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This article is cited in 1 scientific paper (total 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.
Citation:
E. M. Maleko, “The approached calculation of eigenvalues of the discrete operator by means of spectral traces of resolvent degrees”, Izv. Saratov Univ. Math. Mech. Inform., 10:1 (2010), 18–23
Linking options:
https://www.mathnet.ru/eng/isu4 https://www.mathnet.ru/eng/isu/v10/i1/p18
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Abstract page: | 349 | Full-text PDF : | 106 | References: | 38 | First page: | 1 |
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