Sampling Theory for Sturm-Liouville Problem with Boundary and Transmission Conditions Dependent on Eigenparameter

TL;DR

This paper develops a sampling theory framework for a discontinuous Sturm-Liouville problem with eigenparameter-dependent boundary and transmission conditions, analyzing its spectral properties and establishing a sampling theorem.

Contribution

It introduces a novel sampling theorem for Sturm-Liouville problems with eigenparameter-dependent boundary and transmission conditions, expanding the theoretical understanding.

Findings

Spectral properties of the problem are characterized.

A sampling theorem specific to this problem is proved.

The framework can be applied to similar discontinuous spectral problems.

Abstract

In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two transmission conditions. We establish briefly spectral properties of the problem and then we prove the sampling theorem associated with the problem.