# Resonances for 1d Stark operators

## TL;DR

This paper studies the resonances of a one-dimensional Stark operator with a compactly supported potential, establishing bounds, a trace formula, and uniqueness of potential determination from resonances.

## Contribution

It provides new bounds, a trace formula, and a uniqueness result for resonances of 1D Stark operators with compactly supported potentials.

## Key findings

- Bounds on the number of resonances in large discs
- Trace formula expressed solely via resonances
- Uniqueness of potential determined by all resonances

## Abstract

We consider the Stark operator perturbed by a compactly supported potential (of a certain class) on the real line. We prove the following results: (a) upper and lower bounds on the number of resonances in complex discs with large radii, (b) the trace formula in terms of resonances only, (c) all resonances determine the potential uniquely.