Lower bounds for self-adjoint Sturm-Liouville operators

TL;DR

This paper establishes lower bound estimates for self-adjoint Sturm-Liouville operators with three coefficients in a weighted L^2 space, contributing to spectral analysis of differential operators.

Contribution

It provides new lower bound estimates for the self-adjoint Sturm-Liouville operators with three coefficients in weighted spaces.

Findings

Derived explicit lower bounds for the operator

Extended spectral analysis techniques for weighted spaces

Applicable to a broad class of Sturm-Liouville problems

Abstract

In this note we provide estimates for the lower bound of the self-adjoint operator associated with the three-coefficient Sturm-Liouville differential expression $$ \frac{1}{r} \left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) $$ in the weighted $L^2$-Hilbert space $L^2(\mathbb R; rdx)$.