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

E. M. Maleko

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 18-23

Résumé

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 $T+P$.