Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices

David Damanik; Long Li

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arXiv · 2404.03864

Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices

David Damanik·Long Li

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Abstract

We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labelling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic analytic sampling functions in the subcritical region following from the analyticity of resonance tongue boundaries for both Jacobi and CMV matrices.

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BibTeX RIS

David Damanik, Long Li. 2024-04-05. Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices. https://arxiv.org/abs/2404.03864

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