On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems

TL;DR

This paper establishes criteria for when systems of root functions of nonselfadjoint Sturm-Liouville operators with periodic or antiperiodic boundary conditions form a Riesz basis, based on Fourier coefficients of the potential q.

Contribution

It provides necessary and sufficient conditions for Riesz basisness of root function systems in terms of Fourier coefficients, advancing spectral theory for nonselfadjoint operators.

Findings

Criteria for Riesz basisness based on Fourier coefficients

Conditions depend on boundary conditions (periodic or antiperiodic)

Enhances understanding of spectral properties of nonselfadjoint Sturm-Liouville operators

Abstract

In this paper, we consider the nonselfadjoint Sturm Liouville operator with and either periodic, or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis in in terms of the Fourier coefficients of q.