Multiple operator integrals and spectral shift

TL;DR

This paper develops multiple scalar integral representations for operator derivatives and uses them to prove the existence of higher order spectral shift functions, advancing the mathematical understanding of spectral theory.

Contribution

It introduces new integral representations for operator derivatives and demonstrates their application in establishing higher order spectral shift functions.

Findings

Established multiple scalar integral representations for operator derivatives

Proved the existence of higher order spectral shift functions

Enhanced spectral theory techniques

Abstract

Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.