Trace formulae for dissipative and coupled scattering systems

TL;DR

This paper develops trace formulae for dissipative and coupled scattering systems, linking spectral shift functions to Titchmarsh-Weyl functions and establishing a Birman-Krein type formula.

Contribution

It introduces a novel framework connecting spectral shift functions with Titchmarsh-Weyl functions for dissipative and coupled systems, extending classical scattering theory.

Findings

Spectral shift function expressed via Titchmarsh-Weyl function

A variant of the Birman-Krein formula proved for these systems

Framework applicable to systems with finite deficiency indices

Abstract

For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.