Spectral Expansion for the Non-self-adjoint Differential Operators with the Periodic Matrix Coefficients

TL;DR

This paper develops a spectral expansion method for non-self-adjoint differential operators with periodic matrix coefficients, addressing spectral singularities and quasimomenta to advance understanding of their spectral properties.

Contribution

It introduces a novel spectral expansion framework for non-self-adjoint operators with periodic matrix coefficients, incorporating essential spectral singularities and series with parentheses.

Findings

Constructed spectral expansion for non-self-adjoint operators

Addressed spectral singularities and quasimomenta

Enhanced analysis of spectral properties of differential operators

Abstract

In this paper we construct the spectral expansion for the non-self-adjoint differential operators generated in the space of vektor functions by the ordinary differential expression of arbitrary order with the periodic matrix coefficients by using the essential spectral singularities, singular quasimomenta and the series with parenthesis.