Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I

TL;DR

This paper establishes conditions under which root vectors of an indefinite Sturm-Liouville problem with eigenparameter-dependent boundary conditions form a Riesz basis in a weighted Hilbert space, enhancing spectral analysis tools.

Contribution

It provides new sufficient conditions for the root vectors to form a Riesz basis in the context of indefinite Sturm-Liouville problems with eigenparameter dependence.

Findings

Root vectors can form a Riesz basis under certain conditions.

The basis construction applies to problems with eigenparameter-dependent boundary conditions.

Enhances spectral theory for indefinite Sturm-Liouville problems.

Abstract

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.