Essential Spectral Singularities and the Spectral Expansion for the Hill Operator

TL;DR

This paper explores the spectral expansion of the one-dimensional Schrödinger operator with complex periodic potentials, focusing on spectral singularities and introducing new concepts like essential spectral singularities and singular quasimomenta.

Contribution

It introduces the concepts of essential spectral singularities and singular quasimomenta, advancing the understanding of spectral properties of complex periodic Schrödinger operators.

Findings

Identification of essential spectral singularities

Development of spectral expansion theory for complex potentials

Introduction of new spectral concepts

Abstract

In this paper we investigate the spectral expansion for the one-dimensional Schrodinger operator with a periodic complex-valued potential. For this we consider in detail the spectral singularities and introduce new concepts as essential spectral singularities and singular quasimomenta.