Geodesic
Non-Self-Adjoint Sturm--Liouville Operators with Matrix Potentials
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 496-506.

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

We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.
Keywords: Sturm–Liouville operator, non-self-adjoint operator, quasiperiodic boundary condition, Riesz basis, root function, Bessel operator.
Mots-clés : Jordan chain 
@article{MZM_2007_81_4_a2,
     author = {O. A. Veliev},
     title = {Non-Self-Adjoint {Sturm--Liouville} {Operators} with {Matrix} {Potentials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {496--506},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a2/}
}
TY  - JOUR
AU  - O. A. Veliev
TI  - Non-Self-Adjoint Sturm--Liouville Operators with Matrix Potentials
JO  - Matematičeskie zametki
PY  - 2007
SP  - 496
EP  - 506
VL  - 81
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a2/
LA  - ru
ID  - MZM_2007_81_4_a2
ER  - 
%0 Journal Article
%A O. A. Veliev
%T Non-Self-Adjoint Sturm--Liouville Operators with Matrix Potentials
%J Matematičeskie zametki
%D 2007
%P 496-506
%V 81
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a2/
%G ru
%F MZM_2007_81_4_a2
O. A. Veliev. Non-Self-Adjoint Sturm--Liouville Operators with Matrix Potentials. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 496-506. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a2/

[1] M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh–London, 1973 | Zbl

[2] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR | Zbl

[3] R. Carlson, “Large eigenvalues and trace formulas for matrix Sturm–Liouville problems”, SIAM J. Math. Anal., 30:5 (1999), 949–962 | DOI | MR | Zbl

[4] O. A. Veliev, F. G. Maksudov, “Nesamosopryazhennye differentsialnye operatory v prostranstve vektor-funktsii s periodicheskimi koeffitsientami”, Dokl. AN SSSR, 258 (1981), 26–30 | MR | Zbl

[5] O. A. Veliev, F. G. Maksudov, “Spektralnyi analiz differentsialnykh operatorov s periodicheskimi matrichnymi koeffitsientami”, Differents. uravneniya, 25:3 (1989), 400–409 | MR

[6] A. A. Shkalikov, “O bazisnosti Rissa kornevykh vektorov obyknovennykh differentsialnykh operatorov”, UMN, 34:5 (1979), 235–236 | MR | Zbl

[7] A. A. Shkalikov, “O svoistve bazisnosti sobstvennykh i prisoedinennykh funktsii obyknovennykh differentsialnykh operatorov s integralnymi kraevymi usloviyami”, Vestn. MGU. Ser. 1. Matem. mekh., 1982, no. 6, 12–21 | MR | Zbl

[8] A. A. Shkalikov, “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii so spektralnym parametrom v granichnykh usloviyakh”, Tr. sem. im. I. G. Petrovskogo, 1983, no. 9, 190–229 | MR | Zbl

[9] A. A. Shkalikov, “O bazisnosti Rissa sobstvennykh i prisoedinennykh funktsii obyknovennykh differentsialnykh operatorov v prostranstve vektor-funktsii”, Funktsionalnyi analiz i ego prilozheniya v mekhanike i teorii veroyatnosti, Izd. MGU, M., 1984 | MR | Zbl

[10] L. M. Luzhina, “Regulyarnye spektralnye zadachi v prostranstvakh vektor-funktsii”, Vestn. MGU. Ser. 1. Matem. mekh., 1988, no. 1, 31–35 | MR | Zbl

[11] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR | Zbl