Geodesic
Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 16-24

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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.
Keywords: a discrete self-adjoint operator, a separable Hilbert space, eigenvalues and eigenfunctions of an operator, a regularized trace, errors in the perturbation theory. 
@article{IVM_2008_6_a1,
     author = {I. I. Kinzina},
     title = {Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--24},
     publisher = {mathdoc},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_6_a1/}
}
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I. I. Kinzina. Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 16-24. http://geodesic.mathdoc.fr/item/IVM_2008_6_a1/