id	sid	eid	entity	type
m-1152	1	1	bounded linear operators:	ORG
m-1152	1	2	1otobong	CARDINAL
m-1152	1	3	j. tom∗	PERSON
m-1152	1	4	2otobong	QUANTITY
m-1152	2	1	1	CARDINAL
m-1152	3	1	abasi & akwa ibom	ORG
m-1152	4	1	2akwa	CARDINAL
m-1152	6	1	algebraic	PERSON
m-1152	7	1	two	CARDINAL
m-1152	8	1	tom	PERSON
m-1152	8	2	2025	DATE
m-1152	8	3	bounded linear operators	ORG
m-1152	8	4	koch	GPE
m-1152	8	5	wallace	PERSON
m-1152	11	1	two	CARDINAL
m-1152	14	1	1	CARDINAL
m-1152	15	1	algebraic semigroup	PERSON
m-1152	15	2	koch	GPE
m-1152	15	3	wallace	PERSON
m-1152	15	4	1956	DATE
m-1152	16	1	1	CARDINAL
m-1152	16	2	⊆	CARDINAL
m-1152	16	3	⊆	CARDINAL
m-1152	17	1	sab	PERSON
m-1152	18	1	ijo international journal of mathematics	ORG
m-1152	18	2	2992-4421	DATE
m-1152	18	3	08	CARDINAL
m-1152	19	1	9 | september 2025	TIME
m-1152	19	2	4	CARDINAL
m-1152	19	3	20	DATE
m-1152	19	4	21	DATE
m-1152	19	5	22	DATE
m-1152	19	6	23	DATE
m-1152	19	7	24	DATE
m-1152	19	8	25	DATE
m-1152	19	9	26	CARDINAL
m-1152	22	1	2	CARDINAL
m-1152	22	2	6	DATE
m-1152	22	3	11	DATE
m-1152	22	4	12	DATE
m-1152	22	5	13	DATE
m-1152	22	6	15	CARDINAL
m-1152	25	1	5	CARDINAL
m-1152	25	2	7	DATE
m-1152	25	3	8	DATE
m-1152	25	4	9	DATE
m-1152	25	5	10	DATE
m-1152	25	6	17	DATE
m-1152	25	7	32	CARDINAL
m-1152	26	1	algebraic	PERSON
m-1152	28	1	tom	PERSON
m-1152	29	1	3	CARDINAL
m-1152	29	2	bounded linear operators	ORG
m-1152	29	3	koch	GPE
m-1152	29	4	wallace	PERSON
m-1152	31	1	hypersemigroups	ORG
m-1152	31	2	7	CARDINAL
m-1152	31	3	9	DATE
m-1152	31	4	16	DATE
m-1152	31	5	32	CARDINAL
m-1152	34	1	2	CARDINAL
m-1152	34	2	2.1	CARDINAL
m-1152	35	1	normed linear	ORG
m-1152	37	1	0,∞	DATE
m-1152	37	2	1	CARDINAL
m-1152	38	1	0	CARDINAL
m-1152	38	2	0	CARDINAL
m-1152	39	1	2	CARDINAL
m-1152	39	2	∥x∥. 3	DATE
m-1152	39	3	2.2	CARDINAL
m-1152	41	1	0,∞	TIME
m-1152	41	2	lim m	PERSON
m-1152	41	3	n→∞	DATE
m-1152	41	4	0	CARDINAL
m-1152	41	5	lim n→∞	ORG
m-1152	42	1	0	CARDINAL
m-1152	43	1	ijo international journal of mathematics	ORG
m-1152	43	2	2992-4421	DATE
m-1152	43	3	08	CARDINAL
m-1152	44	1	9 | september 2025	TIME
m-1152	45	1	11	CARDINAL
m-1152	45	2	2.3	CARDINAL
m-1152	48	1	∈	ORG
m-1152	48	2	0	CARDINAL
m-1152	48	3	∥t (x)∥y ≤ m∥x∥x	ORG
m-1152	48	4	x.	PERSON
m-1152	48	5	0	CARDINAL
m-1152	49	1	2.4	CARDINAL
m-1152	51	1	1	CARDINAL
m-1152	51	2	2	CARDINAL
m-1152	51	3	0	CARDINAL
m-1152	51	4	3	CARDINAL
m-1152	52	1	3	CARDINAL
m-1152	53	1	2.5	CARDINAL
m-1152	53	2	koch	PERSON
m-1152	53	3	wallace	GPE
m-1152	53	4	1	CARDINAL
m-1152	54	1	∈	ORG
m-1152	54	2	⊆	CARDINAL
m-1152	54	3	⊆ sab	QUANTITY
m-1152	56	1	3	CARDINAL
m-1152	56	2	33	DATE
m-1152	57	1	arab	NORP
m-1152	58	1	3	CARDINAL
m-1152	58	2	3.1	CARDINAL
m-1152	58	3	3	CARDINAL
m-1152	59	1	bounded linear operators	ORG
m-1152	59	2	koch	GPE
m-1152	59	3	wallace	PERSON
m-1152	62	1	t ≥ 0	DATE
m-1152	63	1	t (s	ORG
m-1152	64	1	ab	ORG
m-1152	66	1	⊆	CARDINAL
m-1152	69	1	ab)s ⊆	ORG
m-1152	69	2	⊆	CARDINAL
m-1152	70	1	sab ⊆ sa	ORG
m-1152	73	1	ijo international journal of mathematics	ORG
m-1152	73	2	2992-4421	DATE
m-1152	73	3	08	CARDINAL
m-1152	74	1	9 | september 2025	TIME
m-1152	74	2	12	CARDINAL
m-1152	74	3	3.2	CARDINAL
m-1152	74	4	3	CARDINAL
m-1152	75	1	bounded linear operators	ORG
m-1152	76	1	∈	ORG
m-1152	76	2	sas	ORG
m-1152	76	3	y ∈ s	PERSON
m-1152	77	1	xay	GPE
m-1152	77	2	sas ⊆	ORG
m-1152	78	1	xa ∈ sa	ORG
m-1152	78	2	∈ sas.	ORG
m-1152	79	1	j = l.	PERSON
m-1152	84	1	4	CARDINAL
m-1152	84	2	4.1	CARDINAL
m-1152	90	1	zero	CARDINAL
m-1152	91	1	lim	PERSON
m-1152	91	2	+ ∥t	DATE
m-1152	93	1	af = lim	PERSON
m-1152	93	2	+ t	GPE
m-1152	94	1	x.	GPE
m-1152	94	2	t)f(x)− f(x	ORG
m-1152	94	3	t)− f(x	ORG
m-1152	97	1	f ∈ c0(r	ORG
m-1152	99	1	ijo international journal of mathematics	ORG
m-1152	99	2	2992-4421	DATE
m-1152	99	3	08	CARDINAL
m-1152	100	1	9 | september 2025	TIME
m-1152	100	2	13	CARDINAL
m-1152	101	1	3.1	CARDINAL
m-1152	101	2	koch	GPE
m-1152	101	3	wallace	PERSON
m-1152	102	1	0	CARDINAL
m-1152	102	2	⊆	CARDINAL
m-1152	105	1	∥t	PERSON
m-1152	105	2	1	CARDINAL
m-1152	109	1	f(x	ORG
m-1152	109	2	one	CARDINAL
m-1152	110	1	∥t	PERSON
m-1152	110	2	∥f∥∞	ORDINAL
m-1152	112	1	f(x) f(x	ORG
m-1152	114	1	1	CARDINAL
m-1152	114	2	0−1	CARDINAL
m-1152	114	3	1	CARDINAL
m-1152	114	4	f(x	ORG
m-1152	117	1	4.2	CARDINAL
m-1152	118	1	|xk|2	DATE
m-1152	118	2	n ∈ n	ORG
m-1152	118	3	x3	GPE
m-1152	119	1	0	CARDINAL
m-1152	121	1	0︸	DATE
m-1152	122	1	x3	GPE
m-1152	124	1	n ∈ n	ORG
m-1152	124	2	ijo international journal of mathematics	ORG
m-1152	124	3	2992-4421	DATE
m-1152	124	4	08	CARDINAL
m-1152	125	1	9 | september 2025	TIME
m-1152	128	1	⊆	CARDINAL
m-1152	130	1	|xk|2	DATE
m-1152	130	2	1	CARDINAL
m-1152	132	1	1	CARDINAL
m-1152	135	1	algebraic stability	PERSON
m-1152	140	1	t (1	DATE
m-1152	140	2	2	CARDINAL
m-1152	140	3	1	CARDINAL
m-1152	140	4	one	CARDINAL
m-1152	140	5	0	CARDINAL
m-1152	141	1	4.3	CARDINAL
m-1152	142	1	0	CARDINAL
m-1152	148	1	∈	ORG
m-1152	148	2	the dirac delta distribution δ	ORG
m-1152	148	3	lim	PERSON
m-1152	148	4	+ ∥t	DATE
m-1152	149	1	0	CARDINAL
m-1152	154	1	∈	ORG
m-1152	154	2	∈	ORG
m-1152	155	1	di�erentiating	PERSON
m-1152	155	2	0	CARDINAL
m-1152	156	1	ijo international journal of mathematics	ORG
m-1152	156	2	2992-4421	DATE
m-1152	156	3	08	CARDINAL
m-1152	157	1	9 | september 2025	TIME
m-1152	159	1	3.1	CARDINAL
m-1152	166	1	ω	ORG
m-1152	166	2	0	CARDINAL
m-1152	167	1	∥t (t)f∥2 ≤ e−ωt∥f∥2	ORG
m-1152	167	2	0	CARDINAL
m-1152	175	1	0.2 0.4 x	QUANTITY
m-1152	175	2	0.5	CARDINAL
m-1152	175	3	1	CARDINAL
m-1152	175	4	2	CARDINAL
m-1152	175	5	3	CARDINAL
m-1152	175	6	0.5	CARDINAL
m-1152	176	1	3	CARDINAL
m-1152	177	1	0.5	CARDINAL
m-1152	180	1	2	CARDINAL
m-1152	182	1	16	CARDINAL
m-1152	182	2	18	DATE
m-1152	182	3	19	DATE
m-1152	182	4	27	DATE
m-1152	182	5	28	DATE
m-1152	182	6	29	DATE
m-1152	182	7	30	DATE
m-1152	183	1	ijo international journal of mathematics	ORG
m-1152	183	2	2992-4421	DATE
m-1152	183	3	08	CARDINAL
m-1152	184	1	9 | september 2025	TIME
m-1152	185	1	16 4.1	CARDINAL
m-1152	185	2	3.4	CARDINAL
m-1152	186	1	utt(x	GPE
m-1152	186	2	t)−	ORG
m-1152	186	3	0	CARDINAL
m-1152	187	1	0	CARDINAL
m-1152	187	2	u(x	ORG
m-1152	187	3	t(x	PERSON
m-1152	187	4	∈	ORG
m-1152	187	5	0	CARDINAL
m-1152	187	6	1	CARDINAL
m-1152	187	7	∈	ORG
m-1152	187	8	coe	ORG
m-1152	190	1	0	CARDINAL
m-1152	190	2	0	CARDINAL
m-1152	190	3	u(t	ORG
m-1152	192	1	1	CARDINAL
m-1152	193	1	1 2	CARDINAL
m-1152	193	2	t)∥2l2 + ∥ux	PERSON
m-1152	194	1	first	ORDINAL
m-1152	195	1	1	CARDINAL
m-1152	195	2	h2(0	ORG
m-1152	196	1	0	CARDINAL
m-1152	197	1	0	CARDINAL
m-1152	197	2	0	CARDINAL
m-1152	198	1	0 i ∂xx −αi	WORK_OF_ART
m-1152	199	1	∩h1 0	GPE
m-1152	199	2	0	CARDINAL
m-1152	201	1	∂xx	PERSON
m-1152	202	1	second	ORDINAL
m-1152	202	2	7	CARDINAL
m-1152	202	3	9	DATE
m-1152	202	4	10	DATE
m-1152	202	5	32	DATE
m-1152	202	6	x.	GPE
m-1152	202	7	0	CARDINAL
m-1152	206	1	1	CARDINAL
m-1152	207	1	ijo international journal of mathematics	ORG
m-1152	207	2	2992-4421	DATE
m-1152	207	3	08	CARDINAL
m-1152	208	1	9 | september 2025	TIME
m-1152	208	2	17	CARDINAL
m-1152	209	1	ωn	CARDINAL
m-1152	209	2	u(x	ORG
m-1152	210	1	coe	ORG
m-1152	210	2	q′′n(t	ORG
m-1152	213	1	0	CARDINAL
m-1152	215	1	4ω2	CARDINAL
m-1152	218	1	2	CARDINAL
m-1152	219	1	0	CARDINAL
m-1152	220	1	1	CARDINAL
m-1152	221	1	t)|2 dx	GPE
m-1152	223	1	∈	ORG
m-1152	223	2	0	CARDINAL
m-1152	223	3	0	CARDINAL
m-1152	224	1	27	CARDINAL
m-1152	224	2	28	DATE
m-1152	224	3	29	DATE
m-1152	224	4	30	DATE
m-1152	224	5	31	DATE
m-1152	224	6	1	CARDINAL
m-1152	224	7	0	CARDINAL
m-1152	224	8	∥t	PERSON
m-1152	224	9	0	CARDINAL
m-1152	227	1	0	CARDINAL
m-1152	227	2	1	CARDINAL
m-1152	228	1	s(a	PERSON
m-1152	229	1	0	CARDINAL
m-1152	231	1	0	CARDINAL
m-1152	231	2	ijo international journal of mathematics	ORG
m-1152	231	3	2992-4421	DATE
m-1152	231	4	08	CARDINAL
m-1152	232	1	9 | september 2025	TIME
m-1152	232	2	18	CARDINAL
m-1152	234	1	0	CARDINAL
m-1152	235	1	6	CARDINAL
m-1152	235	2	7	DATE
m-1152	235	3	11	DATE
m-1152	235	4	19	CARDINAL
m-1152	238	1	0	CARDINAL
m-1152	239	1	s(a	PERSON
m-1152	243	1	3.4	CARDINAL
m-1152	244	1	0	CARDINAL
m-1152	244	2	0	CARDINAL
m-1152	244	3	∈	ORG
m-1152	244	4	one	CARDINAL
m-1152	245	1	0	CARDINAL
m-1152	249	1	6	CARDINAL
m-1152	249	2	11	DATE
m-1152	249	3	12	DATE
m-1152	249	4	13	DATE
m-1152	249	5	24	CARDINAL
m-1152	250	1	pde	ORG
m-1152	250	2	8	CARDINAL
m-1152	250	3	14	DATE
m-1152	250	4	18	DATE
m-1152	250	5	19	CARDINAL
m-1152	251	1	5	CARDINAL
m-1152	251	2	5.1	CARDINAL
m-1152	252	1	a. kw	PERSON
m-1152	252	2	s(a	PERSON
m-1152	252	3	σ(t	ORG
m-1152	253	1	0	CARDINAL
m-1152	255	1	s(a	PERSON
m-1152	255	2	r(t	EVENT
m-1152	256	1	ets(a	PERSON
m-1152	256	2	1	CARDINAL
m-1152	256	3	0	CARDINAL
m-1152	257	1	s(a	PERSON
m-1152	257	2	0	CARDINAL
m-1152	257	3	4.1	CARDINAL
m-1152	257	4	4.2	CARDINAL
m-1152	258	1	s(a	PERSON
m-1152	260	1	5.1	CARDINAL
m-1152	260	2	s(a	PERSON
m-1152	260	3	s(a	PERSON
m-1152	261	1	s(a	PERSON
m-1152	262	1	s(a	PERSON
m-1152	262	2	0	CARDINAL
m-1152	263	1	ijo international journal of mathematics	ORG
m-1152	263	2	2992-4421	DATE
m-1152	263	3	08	CARDINAL
m-1152	264	1	9 | september 2025	TIME
m-1152	264	2	19	CARDINAL
m-1152	264	3	koch	GPE
m-1152	264	4	wallace	PERSON
m-1152	264	5	4	CARDINAL
m-1152	264	6	koch	PERSON
m-1152	264	7	wallace	PERSON
m-1152	265	1	6	CARDINAL
m-1152	265	2	bounded linear operators	ORG
m-1152	266	1	koch	GPE
m-1152	266	2	wallace	PERSON
m-1152	269	1	clari	NORP
m-1152	272	1	1	CARDINAL
m-1152	272	2	koch	PERSON
m-1152	272	3	a.d. wallace	PERSON
m-1152	273	1	j.	PERSON
m-1152	273	2	23	CARDINAL
m-1152	273	3	193	CARDINAL
m-1152	273	4	202, 1956	DATE
m-1152	274	1	2	CARDINAL
m-1152	274	2	e. hille	PERSON
m-1152	274	3	r. s. phillips	PERSON
m-1152	274	4	american mathematical society	ORG
m-1152	274	5	1957	DATE
m-1152	275	1	3	CARDINAL
m-1152	275	2	o. j. tom	PERSON
m-1152	275	3	o. g. udouaka	PERSON
m-1152	275	4	e. s. udo	PERSON
m-1152	275	5	bounded linear operators	ORG
m-1152	275	6	2489	CARDINAL
m-1152	275	7	2695-1908	DATE
m-1152	275	8	11	CARDINAL
m-1152	275	9	9	CARDINAL
m-1152	275	10	14 2025	CARDINAL
m-1152	276	1	4	CARDINAL
m-1152	276	2	j. east	ORG
m-1152	276	3	p. higgins	PERSON
m-1152	276	4	101:1	CARDINAL
m-1152	276	5	25, 2020	DATE
m-1152	277	1	ijo international journal of mathematics	ORG
m-1152	277	2	2992-4421	DATE
m-1152	277	3	08	CARDINAL
m-1152	278	1	9 | september 2025	TIME
m-1152	279	1	20	CARDINAL
m-1152	280	1	5	CARDINAL
m-1152	280	2	s. piazzera	PERSON
m-1152	280	3	10	DATE
m-1152	280	4	k peters	ORG
m-1152	280	5	2005	DATE
m-1152	281	1	6	CARDINAL
m-1152	281	2	j. glück	PERSON
m-1152	281	3	a. mironchenko	PERSON
m-1152	281	4	j. evol	PERSON
m-1152	282	1	25	CARDINAL
m-1152	282	2	12	CARDINAL
m-1152	282	3	1424	CARDINAL
m-1152	282	4	2024	DATE
m-1152	284	1	j. mui	PERSON
m-1152	284	2	106	CARDINAL
m-1152	284	3	2	CARDINAL
m-1152	284	4	460	CARDINAL
m-1152	284	5	480	CARDINAL
m-1152	284	6	2023	CARDINAL
m-1152	285	1	8	CARDINAL
m-1152	285	2	r. c. penney	ORG
m-1152	285	3	j. funct	PERSON
m-1152	286	1	21	DATE
m-1152	287	1	305	CARDINAL
m-1152	287	2	315	CARDINAL
m-1152	287	3	1976	DATE
m-1152	288	1	9	CARDINAL
m-1152	288	2	h. h. schaefer	PERSON
m-1152	288	3	halbgeordnete	PERSON
m-1152	289	1	ann.	PERSON
m-1152	289	2	141	DATE
m-1152	289	3	113	CARDINAL
m-1152	289	4	142, 1960	DATE
m-1152	290	1	10	CARDINAL
m-1152	290	2	h. h. schaefer	PERSON
m-1152	290	3	invariant ideals	ORG
m-1152	290	4	c(x	ORG
m-1152	291	1	j. math	PERSON
m-1152	291	2	11	DATE
m-1152	292	1	703	CARDINAL
m-1152	292	2	1967	DATE
m-1152	293	1	11	CARDINAL
m-1152	293	2	h. vogt	PERSON
m-1152	297	1	150 no.	CARDINAL
m-1152	297	2	8	CARDINAL
m-1152	298	1	3513	CARDINAL
m-1152	298	2	3515	DATE
m-1152	298	3	2022	CARDINAL
m-1152	299	1	12	CARDINAL
m-1152	299	2	l. weis	PERSON
m-1152	303	1	123	CARDINAL
m-1152	303	2	10	CARDINAL
m-1152	304	1	3089	CARDINAL
m-1152	304	2	3094, 1995	DATE
m-1152	305	1	13	CARDINAL
m-1152	305	2	l. weis	PERSON
m-1152	310	1	126	CARDINAL
m-1152	310	2	11	CARDINAL
m-1152	311	1	3253	CARDINAL
m-1152	311	2	3256, 1998	DATE
m-1152	312	1	14	CARDINAL
m-1152	312	2	a. w. wickstead	PERSON
m-1152	313	1	ann.	PERSON
m-1152	313	2	212	CARDINAL
m-1152	314	1	271	CARDINAL
m-1152	314	2	284	CARDINAL
m-1152	314	3	1975	DATE
m-1152	315	1	15	CARDINAL
m-1152	315	2	s. v. smickih	PERSON
m-1152	315	3	m. g. kre	PERSON
m-1152	315	4	m. a. rutman	PERSON
m-1152	317	1	13	CARDINAL
m-1152	317	2	3	CARDINAL
m-1152	318	1	81	CARDINAL
m-1152	318	2	82, 1979	DATE
m-1152	319	1	16	CARDINAL
m-1152	319	2	b. simon	PERSON
m-1152	319	3	one	CARDINAL
m-1152	319	4	two	CARDINAL
m-1152	319	5	ann. phys.	ORG
m-1152	319	6	97	DATE
m-1152	319	7	279	CARDINAL
m-1152	319	8	288, 1976	DATE
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