id	sid	eid	entity	type
ma-301	1	1	2025	CARDINAL
ma-301	2	1	j. math	PERSON
ma-301	4	1	5 (	CARDINAL
ma-301	4	2	2025	DATE
ma-301	5	1	10.28924	CARDINAL
ma-301	5	2	quantum	ORG
ma-301	5	3	ahmed chana∗	PERSON
ma-301	5	4	hassan ii	PERSON
ma-301	5	5	b.p 5366	ORG
ma-301	5	6	casablanca	GPE
ma-301	5	7	morocco	GPE
ma-301	6	1	1	CARDINAL
ma-301	6	2	andheisenberg	PERSON
ma-301	8	1	1	CARDINAL
ma-301	9	1	quantum	ORG
ma-301	9	2	20].recently	CARDINAL
ma-301	9	3	2	CARDINAL
ma-301	9	4	31	CARDINAL
ma-301	9	5	15	CARDINAL
ma-301	10	1	6	CARDINAL
ma-301	10	2	theorem[16	ORG
ma-301	11	1	27	CARDINAL
ma-301	11	2	29	CARDINAL
ma-301	12	1	andmikhlin	PERSON
ma-301	13	1	18,25	CARDINAL
ma-301	13	2	rd	GPE
ma-301	14	1	invariant operators	ORG
ma-301	14	2	rd	ORG
ma-301	14	3	f(f	ORG
ma-301	16	1	1.1	CARDINAL
ma-301	16	2	22 nov 2024	DATE
ma-301	18	1	quantum	ORG
ma-301	18	2	extremal functions;heisenberg	PERSON
ma-301	19	1	1	CARDINAL
ma-301	20	1	j. math	PERSON
ma-301	22	1	10.28924	CARDINAL
ma-301	22	2	2the hörmander-mikhlin	PERSON
ma-301	22	3	all 1	CARDINAL
ma-301	22	4	if∣∣∂γλm(λ	LANGUAGE
ma-301	23	1	0 ≤	QUANTITY
ma-301	24	1	1.2	CARDINAL
ma-301	25	1	1.2	CARDINAL
ma-301	26	1	0	CARDINAL
ma-301	26	2	deriva	ORG
ma-301	29	1	hörmander-mikhlin	ORG
ma-301	29	2	mathematical analysisas	PRODUCT
ma-301	29	3	24	CARDINAL
ma-301	29	4	5	CARDINAL
ma-301	29	5	22	CARDINAL
ma-301	30	1	33	CARDINAL
ma-301	30	2	8	CARDINAL
ma-301	30	3	26	CARDINAL
ma-301	30	4	31	DATE
ma-301	30	5	32	CARDINAL
ma-301	30	6	3	CARDINAL
ma-301	31	1	4	CARDINAL
ma-301	31	2	1950	DATE
ma-301	31	3	23	CARDINAL
ma-301	31	4	30	CARDINAL
ma-301	32	1	30].this	CARDINAL
ma-301	32	2	11	CARDINAL
ma-301	32	3	0	CARDINAL
ma-301	32	4	1	CARDINAL
ma-301	35	1	∀x	GPE
ma-301	35	2	6=	DATE
ma-301	35	3	0	CARDINAL
ma-301	36	1	1.3	CARDINAL
ma-301	36	2	1.3	CARDINAL
ma-301	36	3	15	CARDINAL
ma-301	37	1	α(f	ORG
ma-301	39	1	q2)f	ORG
ma-301	40	1	∈	ORG
ma-301	40	2	mq	ORG
ma-301	40	3	σ	ORG
ma-301	40	4	β(f	ORG
ma-301	41	1	α(f	ORG
ma-301	42	1	1.4	CARDINAL
ma-301	43	1	j. math	PERSON
ma-301	45	1	10.28924	CARDINAL
ma-301	45	2	3where	CARDINAL
ma-301	45	3	σβ(λ	ORG
ma-301	46	1	1.5)these	CARDINAL
ma-301	46	2	3	CARDINAL
ma-301	46	3	10,26	DATE
ma-301	46	4	31	DATE
ma-301	46	5	32	CARDINAL
ma-301	47	1	section 2	LAW
ma-301	47	2	section 3,we	LAW
ma-301	47	3	σ	ORG
ma-301	47	4	heisenberg’s	ORG
ma-301	48	1	σ	ORG
ma-301	49	1	2	CARDINAL
ma-301	49	2	1.3	CARDINAL
ma-301	49	3	11,17,19–21,28	CARDINAL
ma-301	50	1	2.1	CARDINAL
ma-301	51	1	jackson	PERSON
ma-301	51	2	jackson	PERSON
ma-301	51	3	19].let	CARDINAL
ma-301	51	4	∈	ORG
ma-301	51	5	1	CARDINAL
ma-301	51	6	n−1∏ k=0	PERSON
ma-301	51	7	1− aqk	MONEY
ma-301	51	8	q)∞	DATE
ma-301	51	9	k=0	PERSON
ma-301	51	10	1− aqk	PRODUCT
ma-301	52	1	jackson	PERSON
ma-301	52	2	1− q)x	DATE
ma-301	52	3	6=	DATE
ma-301	52	4	0	CARDINAL
ma-301	52	5	0	CARDINAL
ma-301	52	6	1− q)a ∞∑	TIME
ma-301	53	1	1−	TIME
ma-301	54	1	14,17,28	CARDINAL
ma-301	56	1	n=0	PERSON
ma-301	56	2	2	CARDINAL
ma-301	57	1	2.1	CARDINAL
ma-301	58	1	j. math	PERSON
ma-301	60	1	10.28924	CARDINAL
ma-301	60	2	4it	ORDINAL
ma-301	60	3	11	CARDINAL
ma-301	60	4	∈	PRODUCT
ma-301	60	5	∣∣jα(x	DATE
ma-301	60	6	≤ 1	DATE
ma-301	61	1	2.2	CARDINAL
ma-301	61	2	2.2	CARDINAL
ma-301	63	1	11	CARDINAL
ma-301	64	1	first	ORDINAL
ma-301	64	2	zero	CARDINAL
ma-301	64	3	convergence.•	ORG
ma-301	64	4	1 ≤	MONEY
ma-301	64	5	x)|pdµq,α(x	ORG
ma-301	65	1	1	CARDINAL
ma-301	65	2	1 ≤	QUANTITY
ma-301	66	1	supx∈r+q	CARDINAL
ma-301	67	1	1 1−	TIME
ma-301	67	2	2.1	CARDINAL
ma-301	68	1	11	CARDINAL
ma-301	68	2	α(f	ORG
ma-301	70	1	q2)f	ORG
ma-301	71	1	2.1	CARDINAL
ma-301	72	1	1	CARDINAL
ma-301	73	1	α(f	ORG
ma-301	74	1	∈	ORG
ma-301	75	1	α(f	ORG
ma-301	76	1	2.3	CARDINAL
ma-301	77	1	−q2	CARDINAL
ma-301	77	2	2.4	CARDINAL
ma-301	77	3	2)(q	CARDINAL
ma-301	77	4	∩ l2α	PERSON
ma-301	81	1	q2)hq	DATE
ma-301	81	2	α(f	ORG
ma-301	81	3	α(λ	GPE
ma-301	81	4	a.e x ∈	PERSON
ma-301	82	1	2.5	CARDINAL
ma-301	82	2	3	CARDINAL
ma-301	83	1	α(f	ORG
ma-301	83	2	α(g)〉q	ORG
ma-301	83	3	2.6	CARDINAL
ma-301	83	4	α(f	ORG
ma-301	85	1	2.7	CARDINAL
ma-301	85	2	4	CARDINAL
ma-301	87	1	j. math	PERSON
ma-301	89	1	10.28924	CARDINAL
ma-301	89	2	52.3	CARDINAL
ma-301	91	1	2.2	CARDINAL
ma-301	92	1	13	CARDINAL
ma-301	95	1	q2)hq	DATE
ma-301	95	2	α(f	ORG
ma-301	95	3	α(λ	GPE
ma-301	95	4	13	CARDINAL
ma-301	96	1	2.2	CARDINAL
ma-301	97	1	1	CARDINAL
ma-301	99	1	2.8	CARDINAL
ma-301	99	2	2	CARDINAL
ma-301	99	3	y)dµq	GPE
ma-301	102	1	y)dµq	GPE
ma-301	103	1	2.9	CARDINAL
ma-301	103	2	3	CARDINAL
ma-301	103	3	∈	ORG
ma-301	104	1	1	CARDINAL
ma-301	105	1	have∥∥τxq	PERSON
ma-301	105	2	∥∥p	ORG
ma-301	105	3	2.10	CARDINAL
ma-301	105	4	4	CARDINAL
ma-301	105	5	∈	ORG
ma-301	107	1	q2)hq	DATE
ma-301	107	2	α(f	ORG
ma-301	107	3	∀λ ∈	PERSON
ma-301	108	1	2.11	CARDINAL
ma-301	108	2	2.11	CARDINAL
ma-301	108	3	1.4	CARDINAL
ma-301	110	1	α(f	ORG
ma-301	112	1	2.3	CARDINAL
ma-301	113	1	1)(q	CARDINAL
ma-301	113	2	∈	ORG
ma-301	114	1	1	CARDINAL
ma-301	114	2	1	CARDINAL
ma-301	114	3	1 + 1	CARDINAL
ma-301	114	4	∈	ORG
ma-301	114	5	∈	ORG
ma-301	114	6	α‖g‖s	ORG
ma-301	114	7	2.12	CARDINAL
ma-301	114	8	2	CARDINAL
ma-301	115	1	α(f	ORG
ma-301	115	2	α(g	PERSON
ma-301	115	3	α(f	ORG
ma-301	115	4	α(g	PERSON
ma-301	116	1	2.13	CARDINAL
ma-301	116	2	3	CARDINAL
ma-301	119	1	α(f	ORG
ma-301	119	2	α(g)(λ)|2	ORG
ma-301	119	3	α(λ	GPE
ma-301	119	4	2.14	CARDINAL
ma-301	121	1	j. math	PERSON
ma-301	123	1	10.28924	CARDINAL
ma-301	123	2	63	DATE
ma-301	125	1	3.1	CARDINAL
ma-301	125	2	calderon	ORG
ma-301	126	1	3.1	CARDINAL
ma-301	127	1	σ ∈ l2α(r+q	PERSON
ma-301	127	2	∈	ORG
ma-301	128	1	mq	ORG
ma-301	128	2	σ	ORG
ma-301	128	3	β(f	ORG
ma-301	129	1	α(f	ORG
ma-301	130	1	3.1	CARDINAL
ma-301	130	2	1.5	CARDINAL
ma-301	130	3	∈	ORG
ma-301	130	4	∈	ORG
ma-301	131	1	1	CARDINAL
ma-301	132	1	3.2	CARDINAL
ma-301	132	2	3.1	CARDINAL
ma-301	133	1	2.13	CARDINAL
ma-301	133	2	mq	ORG
ma-301	133	3	σ	ORG
ma-301	133	4	β(f	ORG
ma-301	133	5	3.3	CARDINAL
ma-301	133	6	1	CARDINAL
ma-301	133	7	α(σ	PERSON
ma-301	134	1	3.4	CARDINAL
ma-301	135	1	3.1	CARDINAL
ma-301	136	1	σ	ORG
ma-301	136	2	β(f	ORG
ma-301	136	3	σ	ORG
ma-301	136	4	β(f	ORG
ma-301	137	1	2,q	MONEY
ma-301	137	2	σ	ORG
ma-301	137	3	β(f	ORG
ma-301	137	4	σ	ORG
ma-301	137	5	β(f	ORG
ma-301	138	1	2,q	MONEY
ma-301	138	2	3.5	CARDINAL
ma-301	138	3	mq	ORG
ma-301	138	4	σ	ORG
ma-301	138	5	β(f	ORG
ma-301	139	1	mq	ORG
ma-301	139	2	σ	ORG
ma-301	139	3	β(f	ORG
ma-301	140	1	α(f	ORG
ma-301	140	2	α(λ	GPE
ma-301	140	3	a.e x ∈	PERSON
ma-301	140	4	3.6	CARDINAL
ma-301	140	5	σ	ORG
ma-301	140	6	β(f	ORG
ma-301	142	1	2.12),(3.3	CARDINAL
ma-301	142	2	that∥∥mq	GPE
ma-301	142	3	σ	ORG
ma-301	142	4	β(f	ORG
ma-301	143	1	2,q	CARDINAL
ma-301	143	2	2.7	CARDINAL
ma-301	143	3	3.2	CARDINAL
ma-301	143	4	plancherel	ORG
ma-301	143	5	2.7	CARDINAL
ma-301	145	1	j. math	PERSON
ma-301	147	1	10.28924	CARDINAL
ma-301	147	2	2.7),(2.12),(3.2	CARDINAL
ma-301	147	3	3.3	CARDINAL
ma-301	147	4	3.6)follows	CARDINAL
ma-301	147	5	2.5	CARDINAL
ma-301	149	1	3.1	CARDINAL
ma-301	150	1	σ ∈ l2α(r+q	PERSON
ma-301	152	1	∣∣2	DATE
ma-301	152	2	1	CARDINAL
ma-301	152	3	∈	ORG
ma-301	152	4	3.7	CARDINAL
ma-301	155	1	σ	ORG
ma-301	155	2	β(f	ORG
ma-301	156	1	2,q	CARDINAL
ma-301	157	1	3.8	CARDINAL
ma-301	157	2	first	ORDINAL
ma-301	157	3	α(f	ORG
ma-301	161	1	mq	ORG
ma-301	161	2	σ	ORG
ma-301	161	3	β(f	ORG
ma-301	161	4	∈	ORG
ma-301	161	5	r. proof	PERSON
ma-301	162	1	2.14	CARDINAL
ma-301	162	2	3.3	CARDINAL
ma-301	163	1	σ	ORG
ma-301	163	2	β(f	ORG
ma-301	165	1	2,q	CARDINAL
ma-301	169	1	σ	ORG
ma-301	169	2	β(f	ORG
ma-301	171	1	α(f	ORG
ma-301	171	2	α(λ	GPE
ma-301	171	3	∣∣2	DATE
ma-301	171	4	3.7	CARDINAL
ma-301	171	5	plancherel	ORG
ma-301	171	6	2.7	CARDINAL
ma-301	171	7	α(f	ORG
ma-301	172	1	2.6),(2.11	CARDINAL
ma-301	172	2	∞ 0	DATE
ma-301	173	1	mq	ORG
ma-301	173	2	σ	ORG
ma-301	173	3	β(f	ORG
ma-301	175	1	α(f	ORG
ma-301	175	2	α(λ	GPE
ma-301	177	1	α(f	ORG
ma-301	177	2	α(λ	GPE
ma-301	178	1	∣∣2	DATE
ma-301	178	2	3.7),inversion	CARDINAL
ma-301	178	3	2.5	CARDINAL
ma-301	179	1	second	ORDINAL
ma-301	179	2	calderon	ORG
ma-301	180	1	3.2	CARDINAL
ma-301	181	1	σ ∈ l2α(r+q	PERSON
ma-301	181	2	∩ l∞α	PERSON
ma-301	181	3	3.7	CARDINAL
ma-301	182	1	δ(λ	ORG
ma-301	182	2	γ ∣∣σβ(λ	GPE
ma-301	182	3	∣∣2	DATE
ma-301	182	4	∩ l∞α	PERSON
ma-301	182	5	eur	PERSON
ma-301	183	1	j. math	PERSON
ma-301	185	1	10.28924	CARDINAL
ma-301	185	2	8	CARDINAL
ma-301	186	1	3.2	CARDINAL
ma-301	186	2	that∥∥φγ	PERSON
ma-301	187	1	2,q	CARDINAL
ma-301	187	2	log(δ/γ)‖σ‖22,q	ORG
ma-301	187	3	α‖σ‖2∞,q	ORG
ma-301	187	4	γ dq(β	GPE
ma-301	188	1	3.7	CARDINAL
ma-301	188	2	∩ l∞α	PERSON
ma-301	189	1	3.2	CARDINAL
ma-301	190	1	second	ORDINAL
ma-301	191	1	σ ∈ l2α(r+q	PERSON
ma-301	191	2	∩ l∞α	PERSON
ma-301	191	3	3.7	CARDINAL
ma-301	191	4	δ(x	PERSON
ma-301	192	1	mq	ORG
ma-301	192	2	σ	ORG
ma-301	192	3	β(f	ORG
ma-301	192	4	∈	ORG
ma-301	192	5	lim	PERSON
ma-301	193	1	3.9	CARDINAL
ma-301	194	1	δ(x	PERSON
ma-301	194	2	q2)hq	DATE
ma-301	194	3	α(f	ORG
ma-301	194	4	α(λ	GPE
ma-301	195	1	α(f	ORG
ma-301	196	1	3.2	CARDINAL
ma-301	196	2	δ(λ	ORG
ma-301	196	3	α(f	ORG
ma-301	196	4	2.7	CARDINAL
ma-301	196	5	lim	PERSON
ma-301	196	6	α(f	ORG
ma-301	196	7	1−φγ	CARDINAL
ma-301	196	8	δ(λ	ORG
ma-301	196	9	2	CARDINAL
ma-301	196	10	α(λ	GPE
ma-301	196	11	3.7	CARDINAL
ma-301	196	12	3.9	CARDINAL
ma-301	197	1	3.2	CARDINAL
ma-301	199	1	σ	ORG
ma-301	200	1	3.2.1	CARDINAL
ma-301	201	1	heisenberg	PERSON
ma-301	201	2	σ	ORG
ma-301	202	1	heisenberg	PERSON
ma-301	202	2	9	CARDINAL
ma-301	202	3	11	CARDINAL
ma-301	203	1	α(f	ORG
ma-301	204	1	2 2,q	DATE
ma-301	204	2	3.10	CARDINAL
ma-301	205	1	1+ √	CARDINAL
ma-301	205	2	1−q2(α+1	CARDINAL
ma-301	206	1	3.10	CARDINAL
ma-301	206	2	α(f	ORG
ma-301	207	1	mq	ORG
ma-301	207	2	σ	ORG
ma-301	208	1	j. math	PERSON
ma-301	210	1	10.28924	CARDINAL
ma-301	210	2	9	CARDINAL
ma-301	210	3	3.3	CARDINAL
ma-301	211	1	α(f	ORG
ma-301	212	1	2,q	MONEY
ma-301	212	2	α kq	PERSON
ma-301	214	1	σ	ORG
ma-301	214	2	β(f	ORG
ma-301	215	1	2,q	CARDINAL
ma-301	215	2	1 2	CARDINAL
ma-301	216	1	α(f	ORG
ma-301	217	1	2,q	MONEY
ma-301	219	1	∥∥|x	NORP
ma-301	219	2	σ	ORG
ma-301	219	3	β(f	ORG
ma-301	220	1	2,q	CARDINAL
ma-301	220	2	3.10	CARDINAL
ma-301	220	3	σ	ORG
ma-301	220	4	β(f	ORG
ma-301	221	1	∥∥|x	NORP
ma-301	221	2	σ	ORG
ma-301	221	3	β(f	ORG
ma-301	221	4	2,q	MONEY
ma-301	221	5	α(f	ORG
ma-301	221	6	2,q	MONEY
ma-301	221	7	3.8	CARDINAL
ma-301	222	1	σ	ORG
ma-301	222	2	β(f	ORG
ma-301	222	3	1 2	CARDINAL
ma-301	223	1	0 ||λσβ(λ)|2 |hq	DATE
ma-301	223	2	α(f	ORG
ma-301	223	3	α(λ	GPE
ma-301	224	1	1 2	CARDINAL
ma-301	224	2	3.7	CARDINAL
ma-301	225	1	3.2.2	CARDINAL
ma-301	226	1	σ	ORG
ma-301	227	1	3	CARDINAL
ma-301	227	2	l2θ(r+q	GPE
ma-301	227	3	l2θ(r+q	GPE
ma-301	230	1	1 2	CARDINAL
ma-301	231	1	dθα(β	GPE
ma-301	231	2	3.2	CARDINAL
ma-301	232	1	12	CARDINAL
ma-301	232	2	1ef	ORDINAL
ma-301	232	3	3.11	CARDINAL
ma-301	232	4	1e	CARDINAL
ma-301	232	5	e. (ii	PERSON
ma-301	232	6	β(f	ORG
ma-301	232	7	β(f	ORG
ma-301	233	1	σ	ORG
ma-301	233	2	β(f	ORG
ma-301	233	3	ρ‖mq	NORP
ma-301	233	4	σ	ORG
ma-301	233	5	β(f	ORG
ma-301	234	1	3.12	CARDINAL
ma-301	234	2	3.4	CARDINAL
ma-301	235	1	σ ∈	ORG
ma-301	236	1	∩ l∞α	PERSON
ma-301	236	2	3.7	CARDINAL
ma-301	236	3	mq	ORG
ma-301	236	4	σ	ORG
ma-301	236	5	β(f	ORG
ma-301	236	6	1 2	CARDINAL
ma-301	236	7	1 2	CARDINAL
ma-301	238	1	j. math	PERSON
ma-301	240	1	10.28924	CARDINAL
ma-301	240	2	10	CARDINAL
ma-301	241	1	σ ∈ l2α(r	PERSON
ma-301	242	1	3.7	CARDINAL
ma-301	242	2	1 2	CARDINAL
ma-301	242	3	3.11),(3.12	CARDINAL
ma-301	242	4	β(f	ORG
ma-301	243	1	σ	ORG
ma-301	243	2	β(f	ORG
ma-301	243	3	σ	ORG
ma-301	243	4	β(f	ORG
ma-301	244	1	σ	ORG
ma-301	244	2	β(f	ORG
ma-301	244	3	ρ‖mq	NORP
ma-301	244	4	σ	ORG
ma-301	244	5	β(f	ORG
ma-301	245	1	β(f	ORG
ma-301	245	2	1ef	ORDINAL
ma-301	245	3	3.8	CARDINAL
ma-301	245	4	β(f	ORG
ma-301	245	5	β(f	ORG
ma-301	246	1	σ	ORG
ma-301	247	1	σ	ORG
ma-301	247	2	σ	ORG
ma-301	247	3	3.13)on	CARDINAL
ma-301	247	4	3.6	CARDINAL
ma-301	247	5	σ	ORG
ma-301	247	6	α(µ(e	ORG
ma-301	247	7	1 2	CARDINAL
ma-301	247	8	1 2	CARDINAL
ma-301	247	9	3.14	CARDINAL
ma-301	247	10	β(f	ORG
ma-301	247	11	1 2	CARDINAL
ma-301	247	12	1 2	CARDINAL
ma-301	247	13	3.8	CARDINAL
ma-301	248	1	4	CARDINAL
ma-301	248	2	extremal	PERSON
ma-301	249	1	4.1	CARDINAL
ma-301	250	1	1	CARDINAL
ma-301	250	2	4.1	CARDINAL
ma-301	250	3	1	CARDINAL
ma-301	250	4	∈	ORG
ma-301	251	1	4.2	CARDINAL
ma-301	252	1	α(f	ORG
ma-301	253	1	g〉ψ =	PERSON
ma-301	254	1	α(f	ORG
ma-301	254	2	α(λ	GPE
ma-301	257	1	j. math	PERSON
ma-301	259	1	10.28924	CARDINAL
ma-301	259	2	11	CARDINAL
ma-301	259	3	4.1	CARDINAL
ma-301	261	1	σ	ORG
ma-301	262	1	σ	ORG
ma-301	262	2	β(f	ORG
ma-301	262	3	2,q	MONEY
ma-301	263	1	4.3	CARDINAL
ma-301	264	1	2.8),(3.5),(4.2	CARDINAL
ma-301	264	2	4.2	CARDINAL
ma-301	267	1	g〉ψ	GPE
ma-301	267	2	η	GPE
ma-301	267	3	g〉ψ	GPE
ma-301	267	4	η = ∫	PERSON
ma-301	269	1	α(f	ORG
ma-301	269	2	α(λ	GPE
ma-301	269	3	η = √ 〈f	PERSON
ma-301	269	4	η theorem 4.1	ORG
ma-301	270	1	σ ∈	PERSON
ma-301	270	2	〉	CARDINAL
ma-301	270	3	η	GPE
ma-301	270	4	η(x	NORP
ma-301	274	1	α(λ	GPE
ma-301	274	2	7→	CARDINAL
ma-301	274	3	η	PERSON
ma-301	276	1	kq	PERSON
ma-301	276	2	η	PERSON
ma-301	276	3	η	GPE
ma-301	277	1	η	PERSON
ma-301	279	1	2.2),(4.1	CARDINAL
ma-301	281	1	η	PERSON
ma-301	281	2	inversionformula	GPE
ma-301	281	3	2.5	CARDINAL
ma-301	281	4	η(x	NORP
ma-301	282	1	α(gy	ORG
ma-301	283	1	η	PERSON
ma-301	283	2	α(kq	DATE
ma-301	283	3	η	PERSON
ma-301	283	4	4.4	CARDINAL
ma-301	283	5	2.2),(4.1	CARDINAL
ma-301	283	6	4.4	CARDINAL
ma-301	283	7	α(kq	DATE
ma-301	283	8	η	PERSON
ma-301	284	1	j. math	PERSON
ma-301	286	1	10.28924	CARDINAL
ma-301	286	2	12this	DATE
ma-301	286	3	7→	CARDINAL
ma-301	286	4	η	PERSON
ma-301	287	1	4.4	CARDINAL
ma-301	287	2	∈	ORG
ma-301	287	3	kq	PERSON
ma-301	287	4	η	PERSON
ma-301	287	5	η =	PERSON
ma-301	288	1	α(f	ORG
ma-301	288	2	α(kq	DATE
ma-301	288	3	η	PERSON
ma-301	288	4	α(λ	GPE
ma-301	291	1	q2)hq	DATE
ma-301	291	2	α(f	ORG
ma-301	291	3	α(λ	GPE
ma-301	291	4	2.5	CARDINAL
ma-301	292	1	1ψ	CARDINAL
ma-301	297	1	n∑ r=1 n∑ l=1 zrzlkq	PERSON
ma-301	297	2	η(xr	ORG
ma-301	297	3	xl	ORG
ma-301	301	1	n∑ r=1 n∑ l=1 zrzl	PERSON
ma-301	302	1	1 ψ	CARDINAL
ma-301	302	2	α(λ	GPE
ma-301	305	1	n∑ r=1 zr j	PERSON
ma-301	305	2	2 1	DATE
ma-301	305	3	α(λ	GPE
ma-301	305	4	0	CARDINAL
ma-301	305	5	η	PERSON
ma-301	306	1	4.2	CARDINAL
ma-301	307	1	σ ∈	PERSON
ma-301	307	2	∈	ORG
ma-301	307	3	∈	PRODUCT
ma-301	307	4	0	CARDINAL
ma-301	307	5	η	GPE
ma-301	307	6	η‖f ‖2ψ	ORG
ma-301	307	7	σ	ORG
ma-301	307	8	β(f	ORG
ma-301	308	1	2,q	CARDINAL
ma-301	308	2	4.5	CARDINAL
ma-301	309	1	η	GPE
ma-301	309	2	η	GPE
ma-301	309	3	h(y	GPE
ma-301	310	1	η	GPE
ma-301	310	2	β(x	GPE
ma-301	310	3	y)dµq	GPE
ma-301	310	4	η	PERSON
ma-301	310	5	η	GPE
ma-301	310	6	β(x	GPE
ma-301	312	1	α(λ	GPE
ma-301	313	1	η	GPE
ma-301	313	2	4.5	CARDINAL
ma-301	313	3	η	GPE
ma-301	313	4	η	GPE
ma-301	313	5	h(y	GPE
ma-301	314	1	mq	ORG
ma-301	314	2	σ	GPE
ma-301	314	3	β(kq	GPE
ma-301	314	4	η	PERSON
ma-301	314	5	y))〉q	PERSON
ma-301	314	6	2.5	CARDINAL
ma-301	314	7	4.4	CARDINAL
ma-301	314	8	mq	ORG
ma-301	314	9	σ	GPE
ma-301	314	10	β(kq	GPE
ma-301	314	11	η	PERSON
ma-301	316	1	α(λ	GPE
ma-301	317	1	η	GPE
ma-301	317	2	β(x	GPE
ma-301	319	1	j. math	PERSON
ma-301	321	1	10.28924	CARDINAL
ma-301	321	2	13	CARDINAL
ma-301	321	3	4.3	CARDINAL
ma-301	322	1	σ ∈ l∞α	PERSON
ma-301	322	2	∈	PRODUCT
ma-301	322	3	η	GPE
ma-301	322	4	α(f	ORG
ma-301	322	5	η	GPE
ma-301	322	6	σβ(λ	ORG
ma-301	324	1	4.6	CARDINAL
ma-301	324	2	η	GPE
ma-301	330	1	2.5	CARDINAL
ma-301	330	2	η	GPE
ma-301	330	3	β(x	GPE
ma-301	331	1	α(ky	CARDINAL
ma-301	331	2	2.6	CARDINAL
ma-301	331	3	η	ORG
ma-301	331	4	η	GPE
ma-301	331	5	h(y	GPE
ma-301	333	1	α(λ	GPE
ma-301	335	1	α(λ	GPE
ma-301	336	1	λ −→ σβ(λ)hq	ORG
ma-301	337	1	2.5	CARDINAL
ma-301	337	2	plancherel	ORG
ma-301	337	3	η	GPE
ma-301	337	4	α(f	ORG
ma-301	337	5	η	GPE
ma-301	339	1	|hq	GPE
ma-301	339	2	α(f	ORG
ma-301	339	3	η	GPE
ma-301	339	4	|hq	GPE
ma-301	339	5	plancherel	ORG
ma-301	339	6	2.7	CARDINAL
ma-301	339	7	η	GPE
ma-301	339	8	4.4	CARDINAL
ma-301	340	1	third	ORDINAL
ma-301	340	2	σ ∈	PERSON
ma-301	340	3	f ∈	ORG
ma-301	342	1	η	GPE
ma-301	344	1	σ	ORG
ma-301	344	2	β(f	ORG
ma-301	344	3	x)θq	GPE
ma-301	344	4	η	GPE
ma-301	344	5	β(x	GPE
ma-301	344	6	y)dµq	GPE
ma-301	344	7	lim	PERSON
ma-301	344	8	η	GPE
ma-301	344	9	4.7	CARDINAL
ma-301	344	10	η	GPE
ma-301	344	11	η −→ 0+.	ORG
ma-301	345	1	j. math	PERSON
ma-301	347	1	10.28924	CARDINAL
ma-301	347	2	14	CARDINAL
ma-301	349	1	σ	ORG
ma-301	349	2	β(f	ORG
ma-301	349	3	η	GPE
ma-301	349	4	η	GPE
ma-301	349	5	4.6	CARDINAL
ma-301	349	6	α(f	ORG
ma-301	349	7	η	GPE
ma-301	349	8	α(f	ORG
ma-301	349	9	4.8	CARDINAL
ma-301	349	10	η	GPE
ma-301	351	1	α(f	ORG
ma-301	352	1	α(f	ORG
ma-301	352	2	|hq	GPE
ma-301	352	3	α(f	ORG
ma-301	352	4	4.9	CARDINAL
ma-301	352	5	4.7	CARDINAL
ma-301	352	6	4.9	CARDINAL
ma-301	354	1	α(f	ORG
ma-301	355	1	2.5	CARDINAL
ma-301	355	2	4.8	CARDINAL
ma-301	355	3	η	GPE
ma-301	355	4	β(y)−	GPE
ma-301	357	1	α(f	ORG
ma-301	358	1	α(λ	GPE
ma-301	358	2	α(f	ORG
ma-301	359	1	α(f	ORG
ma-301	359	2	4.10	CARDINAL
ma-301	359	3	4.10	CARDINAL
ma-301	360	1	lim	PERSON
ma-301	360	2	η	GPE
ma-301	360	3	β(y)−	GPE
ma-301	361	1	0	CARDINAL
ma-301	363	1	1	CARDINAL
ma-301	363	2	l.d. abreu	PERSON
ma-301	363	3	f. bouzeffour	PERSON
ma-301	363	4	askey-wilson	ORG
ma-301	364	1	amer	PERSON
ma-301	365	1	138	CARDINAL
ma-301	365	2	2010	DATE
ma-301	366	1	2853–2853	CARDINAL
ma-301	366	2	sturm	GPE
ma-301	366	3	j. phys	PERSON
ma-301	367	1	38 (2005	DATE
ma-301	367	2	10311–10319	CARDINAL
ma-301	368	1	n. akram	PERSON
ma-301	369	1	2066812	DATE
ma-301	370	1	n. aronszajn	PERSON
ma-301	371	1	amer	PERSON
ma-301	373	1	68	CARDINAL
ma-301	373	2	1950	DATE
ma-301	373	3	337–404	CARDINAL
ma-301	375	1	1090	CARDINAL
ma-301	375	2	9947-1950-0051437	DATE
ma-301	375	3	r. bañuelos	PERSON
ma-301	375	4	k. bogdan	PERSON
ma-301	375	5	j. funct	PERSON
ma-301	377	1	250	CARDINAL
ma-301	377	2	2007	DATE
ma-301	378	1	197–213	CARDINAL
ma-301	378	2	//doi.org/10.1016	PERSON
ma-301	378	3	s. bouaziz	PERSON
ma-301	378	4	k. mezlini	PERSON
ma-301	378	5	a. fitouhi	PERSON
ma-301	378	6	j. math	PERSON
ma-301	379	1	6 (2018	PERCENT
ma-301	379	2	311	CARDINAL
ma-301	379	3	k. brahim	PERSON
ma-301	379	4	s. chefai	PERSON
ma-301	379	5	71	CARDINAL
ma-301	379	6	2016),81-97	DATE
ma-301	381	1	https://doi.org/10.1090/s0002-9947-1950-0051437-7 https://doi.org/10.1090/s0002-9947-1950-0051437-7 https://doi.org/10.1016/j.jfa.2007.05.013 https://doi.org/10.1016/j.jfa.2007.05.013	PERSON
ma-301	382	1	j. math	PERSON
ma-301	384	1	10.28924	CARDINAL
ma-301	384	2	15	CARDINAL
ma-301	384	3	8	CARDINAL
ma-301	384	4	a. akhlidj	PERSON
ma-301	384	5	calderon	ORG
ma-301	386	1	funct	PERSON
ma-301	387	1	35	CARDINAL
ma-301	387	2	2024	CARDINAL
ma-301	387	3	747–764	CARDINAL
ma-301	388	1	s. chefai	PERSON
ma-301	388	2	quantum	ORG
ma-301	388	3	j. pseudo	PERSON
ma-301	390	1	2017	CARDINAL
ma-301	391	1	723–749	CARDINAL
ma-301	392	1	s. chefai	PERSON
ma-301	392	2	l. dhaouadi	PERSON
ma-301	392	3	a. fitouhi	PERSON
ma-301	392	4	quantum	ORG
ma-301	392	5	afr.	PERSON
ma-301	393	1	diaspora	PERSON
ma-301	394	1	17	CARDINAL
ma-301	394	2	2014	DATE
ma-301	394	3	75–84.[11	CARDINAL
ma-301	397	1	5	CARDINAL
ma-301	397	2	2013	DATE
ma-301	397	3	42–60.[12	CARDINAL
ma-301	398	1	j. appl	PERSON
ma-301	399	1	49	CARDINAL
ma-301	399	2	1989	DATE
ma-301	399	3	906–931	CARDINAL
ma-301	400	1	l. dhaouadi	PERSON
ma-301	400	2	34 (2011	DATE
ma-301	400	3	453–472	DATE
ma-301	401	1	a. fitouhi	PERSON
ma-301	401	2	m.m. hamza	PERSON
ma-301	401	3	f. bouzeffour	PERSON
ma-301	401	4	j. approx	PERSON
ma-301	402	1	115	CARDINAL
ma-301	402	2	2002	DATE
ma-301	402	3	144–166	CARDINAL
ma-301	404	1	a. fitouhi	PERSON
ma-301	404	2	n. bettaibi	PERSON
ma-301	404	3	quantum	ORG
ma-301	404	4	j. nonlinear math	PERSON
ma-301	406	1	13 (2006	DATE
ma-301	407	1	492	CARDINAL
ma-301	407	2	k. brahim	PERSON
ma-301	407	3	n. bettaibi	PERSON
ma-301	407	4	ramanujan	NORP
ma-301	407	5	master theorem	PERSON
ma-301	407	6	j. 50	PERSON
ma-301	407	7	2019),433–458	CARDINAL
ma-301	408	1	https://doi.org/10.1007/s11139-019-00141-4.[17	TIME
ma-301	408	2	g. gasper	PERSON
ma-301	408	3	m. rahman	PERSON
ma-301	408	4	cambridge university press	ORG
ma-301	408	5	2011).[18	CARDINAL
ma-301	408	6	l. hörmander	PERSON
ma-301	409	1	104	CARDINAL
ma-301	409	2	1960	DATE
ma-301	410	1	93–140	CARDINAL
ma-301	410	2	https	PERSON
ma-301	410	3	//doi.org/10.1007/bf02547187.[19] f.h	ORG
ma-301	410	4	jackson	PERSON
ma-301	412	1	41	CARDINAL
ma-301	412	2	1910	DATE
ma-301	412	3	193-203.[20	QUANTITY
ma-301	412	4	kac	ORG
ma-301	412	5	p. cheung	PERSON
ma-301	412	6	quantum	ORG
ma-301	412	7	new york	GPE
ma-301	412	8	r.f. swarttouw	PERSON
ma-301	413	1	amer	PERSON
ma-301	414	1	1992	DATE
ma-301	414	2	445–461	DATE
ma-301	415	1	v. kumar	PERSON
ma-301	415	2	m. ruzhansky	PERSON
ma-301	417	1	2023	CARDINAL
ma-301	417	2	2023	CARDINAL
ma-301	417	3	1073-1093	CARDINAL
ma-301	418	1	t. matsuura	PERSON
ma-301	418	2	s. saitoh	PERSON
ma-301	418	3	d.d. trong	PERSON
ma-301	418	4	j. inverse ill	ORG
ma-301	419	1	13 (2005	DATE
ma-301	419	2	479–493	CARDINAL
ma-301	420	1	mcconnell	PERSON
ma-301	421	1	amer	PERSON
ma-301	423	1	285(1984	CARDINAL
ma-301	423	2	739	CARDINAL
ma-301	424	1	akad	PERSON
ma-301	425	1	109	CARDINAL
ma-301	425	2	1956	DATE
ma-301	425	3	701-703.[26	CARDINAL
ma-301	425	4	a. nemri	ORG
ma-301	425	5	f. soltani	PERSON
ma-301	425	6	quantum	ORG
ma-301	427	1	22	CARDINAL
ma-301	427	2	2017),2075-2090.[27	CARDINAL
ma-301	427	3	b. selmi	PERSON
ma-301	427	4	quantum	ORG
ma-301	427	5	j. math	PERSON
ma-301	429	1	359	CARDINAL
ma-301	429	2	2009	DATE
ma-301	429	3	588–601	CARDINAL
ma-301	429	4	https	PERSON
ma-301	430	1	//doi.org/10.1016	PERSON
ma-301	430	2	rubin	PERSON
ma-301	430	3	j. math	PERSON
ma-301	433	1	212	CARDINAL
ma-301	433	2	1997	DATE
ma-301	434	1	571-582.[29	CARDINAL
ma-301	434	2	rubin	GPE
ma-301	434	3	duhamel	PERSON
ma-301	435	1	amer	PERSON
ma-301	438	1	777–785	CARDINAL
ma-301	438	2	t. matsuura	PERSON
ma-301	438	3	s. saitoh	PERSON
ma-301	439	1	85	CARDINAL
ma-301	439	2	2006	DATE
ma-301	439	3	901–915	CARDINAL
ma-301	440	1	q-rubin	NORP
ma-301	442	1	anal.appl	PERSON
ma-301	442	2	14	CARDINAL
ma-301	442	3	2022	CARDINAL
ma-301	442	4	1-10	CARDINAL
ma-301	446	1	j. math	PERSON
ma-301	448	1	10.28924	CARDINAL
ma-301	448	2	16	CARDINAL
ma-301	449	1	32	CARDINAL
ma-301	449	2	q-rubin	NORP
ma-301	450	1	j. anal	PERSON
ma-301	451	1	appl.18	PRODUCT
ma-301	451	2	2020	DATE
ma-301	451	3	366-380.[33	CARDINAL
ma-301	451	4	f. soltani	PERSON
ma-301	451	5	i. maktouf	PERSON
ma-301	451	6	mediterranean j.	NORP
ma-301	452	1	21	CARDINAL
ma-301	452	2	2024	CARDINAL
ma-301	452	3	80	DATE
ma-301	453	1	1	CARDINAL
ma-301	453	2	2	CARDINAL
ma-301	453	3	2.1	CARDINAL
ma-301	453	4	2.2	CARDINAL
ma-301	454	1	2.3	CARDINAL
ma-301	455	1	3	CARDINAL
ma-301	456	1	3.1	CARDINAL
ma-301	456	2	calderon	ORG
ma-301	456	3	3.2	CARDINAL
ma-301	457	1	4	CARDINAL
ma-301	457	2	extremal	PERSON