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


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Ergun E.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.68, ss.1273-1288, 2019 (ESCI İndekslerine Giren Dergi)

  • Cilt numarası: 68 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.31801/cfsuasmas.419098
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Sayfa Sayısı: ss.1273-1288

Özet

This paper deals with the inverse spectral problem consisting in the reconstruction of a finite dissipative Jacobi matrix with a rank-one imaginary part from its eigenvalues. Necessary and sufficient conditions are formulated for a prescribed collection of complex numbers to be the spectrum of a finite dissipative Jacobi matrix with a rank-one imaginary part. Uniqueness of the matrix having prescribed eigenvalues is shown and an algorithm for reconstruction of the matrix from prescribed eigenvalues is given.