De Branges functions of Schroedinger equations

TL;DR

This paper characterizes de Branges functions associated with Schrödinger operators with L^2 potentials on finite intervals, providing insights into their structure and resonance locations.

Contribution

It offers a new characterization of Hermite-Biehler functions linked to Schrödinger operators with L^2 potentials, extending previous results and deducing recent theorems.

Findings

Characterization of de Branges functions for Schrödinger operators

Deduction of a recent theorem by Horvath

Results on the location of resonances

Abstract

We characterize the Hermite-Biehler (de Branges) functions $E$ which correspond to Shroedinger operators with $L^2$ potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances.