This article is cited in 2 papers

About the inverse problem of the spectral analysis

A. I. Sedov

Magnitogorsk State University

Abstract: We give the sufficient conditions imposed on a sequence of complex numbers for which there exists such perturbation operator, that its spectrum is equal to the given sequence. The algorithm of the approximate finding of the perturbation operator is given.

Keywords: a self-adjoint discrete operator, Hilbert space, Laplace operator, an operator of trace class, spectrum, trace, perturbation, eigenvalues.

UDC: 517.984.54

Received: 27.11.2010