The Regularized Trace of Sturm-Liouville Problem with Discontinuities at Two Points

TL;DR

This paper derives a regularized trace formula for a Sturm-Liouville problem with two discontinuities and an eigenparameter in the boundary condition, advancing spectral analysis techniques for such complex boundary value problems.

Contribution

It introduces a novel regularized trace formula for Sturm-Liouville problems with multiple discontinuities and eigenparameter-dependent boundary conditions.

Findings

Derived explicit trace formula for the problem.

Extended spectral analysis to discontinuous Sturm-Liouville operators.

Provided insights into eigenvalue distribution with discontinuities.

Abstract

In this paper, we obtain a regularized trace formula for a Sturm Liouville problem which has two points of discontinuity and also contains an eigenparameter in a boundary ondition.