Resonances sets of Schr\"{o}dinger operators

TL;DR

This paper investigates the distribution of resonances for Schrödinger operators with compactly supported potentials, showing they can include arbitrary subsets within certain angular regions satisfying the Blaschke condition.

Contribution

It demonstrates that resonances can form arbitrary subsets within specific angular regions, extending understanding of their possible distributions.

Findings

Resonances can contain arbitrary subsets satisfying the Blaschke condition.

Sufficient conditions are established for resonances in wider domains.

The results generalize previous knowledge on resonance distributions.

Abstract

We prove that resonances of the Schr\"{o}dinger operator with compactly supported potential can contain arbitrary subset of the angle $\{z: -\text{Im} z > C |\text{Re} z|\}$ that satisfies Blaschke condition. We also establish sufficient conditions for the subsets of wider domains.