Spectral resolutions for non-self-adjoint block convolution operators

TL;DR

This paper develops spectral theory for non-self-adjoint block convolution operators on Banach spaces, providing spectral representations and applying results to periodic Jacobi matrices.

Contribution

It introduces spectral analysis methods for a broad class of non-self-adjoint operators, extending existing theory and applying it to specific matrix classes.

Findings

Spectral representations for non-self-adjoint block convolution operators.

Application of spectral theory to periodic Jacobi matrices.

Extension of spectral analysis to operators on Banach spaces.

Abstract

The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.