Reflectionless Dirac operators on a finite-gap set are homeomorphic to a product of N probability-measure spaces on circles, with finite-gap operators as the extreme points.
Reflectionless Dirac operators and canonical systems
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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.
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Reflectionless operators and automorphic Herglotz functions
Reflectionless Dirac operators on a finite-gap set are homeomorphic to a product of N probability-measure spaces on circles, with finite-gap operators as the extreme points.