Direct and inverse spectral problems for a class of non-selfadjoint band matrices

TL;DR

This paper investigates the spectral properties of a specific class of non-selfadjoint band matrices and develops conditions for reconstructing these matrices from spectral data, extending existing results for related matrix classes.

Contribution

It provides necessary and sufficient conditions for reconstructing non-selfadjoint band matrices from spectral data, extending prior work on Jacobi and tridiagonal matrices.

Findings

Derived conditions for matrix reconstruction from spectral data

Extended spectral problem results to non-selfadjoint band matrices

Enhanced understanding of spectral properties of specialized matrices

Abstract

The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The obtained results extend some results on the direct and inverse spectral problems for periodic Jacobi matrices and for some non-self-adjoint tridiagonal matrices.