Rational interpolation and mixed inverse spectral problem for finite CMV matrices

TL;DR

This paper addresses the mixed inverse spectral problem for finite CMV matrices, developing rational interpolation techniques to reconstruct matrices from partial spectral data and submatrices, with conditions for solution uniqueness.

Contribution

It introduces a general rational interpolation framework for the mixed inverse spectral problem and provides criteria for the uniqueness of solutions in finite CMV matrices.

Findings

Established a rational interpolation approach for the inverse spectral problem.

Provided sufficient conditions for the uniqueness of matrix reconstruction.

Described the solution space for the interpolation problem.

Abstract

For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed inverse spectral problem is studied, and the description of the space of its solutions is given. We apply the developed technique to give sufficient conditions for the uniqueness of the solution of the mixed inverse spectral problem.