id	sid	eid	entity	type
ma-267	1	1	2024	CARDINAL
ma-267	2	1	j. math	PERSON
ma-267	4	1	4 (2024	CARDINAL
ma-267	4	2	20doi	CARDINAL
ma-267	4	3	10.28924	CARDINAL
ma-267	4	4	calderon	ORG
ma-267	4	5	riemann-liouville	ORG
ma-267	4	6	two	CARDINAL
ma-267	4	7	ahmed chana∗	PERSON
ma-267	4	8	facultyof sciences ain chock	ORG
ma-267	4	9	hassan ii	PERSON
ma-267	4	10	b.p 5366	ORG
ma-267	4	11	casablanca	GPE
ma-267	5	1	riemann-liouville	ORG
ma-267	6	1	riemann-liouville wavelet transform	ORG
ma-267	7	1	firstly	ORDINAL
ma-267	7	2	riemann-liouville	ORG
ma-267	7	3	two	CARDINAL
ma-267	8	1	plancherel	ORG
ma-267	8	2	calderon	ORG
ma-267	9	1	extremal	LOC
ma-267	9	2	riemann-liouville wavelet transform	ORG
ma-267	10	1	1	CARDINAL
ma-267	10	2	r0(f	GPE
ma-267	11	1	1 2π	CARDINAL
ma-267	11	2	2π	CARDINAL
ma-267	13	1	r0(f	GPE
ma-267	13	2	0	CARDINAL
ma-267	15	1	10,11	CARDINAL
ma-267	15	2	5	CARDINAL
ma-267	16	1	3	CARDINAL
ma-267	16	2	riemann-liouville	ORG
ma-267	16	3	17	CARDINAL
ma-267	17	1	riemann-liouville	PERSON
ma-267	17	2	extremal	PERSON
ma-267	18	1	1	CARDINAL
ma-267	19	1	j. math	PERSON
ma-267	21	1	10.28924	CARDINAL
ma-267	24	1	1	CARDINAL
ma-267	24	2	1	CARDINAL
ma-267	25	1	1− y2	QUANTITY
ma-267	25	2	1 2	DATE
ma-267	25	3	1− s2	LAW
ma-267	25	4	0	CARDINAL
ma-267	25	5	1	CARDINAL
ma-267	25	6	1	CARDINAL
ma-267	25	7	1−t2	DATE
ma-267	25	8	riemann-liouville	ORG
ma-267	25	9	1.1	CARDINAL
ma-267	25	10	1–4	CARDINAL
ma-267	26	1	in1984 with mortel	PRODUCT
ma-267	26	2	french	NORP
ma-267	26	3	mortel	PERSON
ma-267	26	4	8	CARDINAL
ma-267	27	1	mortel	PERSON
ma-267	29	1	6	CARDINAL
ma-267	29	2	9].a	CARDINAL
ma-267	29	3	riemann	PERSON
ma-267	29	4	1.1	CARDINAL
ma-267	29	5	riemann-liouville	ORG
ma-267	29	6	by ∆1	ORG
ma-267	29	7	0	CARDINAL
ma-267	29	8	0	CARDINAL
ma-267	29	9	∂2	CARDINAL
ma-267	29	10	0	CARDINAL
ma-267	30	1	3	CARDINAL
ma-267	30	2	riemann-liouville	ORG
ma-267	30	3	1.1	CARDINAL
ma-267	31	1	rα(cos(µ.	PERSON
ma-267	31	2	exp(−iλ·))(x	GPE
ma-267	32	1	1.2	CARDINAL
ma-267	32	2	one	CARDINAL
ma-267	32	3	two	CARDINAL
ma-267	33	1	one	CARDINAL
ma-267	33	2	two	CARDINAL
ma-267	34	1	section 2	LAW
ma-267	34	2	section 3	LAW
ma-267	34	3	riemann-liouville	ORG
ma-267	34	4	two	CARDINAL
ma-267	36	1	j. math	PERSON
ma-267	38	1	10.28924	CARDINAL
ma-267	38	2	3a	CARDINAL
ma-267	38	3	plancherel	ORG
ma-267	38	4	calderon	ORG
ma-267	38	5	riemann-liouville wavelet transform	ORG
ma-267	39	1	2	CARDINAL
ma-267	39	2	riemann-liouville	ORG
ma-267	39	3	riemann-liouville	ORG
ma-267	39	4	1.1	CARDINAL
ma-267	39	5	1–4	CARDINAL
ma-267	39	6	15	CARDINAL
ma-267	40	1	k :	ORG
ma-267	41	1	0,+∞[×r	CARDINAL
ma-267	43	1	2αγ(α+ 1	QUANTITY
ma-267	43	2	dx ⊗	PERSON
ma-267	43	3	1 ≤	MONEY
ma-267	43	4	1	CARDINAL
ma-267	43	5	1,+∞	DATE
ma-267	44	1	k̂	PERSON
ma-267	46	1	0,+∞[×r	CARDINAL
ma-267	47	1	0,+∞[×r	CARDINAL
ma-267	47	2	6 |y |}.•	QUANTITY
ma-267	47	3	σ	ORG
ma-267	47	4	k̂	PERSON
ma-267	47	5	bk̂	ORG
ma-267	47	6	θ(s	PERSON
ma-267	47	7	√ s2 + y2	PERSON
ma-267	48	1	bk̂	ORG
ma-267	48	2	bk̂	ORG
ma-267	49	1	have∫ k̂	PERSON
ma-267	50	1	1 2αγ(α+ 1	CARDINAL
ma-267	50	2	2π	CARDINAL
ma-267	51	1	g(µ	ORG
ma-267	51	2	− µ2	PERSON
ma-267	52	1	2.1	CARDINAL
ma-267	53	1	‖g‖p	GPE
ma-267	54	1	1	CARDINAL
ma-267	55	1	1,+∞[,ess	CARDINAL
ma-267	55	2	m)∈k̂ |g(λ	PERSON
ma-267	56	1	j. math	PERSON
ma-267	58	1	10.28924	CARDINAL
ma-267	58	2	42.1	CARDINAL
ma-267	60	1	∈	ORG
ma-267	60	2		ORG
ma-267	62	1	0	CARDINAL
ma-267	62	2	1	CARDINAL
ma-267	62	3	0	CARDINAL
ma-267	64	1	3	CARDINAL
ma-267	66	1	2.2	CARDINAL
ma-267	66	2	16	CARDINAL
ma-267	68	1	1	CARDINAL
ma-267	69	1	∈	ORG
ma-267	69	2	2.3	CARDINAL
ma-267	69	3	2.2	CARDINAL
ma-267	70	1	riemann-liouville	ORG
ma-267	71	1	2.1	CARDINAL
ma-267	72	1	riemann-liouville op-erator	ORG
ma-267	72	2	1.1	CARDINAL
ma-267	73	1	∈	ORG
ma-267	73	2	2–4	CARDINAL
ma-267	74	1	2.1.(1	CARDINAL
ma-267	74	2	∈	ORG
ma-267	75	1	‖fα(f	ORG
ma-267	76	1	2.4	CARDINAL
ma-267	76	2	2)(inversion	CARDINAL
ma-267	76	3	∩ l2α	PERSON
ma-267	78	1	2.5	CARDINAL
ma-267	78	2	3	CARDINAL
ma-267	78	3	∈	ORG
ma-267	79	1	k̂	PERSON
ma-267	79	2	2.6	CARDINAL
ma-267	79	3	‖fα(f )‖2,γα	ORG
ma-267	80	1	2.7)(4	LAW
ma-267	80	2	plancherel	ORG
ma-267	80	3	reimann-liouville	ORG
ma-267	82	1	j. math	PERSON
ma-267	84	1	10.28924	CARDINAL
ma-267	84	2	52.3	CARDINAL
ma-267	85	1	generalized translation operator	ORG
ma-267	85	2	riemann-liouville	ORG
ma-267	86	1	2.2	CARDINAL
ma-267	87	1	riemann-liouville	ORG
ma-267	87	2	1)√ πγ(α+ 1/2	CARDINAL
ma-267	90	1	riemann-liouville	ORG
ma-267	91	1	2–4	CARDINAL
ma-267	92	1	2.2	CARDINAL
ma-267	94	1	k τ	PERSON
ma-267	96	1	2.8	CARDINAL
ma-267	96	2	2	CARDINAL
ma-267	97	1	1	CARDINAL
ma-267	98	1	2.9	CARDINAL
ma-267	98	2	3	CARDINAL
ma-267	98	3	∈	ORG
ma-267	98	4	∈	ORG
ma-267	98	5	2.10	CARDINAL
ma-267	99	1	k τ	PERSON
ma-267	99	2	s)g(y	PERSON
ma-267	100	1	f̌	ORG
ma-267	100	2	13].we	CARDINAL
ma-267	100	3	2–4	CARDINAL
ma-267	101	1	2.3.(1)(young	DATE
ma-267	101	2	∈	ORG
ma-267	102	1	1	CARDINAL
ma-267	102	2	1p + 1	CARDINAL
ma-267	102	3	1 + 1	CARDINAL
ma-267	102	4	2.11	CARDINAL
ma-267	102	5	2	CARDINAL
ma-267	102	6	∈	ORG
ma-267	104	1	2.12	CARDINAL
ma-267	104	2	3	CARDINAL
ma-267	104	3	∈	ORG
ma-267	105	1	k̂	PERSON
ma-267	105	2	λ)|2 |fα(g)(µ	GPE
ma-267	105	3	λ)|2 dγα(µ	ORG
ma-267	105	4	2.13	CARDINAL
ma-267	107	1	j. math	PERSON
ma-267	109	1	10.28924	CARDINAL
ma-267	109	2	63	CARDINAL
ma-267	110	1	calderón	PERSON
ma-267	110	2	riemann-liouville	ORG
ma-267	110	3	two	CARDINAL
ma-267	110	4	riemann-liouville	ORG
ma-267	110	5	riemann-liouville operatorand	ORG
ma-267	110	6	plancherel	ORG
ma-267	110	7	calderon	ORG
ma-267	110	8	4	CARDINAL
ma-267	111	1	×k),1	ORG
ma-267	112	1		ORG
ma-267	113	1	1	CARDINAL
ma-267	115	1	1,+∞	DATE
ma-267	116	1	⊗ dµα(x	PERSON
ma-267	117	1	3.1	CARDINAL
ma-267	118	1	∈	ORG
ma-267	118	2	two	CARDINAL
ma-267	120	1	3.1	CARDINAL
ma-267	120	2	3.1	CARDINAL
ma-267	121	1	3.2	CARDINAL
ma-267	121	2	riemann-liouville	ORG
ma-267	121	3	l2α(k).let	ORG
ma-267	121	4	0	CARDINAL
ma-267	121	5	da(ψ)(x	GPE
ma-267	123	1	∈	ORG
ma-267	124	1	1 2	CARDINAL
ma-267	124	2	1	CARDINAL
ma-267	124	3	2α+3)‖ψ‖p,µα	CARDINAL
ma-267	125	1	3.3	CARDINAL
ma-267	125	2	∈	ORG
ma-267	125	3	1	CARDINAL
ma-267	126	1	3.4	CARDINAL
ma-267	126	2	riemann-liouville wavelet	ORG
ma-267	126	3	1 ≤	MONEY
ma-267	126	4	0,(x	TIME
ma-267	128	1	3.5	CARDINAL
ma-267	129	1	j. math	PERSON
ma-267	131	1	10.28924	CARDINAL
ma-267	131	2	7by	ORDINAL
ma-267	131	3	2.9	CARDINAL
ma-267	131	4	3.3	CARDINAL
ma-267	131	5	t‖p,µα	ORG
ma-267	131	6	1 2	CARDINAL
ma-267	131	7	1	CARDINAL
ma-267	131	8	2α+3)‖ψ‖p,µα	CARDINAL
ma-267	131	9	3.6	CARDINAL
ma-267	131	10	3.2	CARDINAL
ma-267	132	1	4	CARDINAL
ma-267	132	2	riemann-liouville wavelet	ORG
ma-267	132	3	riemann-liouville	ORG
ma-267	132	4	sαψ(f	GPE
ma-267	135	1	3.7	CARDINAL
ma-267	135	2	3.2	CARDINAL
ma-267	136	1	riemann-liouville wavelet transform	ORG
ma-267	136	2	3.7	CARDINAL
ma-267	136	3	sαψ(f	NORP
ma-267	138	1	3.8	CARDINAL
ma-267	138	2	riemann-liouville	ORG
ma-267	139	1	3.1	CARDINAL
ma-267	140	1	riemann-liouville	ORG
ma-267	140	2	∈	ORG
ma-267	141	1	1	CARDINAL
ma-267	142	1	3.9	CARDINAL
ma-267	143	1	2.12	CARDINAL
ma-267	143	2	3.4),(3.8	DATE
ma-267	145	1	riemann-liouville	ORG
ma-267	145	2	4	CARDINAL
ma-267	146	1	3.1	CARDINAL
ma-267	147	1	two	CARDINAL
ma-267	148	1	∈	ORG
ma-267	150	1	∫ k f	PERSON
ma-267	150	2	3.10	CARDINAL
ma-267	150	3	3.1	CARDINAL
ma-267	152	1	2.5),(2.12),(3.4	CARDINAL
ma-267	152	2	3.8	CARDINAL
ma-267	152	3	t)sαψ1(g)(a	DATE
ma-267	154	1	g)(x	ORG
ma-267	157	1	∫ k̂	PERSON
ma-267	157	2	λ)fα(g)(µ	GPE
ma-267	157	3	λ)dγα(λ	GPE
ma-267	157	4	∫ k̂	PERSON
ma-267	157	5	riemann-liouville	ORG
ma-267	157	6	2.5	CARDINAL
ma-267	158	1	riemann-liouville	ORG
ma-267	158	2	two	CARDINAL
ma-267	160	1	j. math	PERSON
ma-267	162	1	10.28924	CARDINAL
ma-267	162	2	8	CARDINAL
ma-267	162	3	3.2	DATE
ma-267	163	1	riemann-liouville	ORG
ma-267	163	2	two	CARDINAL
ma-267	163	3	∈	ORG
ma-267	164	1	k̂	PERSON
ma-267	164	2	1	CARDINAL
ma-267	165	1	t)ψ2,a	PERSON
ma-267	166	1	proof	PERSON
ma-267	167	1	∈	ORG
ma-267	167	2	3.10	CARDINAL
ma-267	167	3	fubini	PERSON
ma-267	168	1	1	CARDINAL
ma-267	169	1	1	CARDINAL
ma-267	171	1	t)ψ2,a	PERSON
ma-267	172	1	two	CARDINAL
ma-267	173	1	k̂	PERSON
ma-267	173	2	3.11	CARDINAL
ma-267	173	3	3.2	CARDINAL
ma-267	174	1	0	CARDINAL
ma-267	175	1	1 cψ1,ψ2	PERCENT
ma-267	175	2	kε	PERSON
ma-267	175	3	δ(λ	ORG
ma-267	175	4	1 cψ1,ψ2	PERCENT
ma-267	175	5	3.11	CARDINAL
ma-267	175	6	∈	ORG
ma-267	175	7	kε	PERSON
ma-267	175	8	k̂	PERSON
ma-267	175	9	δ)(λ	ORG
ma-267	175	10	δ(λ	ORG
ma-267	175	11	3.12	CARDINAL
ma-267	176	1	c2ψ1,ψ2 ∫ δ	ORG
ma-267	177	1	2.13	CARDINAL
ma-267	178	1	3.4	CARDINAL
ma-267	178	2	c2ψ1,ψ2	ORG
ma-267	178	3	2	CARDINAL
ma-267	178	4	∈	ORG
ma-267	178	5	k̂	PERSON
ma-267	178	6	2.5	CARDINAL
ma-267	178	7	2.10	CARDINAL
ma-267	178	8	3.4	CARDINAL
ma-267	179	1	2.5	CARDINAL
ma-267	179	2	3.12	CARDINAL
ma-267	181	1	j. math	PERSON
ma-267	183	1	10.28924	CARDINAL
ma-267	183	2	3.3	CARDINAL
ma-267	184	1	first	ORDINAL
ma-267	184	2	reimann-liouville	ORG
ma-267	184	3	two	CARDINAL
ma-267	184	4	3.11	CARDINAL
ma-267	184	5	∈	ORG
ma-267	184	6	δ(x	PERSON
ma-267	184	7	1	CARDINAL
ma-267	185	1	lim	PERSON
ma-267	185	2	0	CARDINAL
ma-267	186	1	3.13	CARDINAL
ma-267	187	1	2.7	CARDINAL
ma-267	187	2	3.12	CARDINAL
ma-267	187	3	k̂	PERSON
ma-267	187	4	3.13	CARDINAL
ma-267	187	5	3.1	CARDINAL
ma-267	188	1	4	CARDINAL
ma-267	188	2	extremal	PERSON
ma-267	188	3	riemann-liouville wavelet transform	ORG
ma-267	188	4	18,19	CARDINAL
ma-267	188	5	riemann-liouville wavelet transform	ORG
ma-267	189	1	4.1	CARDINAL
ma-267	189	2	sobolev	PERSON
ma-267	189	3	riemann-liouville	ORG
ma-267	190	1	0	CARDINAL
ma-267	190	2	riemann-liouville	ORG
ma-267	191	1	1 + µ2 + 2λ2	QUANTITY
ma-267	193	1	1 + µ2 + 2λ2	QUANTITY
ma-267	193	2	4.1	CARDINAL
ma-267	194	1	1 + µ2 + 2λ2	QUANTITY
ma-267	194	2	4.2	CARDINAL
ma-267	195	1	4.1	CARDINAL
ma-267	196	1	riemann-liouville wavelet	ORG
ma-267	198	1	4.3	CARDINAL
ma-267	199	1	j. math	PERSON
ma-267	201	1	10.28924	CARDINAL
ma-267	202	1	4.4	CARDINAL
ma-267	202	2	4.1	CARDINAL
ma-267	203	1	2α+3 2	LAW
ma-267	203	2	0	CARDINAL
ma-267	205	1	4.5	CARDINAL
ma-267	206	1	β(k	PERSON
ma-267	206	2	2.9	CARDINAL
ma-267	206	3	3.9	CARDINAL
ma-267	206	4	4.2	CARDINAL
ma-267	206	5	4.4	CARDINAL
ma-267	208	1	1 + µ2 + 2λ2	QUANTITY
ma-267	209	1	4.6	CARDINAL
ma-267	209	2	2.1	CARDINAL
ma-267	209	3	1 + µ2 + 2λ2)s + cψ	QUANTITY
ma-267	209	4	1 2	CARDINAL
ma-267	210	1	4.1	CARDINAL
ma-267	211	1	2α+3 2	LAW
ma-267	211	2	riemann-liouville wavelet	ORG
ma-267	211	3	0	CARDINAL
ma-267	212	1	β(k	PERSON
ma-267	212	2	〉	CARDINAL
ma-267	212	3	kψ,β[(x	ORG
ma-267	213	1	k̂ ϕµ,−λ(x	PERSON
ma-267	213	2	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	213	3	4.7	CARDINAL
ma-267	213	4	t)→ kr	PERSON
ma-267	213	5	h[(x	ORG
ma-267	213	6	β(k	PERSON
ma-267	214	1	〈 f	PERSON
ma-267	214	2	kψ	ORG
ma-267	217	1	2.3	CARDINAL
ma-267	217	2	λ)→	NORP
ma-267	217	3	1 + µ2 + 2λ2)s +	QUANTITY
ma-267	217	4	riemann-liouville	ORG
ma-267	217	5	kψ	ORG
ma-267	219	1	1	CARDINAL
ma-267	219	2	1 +m2)]s + ch	QUANTITY
ma-267	219	3	4.8	CARDINAL
ma-267	219	4	2.5	CARDINAL
ma-267	219	5	kψ,β[(x	ORG
ma-267	220	1	k̂ ϕµ,−λ(x	PERSON
ma-267	220	2	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	221	1	j. math	PERSON
ma-267	223	1	10.28924	CARDINAL
ma-267	223	2	2.3	CARDINAL
ma-267	223	3	4.6	CARDINAL
ma-267	223	4	4.8	CARDINAL
ma-267	223	5	that∥∥kψ	ORG
ma-267	224	1	1 + µ2 + 2λ2)s + cψ	QUANTITY
ma-267	224	2	β(k	PERSON
ma-267	225	1	β(k	PERSON
ma-267	225	2	4.8	CARDINAL
ma-267	225	3	kψ	ORG
ma-267	225	4	hsr	GPE
ma-267	225	5	k̂ ϕµ,λ(y	PERSON
ma-267	225	6	z)fα(f	ORG
ma-267	225	7	2.5	CARDINAL
ma-267	227	1	4.2	CARDINAL
ma-267	228	1	riemann-liouville	ORG
ma-267	228	2	2α+3 2	LAW
ma-267	228	3	∈	PRODUCT
ma-267	229	1	− g ∥∥2	PERSON
ma-267	229	2	4.9	CARDINAL
ma-267	229	3	β(x	GPE
ma-267	231	1	k g(a	PERSON
ma-267	232	1	4.10	CARDINAL
ma-267	233	1	2α+3 2	DATE
ma-267	233	2	∫ k̂ ϕµ,−λ(x	PERSON
ma-267	233	3	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	234	1	4.11	CARDINAL
ma-267	235	1	4.9	CARDINAL
ma-267	235	2	18,19	CARDINAL
ma-267	235	3	β(x	GPE
ma-267	236	1	〈 g	PERSON
ma-267	236	2	4.12	CARDINAL
ma-267	236	3	4.8	CARDINAL
ma-267	236	4	2.6	CARDINAL
ma-267	236	5	2.10	CARDINAL
ma-267	236	6	3.4	CARDINAL
ma-267	236	7	4.8	CARDINAL
ma-267	239	1	2α+3 2	DATE
ma-267	239	2	∫ k̂ ϕµ,λ(x	PERSON
ma-267	239	3	t)ϕµ,−λ(y	ORG
ma-267	239	4	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	239	5	4.13	CARDINAL
ma-267	239	6	4.12	CARDINAL
ma-267	239	7	4.13	CARDINAL
ma-267	240	1	4.3	CARDINAL
ma-267	241	1	2α+3 2	LAW
ma-267	241	2	riemann-liouville wavelet	ORG
ma-267	241	3	∈	PRODUCT
ma-267	243	1	β(x	GPE
ma-267	245	1	1 + µ2 + 2λ2)s +	QUANTITY
ma-267	247	1	1 + µ2 + 2λ2)s +	QUANTITY
ma-267	247	2	4.15	CARDINAL
ma-267	248	1	j. math	PERSON
ma-267	250	1	10.28924	CARDINAL
ma-267	250	2	12	CARDINAL
ma-267	251	1	2β	CARDINAL
ma-267	252	1	4.16	CARDINAL
ma-267	253	1	4.10	CARDINAL
ma-267	253	2	4.11	CARDINAL
ma-267	254	1	fubini	PERSON
ma-267	254	2	2.5),(4.10	CARDINAL
ma-267	254	3	4.11).(iii)by	CARDINAL
ma-267	254	4	4.2	CARDINAL
ma-267	255	1	1 + µ2 + 2λ2	QUANTITY
ma-267	255	2	1 2β	CARDINAL
ma-267	255	3	∫ k̂	PERSON
ma-267	256	1	plancherel	ORG
ma-267	256	2	2.7	CARDINAL
ma-267	256	3	1 2β	CARDINAL
ma-267	257	1	4.1	CARDINAL
ma-267	258	1	2α+3 2	LAW
ma-267	258	2	riemann-liouville wavelet	ORG
ma-267	258	3	0	CARDINAL
ma-267	258	4	∈	ORG
ma-267	258	5	1 + µ2 + 2λ2)s +	QUANTITY
ma-267	259	1	4.17	CARDINAL
ma-267	260	1	2β	CARDINAL
ma-267	260	2	4.18	CARDINAL
ma-267	261	1	3.2	CARDINAL
ma-267	261	2	3.9	CARDINAL
ma-267	261	3	4.15	CARDINAL
ma-267	261	4	3.9	CARDINAL
ma-267	261	5	4.16	CARDINAL
ma-267	262	1	4.4	CARDINAL
ma-267	263	1	second	ORDINAL
ma-267	263	2	calderon	ORG
ma-267	263	3	2α+3 2	LAW
ma-267	263	4	riemann-liouville wavelet	ORG
ma-267	263	5	0	CARDINAL
ma-267	263	6	∈	ORG
ma-267	263	7	lim	PERSON
ma-267	264	1	0	CARDINAL
ma-267	266	1	4.17	CARDINAL
ma-267	267	1	1 + µ2 + 2λ2	QUANTITY
ma-267	267	2	1 + µ2 + 2λ2)s + cψ	QUANTITY
ma-267	267	3	4.19	CARDINAL
ma-267	268	1	j. math	PERSON
ma-267	270	1	10.28924	CARDINAL
ma-267	271	1	that∥∥∥f	ORG
ma-267	272	1	1 + µ2 + 2λ2	QUANTITY
ma-267	272	2	3s	CARDINAL
ma-267	272	3	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	272	4	1 + µ2 + 2λ2	QUANTITY
ma-267	272	5	3s	CARDINAL
ma-267	272	6	1 + µ2 + 2λ2)s + cψ ≤	QUANTITY
ma-267	272	7	1 + µ2 + 2λ2	QUANTITY
ma-267	272	8	lim	PERSON
ma-267	273	1	0on	DATE
ma-267	273	2	2.5	CARDINAL
ma-267	273	3	4.19	CARDINAL
ma-267	274	1	k̂	PERSON
ma-267	274	2	1 + µ2 + 2λ2	QUANTITY
ma-267	274	3	1 + µ2 + 2λ2)s + cψ dγα(µ	QUANTITY
ma-267	274	4	1 + µ2 + 2λ2	QUANTITY
ma-267	274	5	1 + µ2 + 2λ2)s + cψ ∣∣∣∣∣	QUANTITY
ma-267	274	6	lim	PERSON
ma-267	274	7	0	CARDINAL
ma-267	275	1	1	CARDINAL
ma-267	275	2	l. t. rachdi	PERSON
ma-267	275	3	riemann	PERSON
ma-267	277	1	j. math	PERSON
ma-267	278	1	24(2013	CARDINAL
ma-267	278	2	1350070	DATE
ma-267	279	1	b. amri	PERSON
ma-267	279	2	l. t. rachdi	PERSON
ma-267	279	3	riemann	PERSON
ma-267	280	1	bull	ORG
ma-267	282	1	sci	ORG
ma-267	283	1	39	CARDINAL
ma-267	283	2	2016	CARDINAL
ma-267	283	3	457	CARDINAL
ma-267	284	1	n. b. hamadi	PERSON
ma-267	284	2	l. t. rachdi	PERSON
ma-267	284	3	riemann-liouville	ORG
ma-267	285	1	2006(2006	CARDINAL
ma-267	285	2	086238	DATE
ma-267	286	1	n. b. hamadi	PERSON
ma-267	286	2	riemann	PERSON
ma-267	288	1	j. math	PERSON
ma-267	289	1	27	CARDINAL
ma-267	289	2	2016	CARDINAL
ma-267	289	3	1650036	DATE
ma-267	290	1	j. k. cohen	PERSON
ma-267	290	2	n. bleistein	PERSON
ma-267	291	1	44	DATE
ma-267	291	2	1979	DATE
ma-267	291	3	1077-1087	CARDINAL
ma-267	292	1	i. daubechies	PERSON
ma-267	292	2	ten	CARDINAL
ma-267	292	3	siam	GPE
ma-267	292	4	1992).[7	CARDINAL
ma-267	292	5	j. appl	PERSON
ma-267	293	1	45	CARDINAL
ma-267	293	2	1985	DATE
ma-267	293	3	336–341	CARDINAL
ma-267	293	4	https	ORG
ma-267	295	1	j. math	PERSON
ma-267	297	1	10.28924	CARDINAL
ma-267	297	2	14	CARDINAL
ma-267	297	3	8	CARDINAL
ma-267	297	4	j. morlet	PERSON
ma-267	300	1	15	CARDINAL
ma-267	300	2	1984	DATE
ma-267	301	1	723–736	DATE
ma-267	302	1	a. grossmann	PERSON
ma-267	302	2	j. morlet	PERSON
ma-267	302	3	23	CARDINAL
ma-267	302	4	1984	DATE
ma-267	302	5	85–102	CARDINAL
ma-267	302	6	h. hellsten	PERSON
ma-267	302	7	l.e. andersson	PERSON
ma-267	302	8	1987	DATE
ma-267	302	9	111–124	DATE
ma-267	303	1	https://doi.org/10.1088/0266-5611/3/1/013.[11] l.h. herbertson	ORG
ma-267	304	1	the pennsylvania state university	ORG
ma-267	304	2	2009).[12	CARDINAL
ma-267	304	3	riemann-liouville	ORG
ma-267	305	1	j. math	PERSON
ma-267	307	1	2006	DATE
ma-267	307	2	094768	DATE
ma-267	308	1	jewett	ORG
ma-267	308	2	adv	ORG
ma-267	309	1	18	CARDINAL
ma-267	309	2	1975	DATE
ma-267	309	3	1–101	DATE
ma-267	311	1	1016/0001-8708(75)90002	DATE
ma-267	311	2	h. mejjaoli	PERSON
ma-267	311	3	two	CARDINAL
ma-267	311	4	j. pseudo	PERSON
ma-267	313	1	8 (2017	CARDINAL
ma-267	313	2	349–387	CARDINAL
ma-267	314	1	s. omri	PERSON
ma-267	314	2	l.t.	PERSON
ma-267	314	3	rachdi	NORP
ma-267	314	4	heisenberg-pauli	PERSON
ma-267	314	5	riemann-liouville	ORG
ma-267	317	1	9 (2008	DATE
ma-267	317	2	1-23.[16	CARDINAL
ma-267	317	3	m. rosler	PERSON
ma-267	317	4	hypergroups	GPE
ma-267	317	5	r.	NORP
ma-267	318	1	292	CARDINAL
ma-267	318	2	1994.[17	CARDINAL
ma-267	319	1	2023	CARDINAL
ma-267	319	2	14	CARDINAL
ma-267	321	1	s. saitoh,	PERSON
ma-267	321	2	singapore	GPE
ma-267	321	3	springer singapore	GPE
ma-267	321	4	2016.[19	ORG
ma-267	321	5	s. saitoh,	PERSON
ma-267	321	6	j. phys	ORG
ma-267	322	1	ser.73	ORG
ma-267	322	2	2007	DATE
ma-267	322	3	012019	DATE
ma-267	323	1	https://doi.org/10.1088/1742-6596/73/1/012019	CARDINAL
ma-267	325	1	2	CARDINAL
ma-267	325	2	riemann-liouville	ORG
ma-267	325	3	2.1	CARDINAL
ma-267	326	1	1 and 2 2.2	QUANTITY
ma-267	327	1	riemann-liouville	ORG
ma-267	327	2	2.3	CARDINAL
ma-267	328	1	generalized translation operator	ORG
ma-267	328	2	riemann-liouville	ORG
ma-267	328	3	3	CARDINAL
ma-267	329	1	calderón	ORG
ma-267	329	2	riemann-liouville	ORG
ma-267	329	3	two	CARDINAL
ma-267	329	4	4	CARDINAL
ma-267	329	5	extremal	PERSON
ma-267	329	6	riemann-liouville wavelet	ORG
ma-267	329	7	4.1	CARDINAL
ma-267	329	8	sobolev	ORG
ma-267	329	9	riemann-liouville	ORG