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.
Beardon, The geometry of discrete groups, Graduate Tex ts in Mathe- matics 91, Springer-Verlag, New York, 1995
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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.