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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2009 Volume 200, Number 2, Pages 61–74 (Mi sm4111)

This article is cited in 3 papers

Asymptotic behaviour of the discrete spectrum of a quasi-periodic boundary value problem for a two-dimensional hyperbolic equation

V. M. Kaplitskiiab

a Institute of Applied Mathematics and Informatics, Vladikavkaz Scientific Centre, RAS
b Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences

Abstract: This paper is concerned with the asymptotic properties of the discrete spectrum of two-dimensional self-adjoint operators of hyperbolic type. For the operator of the model quasi-periodic boundary value problem associated with a self-adjoint hyperbolic equation with smooth coefficients on a two-dimensional torus we obtain an asymptotic formula for the distribution function of the eigenvalues.
Bibliography: 9 titles.

Keywords: two-dimensional hyperbolic equation, quasi-periodic boundary value problem, spectrum, distribution of eigenvalues.

UDC: 517.984.56

MSC: Primary 34L20; Secondary 35L20

Received: 21.11.2007

DOI: 10.4213/sm4111


 English version:
Sbornik: Mathematics, 2009, 200:2, 215–228

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