On the Spectral Singularities and Spectrality of the Hill Operator

TL;DR

This paper investigates the spectral properties of the Hill operator, focusing on spectral singularities at infinity and their impact on spectrality and spectral expansion.

Contribution

It provides new insights into the relationship between spectral singularities at infinity and the spectrality of the Hill operator, including conditions for spectral expansion.

Findings

Characterization of spectral singularities at infinity

Connections between spectral singularities and spectrality

Conditions for spectral expansion without singularities

Abstract

First we study the spectral singularity at infinity and investigate the connections of the spectral singularities and the spectrality of the Hill operator. Then we consider the spectral expansion when there is not the spectral singularity at infinity.