Geodesic
Regularized trace of a two-dimensional harmonic oscillator
Sbornik. Mathematics, Tome 192 (2001) no. 5, pp. 725-761 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The spectrum of a perturbation with compact support of a two-dimensional harmonic oscillator is investigated and the classical formula for the first regularized trace is obtained. 
@article{SM_2001_192_5_a4,
     author = {Z. Yu. Fazullin and Kh. Kh. Murtazin},
     title = {Regularized trace of a~two-dimensional harmonic oscillator},
     journal = {Sbornik. Mathematics},
     pages = {725--761},
     year = {2001},
     volume = {192},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_5_a4/}
}
TY  - JOUR
AU  - Z. Yu. Fazullin
AU  - Kh. Kh. Murtazin
TI  - Regularized trace of a two-dimensional harmonic oscillator
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 725
EP  - 761
VL  - 192
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_5_a4/
LA  - en
ID  - SM_2001_192_5_a4
ER  - 
%0 Journal Article
%A Z. Yu. Fazullin
%A Kh. Kh. Murtazin
%T Regularized trace of a two-dimensional harmonic oscillator
%J Sbornik. Mathematics
%D 2001
%P 725-761
%V 192
%N 5
%U http://geodesic.mathdoc.fr/item/SM_2001_192_5_a4/
%G en
%F SM_2001_192_5_a4
Z. Yu. Fazullin; Kh. Kh. Murtazin. Regularized trace of a two-dimensional harmonic oscillator. Sbornik. Mathematics, Tome 192 (2001) no. 5, pp. 725-761. http://geodesic.mathdoc.fr/item/SM_2001_192_5_a4/

[1] Gelfand I. M., Levitan B. M., “Ob odnom prostom tozhdestve dlya sobstvennykh znachenii differentsialnogo operatora vtorogo poryadka”, Dokl. AN SSSR, 88 (1953), 593–596 | MR | Zbl

[2] Lidskii V. B., Sadovnichii V. A., “Regulyarizovannye summy kornei odnogo klassa tselykh funktsii”, Funkts. analiz i ego prilozh., 1:2 (1967), 52–59 | MR | Zbl

[3] Sadovnichii V. A., Dubrovskii V. V., “Klassicheskaya formula regulyarizovannogo sleda dlya sobstvennykh chisel operatora Laplasa–Beltrami s potentsialom na sfere”, Dokl. AN SSSR, 319:1 (1991), 61–62 | MR

[4] Podolskii V. E., “On summability of regularized sums of eigenvalues of the Laplace–Beltrami operator with potential on symmetric spaces of rank one”, Russian J. Math. Phys., 3:4 (1996), 1–8 | MR

[5] Lyubishkin V. A., “Regulyarizovannyi sled dvumernogo garmonicheskogo ostsillyatora”, Matem. zametki, 53:3 (1993), 156–158 | MR | Zbl

[6] Nikiforov A. F., Uvarov V. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984 | MR

[7] Sege G., Ortogonalnye mnogochleny, GIFML, M., 1962

[8] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[9] Berezanskii Yu. M., Razlozheniya po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[10] Vatson G. N., Teoriya besselevykh funktsii, IL, M., 1949

[11] Murtazin Kh. Kh., Sadovnichii V. A., Spektralnyi analiz mnogochastichnogo operatora Shredingera, Izd-vo MGU, M., 1988

[12] Olver F., Asimptotika i spetsialnye funktsii, Nauka, M., 1990 | MR | Zbl