Riesz bases of root vectors of indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions. II

TL;DR

This paper establishes conditions under which the root vectors of a specific class of indefinite Sturm-Liouville problems with eigenparameter-dependent boundary conditions form a Riesz basis, aiding spectral analysis.

Contribution

It provides sufficient criteria for the root vectors to constitute 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.

Sufficient conditions are identified for basis formation.

Results facilitate spectral analysis of indefinite Sturm-Liouville problems.

Abstract

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be selected to form a Riesz basis of a corresponding weighted Hilbert space.