Scattering theory and Banach space valued singular integrals

TL;DR

This paper introduces a new sufficient condition for the existence and completeness of wave operators in abstract scattering theory, generalizing previous approaches by using estimates for Cauchy transforms of operator-valued measures.

Contribution

It provides a novel condition that unifies trace class and smooth methods in scattering theory through operator-valued measure estimates.

Findings

New sufficient condition for wave operators

Generalizes trace class and smooth approaches

Based on Cauchy transform estimates

Abstract

We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy transforms of operator valued measures.