RECONSTRUCTION OF COMPLEX JACOBI MATRICES FROM SPECTRAL DATA

Year 2009, Volume: 38 Issue: 3, 317 - 327, 01.03.2009

Gusein Sh. Guseinov

Abstract

RECONSTRUCTION OF COMPLEX JACOBI MATRICES FROM SPECTRAL DATA

Abstract

In this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrix from its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data is given.

Keywords

Jacobi matrix, Difference equation, Spectral data, Inverse spectral problem, 2000 AMS Classification: 15 A 29

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