Trace formulas for Schr\"odinger operators with complex potentials

TL;DR

This paper develops new trace formulas for 3D Schrödinger operators with complex potentials by analyzing the analytic properties of a modified Fredholm determinant within Hardy spaces.

Contribution

It introduces novel trace formulas for complex potentials and connects spectral theory with Hardy space analysis of Fredholm determinants.

Findings

Derived new trace formulas for complex Schrödinger operators

Linked spectral problems to Hardy space analytic functions

Analyzed properties of modified Fredholm determinants

Abstract

We consider 3-dim Schr\"odinger operators with a complex potential. We obtain new trace formulas. In order to prove these results we study analytic properties of a modified Fredholm determinant. In fact we reformulate spectral theory problems as the problems of analytic functions from Hardy spaces in upper half-plane.