Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 2

ON THE INVERSE PROBLEM FOR FINITE DISSIPATIVE JACOBI MATRICES WITH A RANK-ONE IMAGINARY PART

ON THE INVERSE PROBLEM FOR FINITE DISSIPATIVE JACOBI MATRICES WITH A RANK-ONE IMAGINARY PART

Ebru ERGÜN

Sayfa
1273–1288
DOI
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Abstract

This paper deals with the inverse spectral problem consisting inthe reconstruction of a Önite dissipative Jacobi matrix with a rank-one imaginary part from its eigenvalues. Necessary and su¢ cient conditions are formulated for a prescribed collection of complex numbers to be the spectrum of aÖnite dissipative Jacobi matrix with a rank-one imaginary part. Uniquenessof the matrix having prescribed eigenvalues is shown and an algorithm forreconstruction of the matrix from prescribed eigenvalues is given.