Sturm-Liouville operators on time scales

TL;DR

This paper explores the relationship between Sturm-Liouville equations on time scales and those with measure-valued coefficients, generalizing existing results in the field.

Contribution

It establishes a novel connection between Sturm-Liouville equations on time scales and measure-valued coefficients, extending previous research.

Findings

Unified framework for Sturm-Liouville equations on time scales and measure coefficients

Generalized several classical results to the time scales setting

Enhanced understanding of spectral properties on time scales

Abstract

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.