Spectral analysis of a differential operator with an involution

被引：28

作者：

Baskakov, Anatoly G. ^{[1
]}

Krishtal, Ilya A. ^{[2
]}

Romanova, Elena Yu. ^{[1
]}

机构：

[1] Voronezh State Univ, Dept Appl Math & Mech, Voronezh 394693, Russia

[2] Northern Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2017年 / 17卷 / 02期

基金：

美国国家科学基金会;

关键词：

Spectral asymptotic analysis; Method of similar operators; PERTURBATION;

D O I：

10.1007/s00028-016-0332-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use the method of similar operators to perform the asymptotic analysis of the spectrum of a differential operator with an involution. We show that such operators have compact resolvent, and that their large eigenvalues are determined by the values of (the Fourier coefficients) of their potential up to a summable sequence.

引用

页码：669 / 684

页数：16

共 49 条

[1] Spectral analysis of a differential operator with an involution [J].

Anatoly G. Baskakov ;

Ilya A. Krishtal ;

Elena Yu. Romanova .

Journal of Evolution Equations, 2017, 17 :669-684

[2] LINEAR DIFFERENTIAL OPERATOR WITH AN INVOLUTION AS A GENERATOR OF AN OPERATOR GROUP [J].

Baskakov, Anatoly G. ;

Krishtal, Ilya A. ;

Uskova, Natalia B. .

OPERATORS AND MATRICES, 2018, 12 (03) :723-756

[3] SPECTRAL ANALYSIS OF A FOURTH ORDER DIFFERENTIAL OPERATOR WITH PERIODIC AND ANTIPERIODIC BOUNDARY CONDITIONS [J].

Polyakov, D. M. .

ST PETERSBURG MATHEMATICAL JOURNAL, 2016, 27 (05) :789-811

[4] Similarity techniques in the spectral analysis of perturbed operator matrices [J].

Baskakov, Anatoly G. ;

Krishtal, Ilya A. ;

Uskova, Natalia B. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 477 (02) :930-960

[5] SPECTRAL PROPERTIES OF FIRST-ORDER DIFFERENTIAL OPERATORS WITH AN INVOLUTION AND GROUPS OF OPERATORS [J].

Krishtal, I. A. ;

Uskova, N. B. .

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 :1091-1132

[6] The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential [J].

Baskakov, A. G. ;

Polyakov, D. M. .

SBORNIK MATHEMATICS, 2017, 208 (01) :1-43

[7] Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients [J].

Polyakov, D. M. .

SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (01) :138-154

[8] On spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions [J].

Polyakov D.M. .

Russian Mathematics, 2015, 59 (5) :64-68

[9] ABOUT THE APPROXIMATE SOLUTION OF THE INVERSE PROBLEM OF THE SPECTRAL ANALYSIS FOR LAPLACE OPERATOR [J].

Sedov, A. I. .

BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2010, (05) :73-78

[10] Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients [J].

D. M. Polyakov .

Siberian Mathematical Journal, 2015, 56 :138-154

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