$L_p$-spectrum and Lieb-Thirring inequalities for Schr\"odinger operators on the hyperbolic plane

TL;DR

This paper investigates the $L_p$-spectrum of Schr"odinger operators on the hyperbolic plane, establishing Lieb-Thirring inequalities for eigenvalues and analyzing their dependence on $p$ with bounds on individual eigenvalues.

Contribution

It introduces Lieb-Thirring inequalities for Schr"odinger operators on the hyperbolic plane and explores how these bounds vary with $p$, providing new spectral estimates.

Findings

Established Lieb-Thirring inequalities for the hyperbolic plane

Derived bounds on individual eigenvalues

Analyzed eigenvalue dependence on $p$

Abstract

This paper deals with the $L_p$-spectrum of Schr\"odinger operators on the hyperbolic plane. We establish Lieb-Thirring type inequalities for discrete eigenvalues and study their dependence on $p$. Some bounds on individual eigenvalues are derived as well.