On the differential operators of odd order with PT-symmetric periodic matrix coefficients

TL;DR

This paper studies the spectral properties of odd-order differential operators with PT-symmetric periodic matrix coefficients, contributing to understanding their mathematical structure and potential physical applications.

Contribution

It introduces a detailed analysis of the spectrum for differential operators with PT-symmetric periodic matrix coefficients of odd order, a novel area in spectral theory.

Findings

Characterization of the spectrum of the operators

Conditions for spectral stability

Insights into PT-symmetry effects on spectral properties

Abstract

In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients