PERSON
ma-254	263	3	rellich-kondrachov theorem	ORG
ma-254	263	4	m. rosaria lancia	PERSON
ma-254	263	5	a. rozanova-pierrat	PERSON
ma-254	263	6	2021	CARDINAL
ma-254	265	1	155-173	CARDINAL
ma-254	266	1	1	CARDINAL
ma-254	266	2	2	CARDINAL
ma-254	266	3	3	CARDINAL