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.
Topological properties of reflectionless canonical systems
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We study the topological properties of spaces of reflectionless canonical systems. In this analysis, a key role is played by a natural action of the group $\operatorname{PSL}(2,\mathbb R)$ on these spaces.
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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.