id	sid	eid	entity	type
ap-10553	1	1	acta polytechnica	PERSON
ap-10553	1	2	65(5):539–545	CARDINAL
ap-10553	1	3	2025	DATE
ap-10553	1	4	2025	CARDINAL
ap-10553	2	1	4.0	CARDINAL
ap-10553	2	2	the czech technical university	ORG
ap-10553	2	3	pavel exnera	PERSON
ap-10553	2	4	czech	NORP
ap-10553	2	5	prague	GPE
ap-10553	2	6	7	CARDINAL
ap-10553	2	7	115 19	CARDINAL
ap-10553	2	8	prague	GPE
ap-10553	2	9	czech	NORP
ap-10553	2	10	czech academy of sciences	ORG
ap-10553	2	11	250	CARDINAL
ap-10553	2	12	68	MONEY
ap-10553	2	13	czech	NORP
ap-10553	5	1	quantum	ORG
ap-10553	6	1	1	CARDINAL
ap-10553	6	2	no less than six decades	DATE
ap-10553	6	3	last year	DATE
ap-10553	7	1	algebras	ORG
ap-10553	8	1	jiří	PERSON
ap-10553	12	1	quantum	ORG
ap-10553	12	2	1	CARDINAL
ap-10553	12	3	only half a century later	DATE
ap-10553	13	1	2–4	CARDINAL
ap-10553	14	1	one	CARDINAL
ap-10553	14	2	one	CARDINAL
ap-10553	16	1	simon	PERSON
ap-10553	16	2	5	CARDINAL
ap-10553	16	3	sec	ORG
ap-10553	17	1	x.1	ORG
ap-10553	18	1	kirchhoff conditions	ORG
ap-10553	19	1	2	CARDINAL
ap-10553	20	1	fourth	ORDINAL
ap-10553	21	1	n ≥ 3	DATE
ap-10553	22	1	2	CARDINAL
ap-10553	22	2	6	CARDINAL
ap-10553	23	1	2.	CARDINAL
ap-10553	24	1	j ⊕ l2(r+	PERSON
ap-10553	26	1	− x4ψj(x	PERSON
ap-10553	26	2	1	CARDINAL
ap-10553	26	3	j ⊕ c∞	PERSON
ap-10553	26	4	kirchhoff	ORG
ap-10553	26	5	1	CARDINAL
ap-10553	28	1	2a	CARDINAL
ap-10553	30	1	0	CARDINAL
ap-10553	30	2	2b	CARDINAL
ap-10553	30	3	ψ′ j(0	LOC
ap-10553	30	4	539	CARDINAL
ap-10553	30	5	https://www.cvut.cz/en	DATE
ap-10553	30	6	acta polytechnica	PERSON
ap-10553	31	1	1	CARDINAL
ap-10553	31	2	∈	ORG
ap-10553	31	3	∈	ORG
ap-10553	31	4	j − x4ψj	PERSON
ap-10553	32	1	h∗	ORG
ap-10553	32	2	h∗ϕ	ORG
ap-10553	32	3	3a	CARDINAL
ap-10553	32	4	∈	ORG
ap-10553	34	1	3b	CARDINAL
ap-10553	35	1	3c	CARDINAL
ap-10553	36	1	2	CARDINAL
ap-10553	36	2	0	CARDINAL
ap-10553	37	1	2.1	CARDINAL
ap-10553	38	1	1	CARDINAL
ap-10553	41	1	two	CARDINAL
ap-10553	42	1	δj1σ − 1 2	PRODUCT
ap-10553	42	2	0	CARDINAL
ap-10553	42	3	supp f ⊂	ORG
ap-10553	43	1	1	CARDINAL
ap-10553	43	2	2	CARDINAL
ap-10553	44	1	σ	ORG
ap-10553	46	1	j ⊕ hd j	PERSON
ap-10553	46	2	1	CARDINAL
ap-10553	49	1	zero	CARDINAL
ap-10553	49	2	1	CARDINAL
ap-10553	49	3	1	CARDINAL
ap-10553	50	1	7	CARDINAL
ap-10553	50	2	sec	ORG
ap-10553	51	1	5	CARDINAL
ap-10553	51	2	sec	ORG
ap-10553	52	1	x.1	ORG
ap-10553	56	1	7→	CARDINAL
ap-10553	56	2	1 2	CARDINAL
ap-10553	56	3	7→	CARDINAL
ap-10553	56	4	3 2	CARDINAL
ap-10553	57	1	5 2	CARDINAL
ap-10553	58	1	j = 1	WORK_OF_ART
ap-10553	61	1	7	CARDINAL
ap-10553	61	2	sec	ORG
ap-10553	62	1	xiii.7.16	PERSON
ap-10553	62	2	σess(hd	GPE
ap-10553	64	1	one	CARDINAL
ap-10553	64	2	sturm-liouville	ORG
ap-10553	66	1	8	CARDINAL
ap-10553	68	1	8.19	CARDINAL
ap-10553	70	1	2	CARDINAL
ap-10553	71	1	krein	PERSON
ap-10553	71	2	9	CARDINAL
ap-10553	71	3	σess(ĥ	PERSON
ap-10553	74	1	j = 1	WORK_OF_ART
ap-10553	74	2	zeros	CARDINAL
ap-10553	74	3	second	ORDINAL
ap-10553	74	4	krein	GPE
ap-10553	74	5	σdisc(ĥ	ORG
ap-10553	76	1	⊕	GPE
ap-10553	76	2	⊕ k−	GPE
ap-10553	76	3	4	CARDINAL
ap-10553	76	4	540	CARDINAL
ap-10553	77	1	65	CARDINAL
ap-10553	78	1	5/2025	CARDINAL
ap-10553	78	2	k±	ORG
ap-10553	78	3	∓	PERSON
ap-10553	80	1	j. von neumann	PERSON
ap-10553	80	2	k−	NORP
ap-10553	81	1	5	CARDINAL
ap-10553	81	2	sec	ORG
ap-10553	81	3	x.1	ORG
ap-10553	82	1	10	CARDINAL
ap-10553	83	1	two	CARDINAL
ap-10553	83	2	second	ORDINAL
ap-10553	83	3	3b	CARDINAL
ap-10553	85	1	x4 ±	CARDINAL
ap-10553	85	2	0	CARDINAL
ap-10553	86	1	3 x	QUANTITY
ap-10553	86	2	5a	CARDINAL
ap-10553	87	1	5b	CARDINAL
ap-10553	88	1	11	CARDINAL
ap-10553	89	1	5a	CARDINAL
ap-10553	90	1	5	CARDINAL
ap-10553	91	1	2.2	CARDINAL
ap-10553	92	1	∈	ORG
ap-10553	92	2	lim	PERSON
ap-10553	93	1	x→∞ ψ′ j(x	DATE
ap-10553	94	1	1	CARDINAL
ap-10553	95	1	n. proof	PERSON
ap-10553	96	1	4	CARDINAL
ap-10553	97	1	∈	ORG
ap-10553	98	1	0	CARDINAL
ap-10553	100	1	0	CARDINAL
ap-10553	100	2	6	CARDINAL
ap-10553	100	3	second	ORDINAL
ap-10553	101	1	second	ORDINAL
ap-10553	101	2	h∗	ORG
ap-10553	101	3	0	CARDINAL
ap-10553	101	4	x̃	ORG
ap-10553	103	1	0	CARDINAL
ap-10553	104	1	0	CARDINAL
ap-10553	104	2	2	CARDINAL
ap-10553	104	3	lim	PERSON
ap-10553	106	1	0	CARDINAL
ap-10553	106	2	7a	CARDINAL
ap-10553	106	3	1	CARDINAL
ap-10553	108	1	∈	ORG
ap-10553	110	1	0	CARDINAL
ap-10553	111	1	7b	CARDINAL
ap-10553	111	2	7a	CARDINAL
ap-10553	111	3	one	CARDINAL
ap-10553	111	4	5	CARDINAL
ap-10553	112	1	φ−	GPE
ap-10553	115	1	3	CARDINAL
ap-10553	115	2	0	CARDINAL
ap-10553	115	3	7b	CARDINAL
ap-10553	118	1	3	CARDINAL
ap-10553	118	2	0	CARDINAL
ap-10553	119	1	two	CARDINAL
ap-10553	119	2	zero	CARDINAL
ap-10553	120	1	5	CARDINAL
ap-10553	120	2	∈	ORG
ap-10553	121	1	3 x +	QUANTITY
ap-10553	122	1	1 2i	CARDINAL
ap-10553	123	1	±	CARDINAL
ap-10553	124	1	9	CARDINAL
ap-10553	124	2	ain	PERSON
ap-10553	124	3	0	CARDINAL
ap-10553	124	4	∈	ORG
ap-10553	128	1	9	CARDINAL
ap-10553	128	2	2.2	CARDINAL
ap-10553	128	3	2i	CARDINAL
ap-10553	131	1	10a	CARDINAL
ap-10553	131	2	ain	PERSON
ap-10553	131	3	2i	CARDINAL
ap-10553	131	4	ain(ϕ	NORP
ap-10553	131	5	ain(ψ	ORG
ap-10553	134	1	10b	CARDINAL
ap-10553	134	2	2.3	CARDINAL
ap-10553	135	1	2×2	CARDINAL
ap-10553	136	1	∈	ORG
ap-10553	136	2	ain(ψ	ORG
ap-10553	137	1	11	CARDINAL
ap-10553	137	2	2.4	CARDINAL
ap-10553	138	1	11	CARDINAL
ap-10553	139	1	11	CARDINAL
ap-10553	140	1	541	CARDINAL
ap-10553	140	2	3	CARDINAL
ap-10553	141	1	11	CARDINAL
ap-10553	143	1	0	CARDINAL
ap-10553	143	2	12	CARDINAL
ap-10553	144	1	jth	PRODUCT
ap-10553	145	1	jth	PRODUCT
ap-10553	145	2	ain j	PERSON
ap-10553	146	1	∈	ORG
ap-10553	146	2	eiθ1	ORG
ap-10553	147	1	13	CARDINAL
ap-10553	147	2	∈	ORG
ap-10553	148	1	k ⊂	ORG
ap-10553	148	2	1	CARDINAL
ap-10553	150	1	#k < n	QUANTITY
ap-10553	150	2	ain(ψ	ORG
ap-10553	150	3	k ∈ k	PERSON
ap-10553	150	4	ũ	GPE
ap-10553	150	5	13	CARDINAL
ap-10553	151	1	dirichlet	PERSON
ap-10553	151	2	neumann	ORG
ap-10553	151	3	robin	PERSON
ap-10553	151	4	0	CARDINAL
ap-10553	152	1	zero	CARDINAL
ap-10553	154	1	7→	CARDINAL
ap-10553	154	2	hu	PERSON
ap-10553	154	3	u = ut.	PERSON
ap-10553	155	1	14	CARDINAL
ap-10553	155	2	9	CARDINAL
ap-10553	155	3	∈	ORG
ap-10553	155	4	15	CARDINAL
ap-10553	156	1	j = 1	PERSON
ap-10553	158	1	16	CARDINAL
ap-10553	159	1	3.1	CARDINAL
ap-10553	160	1	jth	PRODUCT
ap-10553	161	1	jth	PRODUCT
ap-10553	161	2	hu	PERSON
ap-10553	163	1	x3 3 +	DATE
ap-10553	163	2	∈	ORG
ap-10553	166	1	two	CARDINAL
ap-10553	166	2	17a	CARDINAL
ap-10553	167	1	1	CARDINAL
ap-10553	167	2	1	CARDINAL
ap-10553	167	3	17b	CARDINAL
ap-10553	167	4	n − 1	PRODUCT
ap-10553	168	1	12	CARDINAL
ap-10553	169	1	−1	DATE
ap-10553	169	2	2 n	CARDINAL
ap-10553	169	3	18	CARDINAL
ap-10553	169	4	2	CARDINAL
ap-10553	170	1	13	CARDINAL
ap-10553	171	1	c0 c1	PERSON
ap-10553	172	1	cn−2 cn−1 cn−1 c0 c1 cn−2	PERSON
ap-10553	176	1	c1 c1 c2	PERSON
ap-10553	176	2	cn−1 c0 	PERSON
ap-10553	176	3	19	CARDINAL
ap-10553	176	4	two	CARDINAL
ap-10553	176	5	17	CARDINAL
ap-10553	176	6	1	CARDINAL
ap-10553	178	1	n−1	ORG
ap-10553	178	2	17b	CARDINAL
ap-10553	179	1	20	CARDINAL
ap-10553	179	2	0	CARDINAL
ap-10553	179	3	1	CARDINAL
ap-10553	181	1	n − 1	ORG
ap-10553	184	1	21	CARDINAL
ap-10553	185	1	cn−1	ORG
ap-10553	186	1	1	CARDINAL
ap-10553	191	1	1 1 1 1	QUANTITY
ap-10553	192	1	1 1 ω	CARDINAL
ap-10553	193	1	1	CARDINAL
ap-10553	195	1	1 ωn−1 ω2(n−1	MONEY
ap-10553	196	1	542	CARDINAL
ap-10553	197	1	65	CARDINAL
ap-10553	198	1	5/2025	CARDINAL
ap-10553	200	1	λn−1	PERSON
ap-10553	201	1	22	CARDINAL
ap-10553	202	1	23	CARDINAL
ap-10553	204	1	r2	GPE
ap-10553	206	1	hu	PERSON
ap-10553	207	1	15	CARDINAL
ap-10553	208	1	2	CARDINAL
ap-10553	209	1	first	ORDINAL
ap-10553	210	1	14	CARDINAL
ap-10553	210	2	15	CARDINAL
ap-10553	211	1	16	CARDINAL
ap-10553	212	1	4.	CARDINAL
ap-10553	213	1	2.1	CARDINAL
ap-10553	213	2	hu	PERSON
ap-10553	214	1	rn2	ORG
ap-10553	215	1	coth a+i coth a−i	PERSON
ap-10553	215	2	rn2	ORG
ap-10553	215	3	1 2n(n	CARDINAL
ap-10553	215	4	1	CARDINAL
ap-10553	216	1	4.1	CARDINAL
ap-10553	218	1	hu	PERSON
ap-10553	218	2	zero	CARDINAL
ap-10553	219	1	hu	PERSON
ap-10553	219	2	n − 1	ORG
ap-10553	221	1	invariant operatorhu	ORG
ap-10553	222	1	3.1	CARDINAL
ap-10553	226	1	first	ORDINAL
ap-10553	227	1	1 2n(n −1	QUANTITY
ap-10553	227	2	n2	PRODUCT
ap-10553	227	3	zero	CARDINAL
ap-10553	227	4	zero	CARDINAL
ap-10553	228	1	second	ORDINAL
ap-10553	228	2	13	CARDINAL
ap-10553	228	3	n(n	NORP
ap-10553	228	4	1	CARDINAL
ap-10553	228	5	zero	CARDINAL
ap-10553	229	1	eiθ1	ORG
ap-10553	231	1	24	CARDINAL
ap-10553	231	2	11	CARDINAL
ap-10553	231	3	ain j	PERSON
ap-10553	232	1	j	PERSON
ap-10553	232	2	j = 1	PERSON
ap-10553	233	1	n.	PERSON
ap-10553	233	2	25	CARDINAL
ap-10553	234	1	2	CARDINAL
ap-10553	235	1	neumann	ORG
ap-10553	235	2	n − 1	ORG
ap-10553	237	1	one	CARDINAL
ap-10553	237	2	neumann	ORG
ap-10553	237	3	1	CARDINAL
ap-10553	238	1	two	CARDINAL
ap-10553	238	2	one	CARDINAL
ap-10553	239	1	neumann	ORG
ap-10553	240	1	4.2	CARDINAL
ap-10553	241	1	543	CARDINAL
ap-10553	241	2	acta polytechnica	PERSON
ap-10553	241	3	zero	CARDINAL
ap-10553	242	1	2	CARDINAL
ap-10553	242	2	18	CARDINAL
ap-10553	243	1	zero	CARDINAL
ap-10553	243	2	neumann	ORG
ap-10553	243	3	zero	CARDINAL
ap-10553	243	4	aout(v	PERSON
ap-10553	243	5	1	CARDINAL
ap-10553	243	6	zero	CARDINAL
ap-10553	243	7	j = 2	WORK_OF_ART
ap-10553	246	1	n − 1	ORG
ap-10553	247	1	n − 1	PRODUCT
ap-10553	247	2	neumann	ORG
ap-10553	248	1	2	CARDINAL
ap-10553	248	2	2.1	CARDINAL
ap-10553	248	3	dirichlet	PERSON
ap-10553	250	1	2	CARDINAL
ap-10553	250	2	6	CARDINAL
ap-10553	252	1	hu	PERSON
ap-10553	253	1	0	CARDINAL
ap-10553	253	2	1	CARDINAL
ap-10553	253	3	±	CARDINAL
ap-10553	253	4	2	CARDINAL
ap-10553	253	5	two	CARDINAL
ap-10553	254	1	2	CARDINAL
ap-10553	254	2	4.1	CARDINAL
ap-10553	255	1	5	CARDINAL
ap-10553	255	2	one	CARDINAL
ap-10553	260	1	2	CARDINAL
ap-10553	263	1	16	CARDINAL
ap-10553	265	1	the european union’s	ORG
ap-10553	265	2	horizon 2020	ORG
ap-10553	265	3	marie skłodowska-curie	PERSON
ap-10553	265	4	no. 873071	DATE
ap-10553	267	1	1	CARDINAL
ap-10553	267	2	l. pauling	PERSON
ap-10553	269	1	677	CARDINAL
ap-10553	269	2	1936	DATE
ap-10553	271	1	2	CARDINAL
ap-10553	271	2	g. berkolaiko	PERSON
ap-10553	271	3	p. kuchment	PERSON
ap-10553	273	1	american mathematical society	ORG
ap-10553	273	2	rhode island	GPE
ap-10553	273	3	usa	GPE
ap-10553	273	4	2013	DATE
ap-10553	274	1	978	CARDINAL
ap-10553	275	1	3	CARDINAL
ap-10553	275	2	a. kostenko	PERSON
ap-10553	275	3	n. nicolussi	PERSON
ap-10553	276	1	laplacians	NORP
ap-10553	277	1	european mathematical society press	ORG
ap-10553	277	2	berlin	GPE
ap-10553	277	3	germany	GPE
ap-10553	277	4	2023	CARDINAL
ap-10553	278	1	4	CARDINAL
ap-10553	278	2	p. kurasov	PERSON
ap-10553	280	1	birkhäuser,	PERSON
ap-10553	280	2	berlin	GPE
ap-10553	280	3	germany	GPE
ap-10553	280	4	2024	DATE
ap-10553	281	1	978	CARDINAL
ap-10553	282	1	5	CARDINAL
ap-10553	282	2	m. reed	PERSON
ap-10553	282	3	b. simon	PERSON
ap-10553	287	1	new york	GPE
ap-10553	287	2	usa	GPE
ap-10553	287	3	1975	DATE
ap-10553	288	1	978-0125850025	CARDINAL
ap-10553	289	1	6	CARDINAL
ap-10553	289	2	t. ichinose	PERSON
ap-10553	289	3	j. klauder	PERSON
ap-10553	292	1	7	CARDINAL
ap-10553	292	2	n. dunford	PERSON
ap-10553	292	3	j. t. schwartz	PERSON
ap-10553	293	1	linear operators	ORG
ap-10553	295	1	interscience	ORG
ap-10553	295	2	new york	GPE
ap-10553	295	3	usa	GPE
ap-10553	295	4	1963	DATE
ap-10553	296	1	13	CARDINAL
ap-10553	297	1	8	CARDINAL
ap-10553	297	2	j. weidmann	PERSON
ap-10553	298	1	linear operators	ORG
ap-10553	298	2	hilbert spaces	ORG
ap-10553	299	1	new york	GPE
ap-10553	299	2	usa	GPE
ap-10553	299	3	1980	DATE
ap-10553	300	1	978-1461260295	CARDINAL
ap-10553	301	1	9	CARDINAL
ap-10553	301	2	s. albeverio	PERSON
ap-10553	301	3	k. pankrashkin	PERSON
ap-10553	302	1	krein	PERSON
ap-10553	303	1	38(22):4859, 2005	DATE
ap-10553	304	1	10	CARDINAL
ap-10553	304	2	j. behrndt	PERSON
ap-10553	304	3	s. hassi	PERSON
ap-10553	304	4	h. de snoo	PERSON
ap-10553	306	1	birkhäuser, cham	ORG
ap-10553	306	2	germany	GPE
ap-10553	306	3	2020	DATE
ap-10553	307	1	978	CARDINAL
ap-10553	308	1	11	CARDINAL
ap-10553	308	2	f. w. j. olver	PERSON
ap-10553	310	1	crc press	ORG
ap-10553	310	2	new york	GPE
ap-10553	310	3	usa	GPE
ap-10553	310	4	1st	ORDINAL
ap-10553	310	5	1997	DATE
ap-10553	311	1	544	CARDINAL
ap-10553	312	1	65	CARDINAL
ap-10553	313	1	5/2025	CARDINAL
ap-10553	313	2	12	CARDINAL
ap-10553	313	3	t. cheon	ORG
ap-10553	314	1	quantum graph vertices with	ORG
ap-10553	315	1	375(43):3775–3780, 2011	DATE
ap-10553	316	1	13	CARDINAL
ap-10553	316	2	j. davis	PERSON
ap-10553	318	1	wiley	ORG
ap-10553	318	2	new york	GPE
ap-10553	318	3	1979	DATE
ap-10553	319	1	14	CARDINAL
ap-10553	319	2	p. kurasov	PERSON
ap-10553	319	3	m. usman	PERSON
ap-10553	320	1	rt -symmetric laplace operators on star	ORG
ap-10553	321	1	2015(1):649795	CARDINAL
ap-10553	321	2	2015	DATE
ap-10553	323	1	15	CARDINAL
ap-10553	323	2	c. m. bender	PERSON
ap-10553	323	3	s. boettcher	PERSON
ap-10553	325	1	80:5243–5246, 1998	DATE
ap-10553	327	1	16	CARDINAL
ap-10553	327	2	m. tater	PERSON
ap-10553	328	1	quantum	ORG
ap-10553	329	1	416:127669	CARDINAL
ap-10553	329	2	2021	DATE
ap-10553	330	1	545	CARDINAL
ap-10553	330	2	65(5):539–545	CARDINAL
ap-10553	330	3	2025 1	DATE
ap-10553	330	4	2	CARDINAL
ap-10553	330	5	3	CARDINAL
ap-10553	330	6	4	CARDINAL
ap-10553	330	7	5	CARDINAL