A Sharp Lieb-Thirring Inequality for Functional Difference Operators

TL;DR

This paper establishes precise Lieb-Thirring inequalities for eigenvalues of certain one-dimensional functional difference operators linked to mirror curves, and shows the bottom of their essential spectrum is a resonance state.

Contribution

It introduces sharp Lieb-Thirring inequalities for a new class of functional difference operators and analyzes their spectral properties.

Findings

Proved sharp Lieb-Thirring inequalities for these operators.

Identified the bottom of the essential spectrum as a resonance state.

Abstract

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators is a resonance state.