Schrodinger operators and the distribution of resonances in sectors

TL;DR

This paper investigates the distribution of resonances in potential scattering using complex analysis techniques, providing asymptotic results for specific potentials and their families.

Contribution

It introduces refined methods from complex variables to analyze resonance distribution, offering new asymptotic formulas for particular potential classes.

Findings

Asymptotic formulas for resonance distribution in sectors

Application of complex analysis techniques to scattering problems

Results valid for specific potential families

Abstract

The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including properties of functions of completely regular growth. This enables us to find asymptotics for the distribution of resonances in sectors for certain potentials and for certain families of potentials.