This article is cited in 1 paper

On the computation of the spectrum of directionally perturbed operators

E. M. Maleko

Magnitogorsk State Technical University, pr. Lenina 38, Magnitogorsk, 455000 Russia

Abstract: A class of operators with special spectral properties is defined. An operator in this class is fairly simple, acts in a separable Hilbert space, and can be perturbed so that an a priori given function from its domain is an eigenfunction of the perturbed operator. This fact is shown to be useful for constructing operators in mathematical physics. Specific examples are given.

Key words: directionally perturbed operators, calculation of spectra of operators, Hermite, Jacobi, Legendre, and Laguerre operators.

UDC: 519.642.8

Received: 25.08.2009
Revised: 14.01.2010

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:7, 1120–1140

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