Spectral Expansion for the Asymptotically Spectral Periodic Differential Operators

TL;DR

This paper studies the spectral expansion of high-order differential operators with periodic matrix coefficients, focusing on their asymptotic spectral properties on the real line.

Contribution

It introduces a spectral expansion framework for asymptotically spectral differential operators with periodic coefficients of arbitrary order.

Findings

Established spectral expansion formulas for these operators

Analyzed asymptotic behavior of the spectral components

Extended spectral theory to higher-order periodic differential operators

Abstract

In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients