This article is cited in 1 paper

Mathematics

The approached calculation of eigenvalues of the discrete operator by means of spectral traces of resolvent degrees

E. M. Maleko

Magnitogorsk State Technical University, Chair of Mathematics

Abstract: Let a discrete self-adjoint operator $T$ acts in a separable Hilbert space and have the kernel resolvent, and eigenvalues and eigenfunctions of the operator $T$ be known. In the paper the method of calculation of eigenvalues of the perturbed operator $T+P$ is considered. Resolvent of this operator is presented as convergent Neumann series on eigenfunctions of the operator $T$. The point of the method is that at first is found a set of numbers which approximate traces of the resolvent degrees of the operator $T+P$. Then by means of the given set, the system of nonlinear algebraic equations is constructed and solved. The solution of the systemis a set of numbers which approximate first eigenvalues of the resolvent of the perturbed operator $T+P$.

Key words: eigenvalues, resolvent, separable Hilbert space.

UDC: 517.984

DOI: 10.18500/1816-9791-2010-10-1-18-23