Existence of resonances for Schrodinger operators on hyperbolic space

TL;DR

This paper establishes the existence and lower bounds of resonances for Schrödinger operators with compactly supported potentials on hyperbolic space, using heat and wave trace techniques.

Contribution

It provides new existence results and quantitative bounds for resonances in hyperbolic space, combining heat and wave trace asymptotics.

Findings

Resonances exist under certain conditions.

Lower bounds for resonance distribution are derived.

Methods involve heat and wave trace asymptotics.

Abstract

We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions and asymptotics of the scattering phase.