Reflectionless Dirac operators and canonical systems

TL;DR

This paper investigates reflectionless canonical systems, especially Dirac operators, revealing how their half-line m-functions can be combined into a single holomorphic function, advancing the theoretical understanding of these operators.

Contribution

It extends previous work by developing a more general framework for reflectionless Dirac operators and their connection to canonical systems.

Findings

Half-line m-functions are holomorphic continuations of each other

Combined into a single holomorphic function for reflectionless systems

Provides a more general and abstract framework for analysis

Abstract

We study canonical systems that are reflectionless on an open set. In this situation, the two half line $m$ functions are holomorphic continuations of each other and may thus be combined into a single holomorphic function. This idea was explored in [11], and we continue these investigations here. We focus on Dirac operators and especially their interplay with canonical systems, and we provide a more general and abstract framework.