Reflectionless Dirac operators and canonical systems

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 [Trans. Amer. Math. Soc. 368 (2016), no. 2, 1251–1270], 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.