A symmetric generalization of Sturm-Liouville problems in $q$-difference spaces

TL;DR

This paper extends classical Sturm-Liouville problems to symmetric $q$-difference spaces, ensuring solutions maintain orthogonality, with illustrative examples demonstrating the approach.

Contribution

It introduces a symmetric generalization of $q$-difference Sturm-Liouville problems, preserving orthogonality of solutions, which was not previously addressed.

Findings

Extended Sturm-Liouville problems to symmetric $q$-spaces

Maintained orthogonality of solutions in the generalized setting

Provided illustrative examples of the new framework

Abstract

Classical Sturm-Liouville problems of $q$-difference variables are extended for symmetric discrete functions such that the corresponding solutions preserve the orthogonality property. Some illustrative examples are given in this sense.