id	sid	eid	entity	type
ma-199	1	1	2024	CARDINAL
ma-199	2	1	j. math	PERSON
ma-199	4	1	4 (2024	CARDINAL
ma-199	5	1	1doi	CARDINAL
ma-199	5	2	10.28924	CARDINAL
ma-199	5	3	shah jahan1	PERSON
ma-199	6	1	1department	CARDINAL
ma-199	6	2	central university of haryana	ORG
ma-199	6	3	123029	DATE
ma-199	7	1	india	GPE
ma-199	8	1	national institute of technology karnataka	ORG
ma-199	8	2	575025	CARDINAL
ma-199	8	3	india	GPE
ma-199	8	4	sam@nitk.edu.in ∗correspondence	PERSON
ma-199	8	5	sam@nitk.edu.in	PERSON
ma-199	9	1	recent years	DATE
ma-199	12	1	two	CARDINAL
ma-199	12	2	one	CARDINAL
ma-199	13	1	1	CARDINAL
ma-199	13	2	schaeffer	ORG
ma-199	15	1	linear	ORG
ma-199	17	1	9	CARDINAL
ma-199	17	2	3	CARDINAL
ma-199	17	3	6	CARDINAL
ma-199	18	1	1.1	CARDINAL
ma-199	19	1	4	CARDINAL
ma-199	21	1	0	CARDINAL
ma-199	21	2	‖2 ≤ ∑ n∈i |〈f	PERSON
ma-199	21	3	∈	ORG
ma-199	21	4	19	CARDINAL
ma-199	22	1	42c15	CARDINAL
ma-199	22	2	46c05	DATE
ma-199	25	1	https://adac.ee	GPE
ma-199	26	1	j. math	PERSON
ma-199	28	1	10.28924	CARDINAL
ma-199	28	2	2we	ORDINAL
ma-199	28	3	3	CARDINAL
ma-199	28	4	fn〉fn ∈ h	ORG
ma-199	28	5	1	CARDINAL
ma-199	28	6	linear	ORG
ma-199	28	7	fn〉fn	ORG
ma-199	28	8	fn}n∈i	GPE
ma-199	32	1	2	CARDINAL
ma-199	32	2	2	CARDINAL
ma-199	32	3	first	ORDINAL
ma-199	32	4	1942	DATE
ma-199	33	1	5	CARDINAL
ma-199	34	1	pontrjagin	PERSON
ma-199	34	2	8	CARDINAL
ma-199	35	1	1	CARDINAL
ma-199	37	1	section 3	LAW
ma-199	38	1	section 4	LAW
ma-199	42	1	2	CARDINAL
ma-199	47	1	0	CARDINAL
ma-199	49	1	1	CARDINAL
ma-199	49	2	2	CARDINAL
ma-199	51	1	j. math	PERSON
ma-199	53	1	10.28924	CARDINAL
ma-199	53	2	3an	ORDINAL
ma-199	54	1	subspace k0	PERSON
ma-199	55	1	k = k0[+̇]k+[+̇]k−.	PERSON
ma-199	55	2	3	CARDINAL
ma-199	55	3	3	CARDINAL
ma-199	55	4	k.an	PERSON
ma-199	56	1	subspace k−	NORP
ma-199	60	1	k =	PERSON
ma-199	60	2	4	CARDINAL
ma-199	61	1	4	CARDINAL
ma-199	63	1	jf	ORG
ma-199	63	2	4	CARDINAL
ma-199	66	1	jf	PERSON
ma-199	68	1	2p	CARDINAL
ma-199	68	2	2[p+f	CARDINAL
ma-199	70	1	5	CARDINAL
ma-199	71	1	1 2	CARDINAL
ma-199	72	1	jf	PERSON
ma-199	72	2	1 2	CARDINAL
ma-199	72	3	2.1	CARDINAL
ma-199	73	1	k =	PERSON
ma-199	73	2	2(n	CARDINAL
ma-199	73	3	gn	ORG
ma-199	73	4	0	CARDINAL
ma-199	74	1	k−	NORP
ma-199	75	1	0	CARDINAL
ma-199	77	1	k−	NORP
ma-199	78	1	2.1	CARDINAL
ma-199	79	1	2	CARDINAL
ma-199	80	1	k.(2	PERSON
ma-199	81	1	j = j∗ = j−1.	PERSON
ma-199	83	1	j. math	PERSON
ma-199	85	1	10.28924	CARDINAL
ma-199	85	2	4different	CARDINAL
ma-199	87	1	2.2	CARDINAL
ma-199	88	1	two	CARDINAL
ma-199	88	2	1	CARDINAL
ma-199	88	3	−1	DATE
ma-199	90	1	k−	NORP
ma-199	91	1	1	CARDINAL
ma-199	92	1	n2	PRODUCT
ma-199	92	2	2n	CARDINAL
ma-199	96	1	jng	PERSON
ma-199	96	2	jng	PERSON
ma-199	97	1	g ∈ k.	PERSON
ma-199	103	1	2(i−	CARDINAL
ma-199	104	1	3.1	CARDINAL
ma-199	105	1	0	CARDINAL
ma-199	105	2	6	CARDINAL
ma-199	105	3	6	CARDINAL
ma-199	105	4	3.1	CARDINAL
ma-199	107	1	k.	PERSON
ma-199	109	1	∑ n∈i+ cnfn	PERSON
ma-199	109	2	2(i−	CARDINAL
ma-199	109	3	‖t‖ ≤ √	FAC
ma-199	110	1	first	ORDINAL
ma-199	110	2	∈	ORG
ma-199	110	3	2(i−	CARDINAL
ma-199	112	1	j. math	PERSON
ma-199	114	1	10.28924	CARDINAL
ma-199	114	2	1 2	CARDINAL
ma-199	114	3	1 2 ≤ √	QUANTITY
ma-199	114	4	1 2	CARDINAL
ma-199	115	1	∈	ORG
ma-199	115	2	2(i−	CARDINAL
ma-199	115	3	k−	GPE
ma-199	117	1	∈	ORG
ma-199	119	1	arewell	ORG
ma-199	120	1	2(i−	CARDINAL
ma-199	123	1	∈	ORG
ma-199	123	2	∈	ORG
ma-199	125	1	3.2	CARDINAL
ma-199	126	1	∑ n∈i+ cnfn	PERSON
ma-199	126	2	∈	ORG
ma-199	126	3	2(i−	CARDINAL
ma-199	128	1	6	CARDINAL
ma-199	129	1	3.3	CARDINAL
ma-199	131	1	k.	PERSON
ma-199	132	1	∑ n∈i+ cnfn	PERSON
ma-199	132	2	n∈i−	NORP
ma-199	132	3	∈	ORG
ma-199	132	4	2(i−	CARDINAL
ma-199	134	1	3.2	CARDINAL
ma-199	135	1	two	CARDINAL
ma-199	135	2	f1	PERSON
ma-199	135	3	f2	ORG
ma-199	135	4	g1	ORG
ma-199	136	1	k−n	GPE
ma-199	139	1	1 4	DATE
ma-199	139	2	2n + 2	MONEY
ma-199	139	3	21 +	QUANTITY
ma-199	139	4	2 2	DATE
ma-199	141	1	1	CARDINAL
ma-199	141	2	1	CARDINAL
ma-199	141	3	1	CARDINAL
ma-199	143	1	1 2(n	CARDINAL
ma-199	145	1	j. math	PERSON
ma-199	147	1	10.28924	CARDINAL
ma-199	147	2	k.	PERSON
ma-199	147	3	⊂	GPE
ma-199	148	1	2(i−	CARDINAL
ma-199	148	2	∑ n∈i+ cnfn	PERSON
ma-199	150	1	2(i−	CARDINAL
ma-199	150	2	fn]}n∈i+	PERSON
ma-199	151	1	∑ n∈i+	PERSON
ma-199	151	2	t−t−∗	PERSON
ma-199	151	3	k− −→ k−	PERSON
ma-199	152	1	k −→ k	PERSON
ma-199	152	2	∑ n∈i+	PERSON
ma-199	154	1	5	CARDINAL
ma-199	154	2	3.2	CARDINAL
ma-199	156	1	3.3	CARDINAL
ma-199	159	1	k −→ k	PERSON
ma-199	159	2	∑ n∈i+	PERSON
ma-199	161	1	3.4	CARDINAL
ma-199	162	1	s.	PERSON
ma-199	163	1	∑ n∈i+	PERSON
ma-199	164	1	−1	DATE
ma-199	164	2	−1	DATE
ma-199	164	3	7	CARDINAL
ma-199	166	1	j. math	PERSON
ma-199	168	1	10.28924	CARDINAL
ma-199	170	1	∑ n∈i+	PERSON
ma-199	171	1	−1	DATE
ma-199	171	2	−1	CARDINAL
ma-199	171	3	∑ n∈i+	PERSON
ma-199	171	4	−1	DATE
ma-199	171	5	−1	DATE
ma-199	171	6	∈	ORG
ma-199	171	7	2(i−	CARDINAL
ma-199	171	8	3.3	CARDINAL
ma-199	172	1	4	CARDINAL
ma-199	172	2	4.1	CARDINAL
ma-199	174	1	a(a	DATE
ma-199	174	2	∈	ORG
ma-199	174	3	k.(c	ORG
ma-199	175	1	4.2	CARDINAL
ma-199	176	1	i.	PERSON
ma-199	178	1	4.3	CARDINAL
ma-199	179	1	k.	PERSON
ma-199	179	2	nk = nk−1	PERSON
ma-199	181	1	k ∈	PERSON
ma-199	185	1	1	CARDINAL
ma-199	185	2	k ≥ 2.	ORG
ma-199	187	1	4.1	CARDINAL
ma-199	188	1	two	CARDINAL
ma-199	189	1	2(i	CARDINAL
ma-199	192	1	2(i−	CARDINAL
ma-199	193	1	2(i−	CARDINAL
ma-199	193	2	t−{[f −nk	ORG
ma-199	197	1	j. math	PERSON
ma-199	199	1	10.28924	CARDINAL
ma-199	199	2	8	CARDINAL
ma-199	199	3	a′	ORG
ma-199	202	1	+nk	PERSON
ma-199	203	1	nk∈i+	TIME
ma-199	204	1	nk∈i+	TIME
ma-199	206	1	∑ nk∈i−	PERSON
ma-199	208	1	k.	PERSON
ma-199	208	2	+nk	PERSON
ma-199	210	1	t ∗1	DATE
ma-199	213	1	2(i−	CARDINAL
ma-199	213	2	t1−{[f −nk	PERSON
ma-199	216	1	−nk	ORG
ma-199	222	1	2(i−	CARDINAL
ma-199	222	2	t2−{[f −mk	PERSON
ma-199	223	1	∗	CARDINAL
ma-199	227	1	t+2	PERSON
ma-199	230	1	∗	CARDINAL
ma-199	230	2	2(i−	CARDINAL
ma-199	230	3	t−{[f −nk	ORG
ma-199	232	1	two	CARDINAL
ma-199	233	1	4.2	CARDINAL
ma-199	235	1	two	CARDINAL
ma-199	241	1	{f −nk	PERSON
ma-199	241	2	k−.	PERSON
ma-199	243	1	k∈i+	WORK_OF_ART
ma-199	245	1	a′	ORG
ma-199	248	1	2	CARDINAL
ma-199	248	2	nk∈i+	TIME
ma-199	249	1	2	CARDINAL
ma-199	251	1	j. math	PERSON
ma-199	253	1	10.28924	CARDINAL
ma-199	253	2	f + ∈ k1	PRODUCT
ma-199	254	1	2	CARDINAL
ma-199	254	2	k∈i+	WORK_OF_ART
ma-199	255	1	2	CARDINAL
ma-199	258	1	fj	NORP
ma-199	258	2	∈	ORG
ma-199	258	3	j ∈	PERSON
ma-199	259	1	′′	ORG
ma-199	261	1	∑ nk∈i+	PERSON
ma-199	262	1	2	CARDINAL
ma-199	265	1	2	CARDINAL
ma-199	265	2	j ∈	PERSON
ma-199	267	1	′′	ORG
ma-199	267	2	2 + ∑	DATE
ma-199	268	1	′′	ORG
ma-199	268	2	2	CARDINAL
ma-199	268	3	2 + ∑	DATE
ma-199	268	4	′′	ORG
ma-199	268	5	2	CARDINAL
ma-199	268	6	2	CARDINAL
ma-199	268	7	2	CARDINAL
ma-199	268	8	+‖2	DATE
ma-199	271	1	4.3	CARDINAL
ma-199	272	1	two	CARDINAL
ma-199	273	1	{g+i	PERSON
ma-199	275	1	4.2	CARDINAL
ma-199	276	1	4.4	CARDINAL
ma-199	279	1	a′	ORG
ma-199	279	2	0	CARDINAL
ma-199	279	3	a′	ORG
ma-199	279	4	b′	PRODUCT
ma-199	281	1	j. math	PERSON
ma-199	283	1	10.28924	CARDINAL
ma-199	283	2	10	CARDINAL
ma-199	285	1	∈	ORG
ma-199	285	2	fm ∈	ORG
ma-199	286	1	6=	CARDINAL
ma-199	286	2	nk = k	PERSON
ma-199	286	3	1	CARDINAL
ma-199	286	4	2	DATE
ma-199	286	5	3	DATE
ma-199	287	1	nk =	PERSON
ma-199	289	1	+ 1	DATE
ma-199	289	2	+ 1	DATE
ma-199	290	1	k−	NORP
ma-199	290	2	a′	ORG
ma-199	290	3	b′	PRODUCT
ma-199	290	4	2 ≤	CARDINAL
ma-199	290	5	∈	ORG
ma-199	290	6	′‖f	ORG
ma-199	290	7	6	CARDINAL
ma-199	290	8	n∈i− |[f	PERSON
ma-199	290	9	9	CARDINAL
ma-199	291	1	∈	ORG
ma-199	292	1	0	CARDINAL
ma-199	293	1	0	CARDINAL
ma-199	293	2	0	CARDINAL
ma-199	294	1	0	CARDINAL
ma-199	296	1	first	ORDINAL
ma-199	296	2	university grants commission(ugc	ORG
ma-199	296	3	india	GPE
ma-199	297	1	second	ORDINAL
ma-199	297	2	serb	NORP
ma-199	297	3	india	GPE
ma-199	298	1	1	CARDINAL
ma-199	298	2	t. y. azizov	PERSON
ma-199	298	3	i. s. iokhvidov	PERSON
ma-199	298	4	linear operators	ORG
ma-199	298	5	john wiley & sons	ORG
ma-199	298	6	j. bognár	PERSON
ma-199	298	7	78	DATE
ma-199	298	8	2012	DATE
ma-199	299	1	10.1007/978	CARDINAL
ma-199	299	2	p. g. casazza and	PERSON
ma-199	299	3	g. kutyniok	PERSON
ma-199	299	4	springer science & business media	ORG
ma-199	299	5	2012	DATE
ma-199	300	1	https://doi.org/10.1007/978-0-8176-8373-3.[4] i. daubechies	ORG
ma-199	300	2	a. grossmann	PERSON
ma-199	300	3	y. meyer	PERSON
ma-199	300	4	j. math	ORG
ma-199	302	1	27	CARDINAL
ma-199	302	2	1271-1283	CARDINAL
ma-199	303	1	a. m. dirac	PERSON
ma-199	304	1	r. soc	PERSON
ma-199	305	1	lond	PERSON
ma-199	306	1	ser	PERSON
ma-199	307	1	113	CARDINAL
ma-199	307	2	1927	DATE
ma-199	307	3	621-641	CARDINAL
ma-199	308	1	d. l. donoho	PERSON
ma-199	308	2	m. elad	PERSON
ma-199	308	3	1	CARDINAL
ma-199	309	1	nat	PERSON
ma-199	310	1	acad	ORG
ma-199	311	1	sci	ORG
ma-199	311	2	100	CARDINAL
ma-199	311	3	2003	DATE
ma-199	311	4	2197-2202	DATE
ma-199	312	1	r. j. duffin	PERSON
ma-199	312	2	a. c. schaeffer	PERSON
ma-199	312	3	amer	PERSON
ma-199	314	1	72	DATE
ma-199	314	2	1952	DATE
ma-199	314	3	341	CARDINAL
ma-199	315	1	j. giribet	PERSON
ma-199	315	2	a. maestripieri	PERSON
ma-199	315	3	f. m. pería	PERSON
ma-199	315	4	p. g.	PERSON
ma-199	319	1	393	CARDINAL
ma-199	319	2	2012)122	CARDINAL
ma-199	320	1	d. han	PERSON
ma-199	320	2	k. kornelson	PERSON
ma-199	320	3	d. larson	PERSON
ma-199	320	4	e. weber	PERSON
ma-199	320	5	40	DATE
ma-199	321	1	american	NORP
ma-199	324	1	2	CARDINAL
ma-199	324	2	3	CARDINAL
ma-199	324	3	4	CARDINAL