Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 22-30.

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

This paper investigates the Dirac system with the continuous potential. Asymptotic formulas for the eigenvalues (including refined) and eigenfunctions are established. As an application we obtain a theorem P. Dzhakova and B. S. Mityagin on the Riesz bases with brackets.
@article{ISU_2012_12_3_a3,
     author = {M. Sh. Burlutskaya and V. P. Kurdyumov and A. P. Khromov},
     title = {Refined asymptotic formulas for eigenvalues and eigenfunctions of the {Dirac} system with nondifferentiable potential},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {22--30},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a3/}
}
TY  - JOUR
AU  - M. Sh. Burlutskaya
AU  - V. P. Kurdyumov
AU  - A. P. Khromov
TI  - Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2012
SP  - 22
EP  - 30
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a3/
LA  - ru
ID  - ISU_2012_12_3_a3
ER  - 
%0 Journal Article
%A M. Sh. Burlutskaya
%A V. P. Kurdyumov
%A A. P. Khromov
%T Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2012
%P 22-30
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a3/
%G ru
%F ISU_2012_12_3_a3
M. Sh. Burlutskaya; V. P. Kurdyumov; A. P. Khromov. Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 22-30. http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a3/

[1] Dzhakov P. V., Mityagin B. S., “Zony neustoichivosti odnomernykh periodicheskikh operatorov Shredingera i Diraka”, UMN, 61:4 (2006), 77–182 | DOI | MR | Zbl

[2] Djakov P., Mityagin B., “Bari–Markus property for Riesz projections of 1D periodic Dirac operators”, Math. Nachr., 283:3 (2010), 443–462 | DOI | MR | Zbl

[3] Baskakov A. G., Derbushev A. V., Scherbakov A. O., “Metod podobnykh operatorov v spektralnom analize nesamosopryazhennogo operatora Diraka s negladkim potentsialom”, Izv. RAN. Ser. matematicheskaya, 75:3 (2011), 3–28 | DOI | MR | Zbl

[4] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Nauk. dumka, Kiev, 1977, 340 pp. | MR

[5] Burlutskaya M. Sh., “Ob asimptotike resheniya odnogo differentsialnogo uravneniya pervogo poryadka s nepreryvnym potentsialom”, Sovremennye metody teorii kraevykh zadach, Materialy Voronezh. vesennei mat. shk. “Pontryaginskie chteniya KhKhI”, Izdat.-poligraf. tsentr Voronezh gos. un-ta, Voronezh, 2010, 3–9

[6] Khromov A. P., “Ob asimptotike reshenii uravneniya Diraka”, Sovremennye metody teorii funktsii i smezhnye problemy, Materialy Voronezh. zimnei mat. shk., Izd.-poligraf. tsentr Voronezh gos. un-ta, Voronezh, 2011, 346–347

[7] Khromov A. P., “Teoremy ravnoskhodimosti dlya integro-differentsialnykh i integralnykh operatorov”, Mat. sb., 114(156):3 (1981), 378–405 | MR | Zbl

[8] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965, 445 pp.