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.
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Original Russian Text © I.I. Kinzina, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 6, pp. 16–24.
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Kinzina, I.I. Calculation of eigenvalues of a discrete self-adjoint operator perturbed by a bounded operator. Russ Math. 52, 13–21 (2008). https://doi.org/10.3103/S1066369X08060029
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DOI: https://doi.org/10.3103/S1066369X08060029