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Reflectionless Dirac operators and canonical systems

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arxiv 2410.20218 v1 pith:6SYAEKY4 submitted 2024-10-26 math.SP math-phmath.CVmath.MP

Christian Remling , Jie Zeng This is my paper · ORCID
classification math.SPmath-phmath.CVmath.MP
keywords canonicalsystemsdiracholomorphicoperatorsreflectionlessabstractcombined
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reflectionless operators and automorphic Herglotz functions

    math.SP 2024-12 conditional novelty 7.0 of 10

    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.

  2. Gelfand-Levitan condition for Dirac operators

    math.SP 2025-08 unverdicted novelty 5.0 of 10

    A generalization of Dirac operators is introduced whose solutions are only of bounded variation, with a spectral theory and a Gelfand-Levitan recovery condition.

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