Geodesic
Spectral Asymptotics for the Sturm--Liouville Operator with Point Interaction
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 4, pp. 14-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the Sturm–Liouville operator with point interaction, weak asymptotics of the discrete spectrum are found. A class of operators for which zero is the unique spectrum accumulation point is specified.
Keywords: point interaction, spectrum, asymptotics, alternating sequences. 
@article{FAA_2010_44_4_a1,
     author = {R. S. Ismagilov and A. G. Kostyuchenko},
     title = {Spectral {Asymptotics} for the {Sturm--Liouville} {Operator} with {Point} {Interaction}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {14--20},
     publisher = {mathdoc},
     volume = {44},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_4_a1/}
}
TY  - JOUR
AU  - R. S. Ismagilov
AU  - A. G. Kostyuchenko
TI  - Spectral Asymptotics for the Sturm--Liouville Operator with Point Interaction
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2010
SP  - 14
EP  - 20
VL  - 44
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2010_44_4_a1/
LA  - ru
ID  - FAA_2010_44_4_a1
ER  - 
%0 Journal Article
%A R. S. Ismagilov
%A A. G. Kostyuchenko
%T Spectral Asymptotics for the Sturm--Liouville Operator with Point Interaction
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2010
%P 14-20
%V 44
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2010_44_4_a1/
%G ru
%F FAA_2010_44_4_a1
R. S. Ismagilov; A. G. Kostyuchenko. Spectral Asymptotics for the Sturm--Liouville Operator with Point Interaction. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 4, pp. 14-20. http://geodesic.mathdoc.fr/item/FAA_2010_44_4_a1/

[1] S. Albeverio, F. Gestztesy, R. Hoegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics, Texts and Monographs in Physics, Springer-Verlag, New York, 1988 | MR | Zbl

[2] J. F. Brasche, “Perturbation of Schrödinger Hamiltonians by measures—selfadjointness and lower semiboundedness”, J. Math. Phys., 26:4 (1985), 621–626 | DOI | MR | Zbl

[3] A. N. Kochubei, “Odnomernye tochechnye vzaimodeistviya”, Ukr. matem. zh., 41:10 (1989), 1391–1395 | MR

[4] V. A. Mikhailets, “Kriterii diskretnosti spektra odnomernogo operatora Shrëdingera s $\delta$-vzaimodeistviyami”, Funkts. analiz i ego pril., 28:4 (1994), 85–87 | MR | Zbl

[5] A. Kostenko, M. Malamud, “1-D Schrodinger operators with local point interactions on a discrete set”, J. Differential Equations, 249:2 (2010), 253–304 | DOI | MR | Zbl

[6] A. M. Savchuk, A. A. Shkalikov, “Operatory Shturma–Liuvillya s potentsialami-raspredeleniyami”, Trudy MMO, 64, 2003, 159–212 | MR | Zbl

[7] R. S. Ismagilov, “Usloviya poluogranichennosti i diskretnosti spektra dlya odnomernykh differentsialnykh operatorov”, Dokl. AN SSSR, 140:1 (1961), 33–36 | MR | Zbl

[8] R. S. Ismagilov, “O spektre uravneniya Shturma–Liuvillya s koleblyuschimsya potentsialom”, Matem. zametki, 37:6 (1985), 869–879 | MR | Zbl

[9] R. S. Ismagilov, “O nepreryvnom spektre obyknovennykh differentsialnykh operatorov vtorogo poryadka”, Matem. zametki, 34:4 (1983), 535–547 | MR | Zbl

[10] R. S. Ismagilov, “O samosopryazhennosti operatora Shturma–Liuvillya”, UMN, 18:5 (1963), 161–166 | MR | Zbl