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Calculation of eigenvalues of a discrete self-adjoint operator perturbed by a bounded operator

Research paper by I. I. Kinzina

Indexed on: 06 Aug '08Published on: 06 Aug '08Published in: Russian Mathematics



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.