This article is cited in 3 papers

Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator

I. I. Kinzina

Magnitogorsk State University

Abstract: We generalize the method of regularized traces which calculates eigenvalues of a perturbed discrete operator for the case of an arbitrary multiplicity of eigenvalues of the unperturbed operator. We obtain a system of equations, enabling one to calculate eigenvalues of the perturbed operator with large ordinal numbers. As an example, we calculate eigenvalues of a perturbed Laplace operator in a rectangle.

Keywords: a discrete self-adjoint operator, a separable Hilbert space, eigenvalues and eigenfunctions of an operator, a regularized trace, errors in the perturbation theory.

UDC: 517.984.4

Received: 23.01.2006

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:6, 13–21

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