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This is a Quantitative Study study.

October 16, 2025Open Access

The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals

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The spectrum contains distinct intervals on the unit circle, which highlights its structured nature.
Under specific conditions, such as positive Lyapunov exponents, the spectral intervals become evident.
Shifts on the d-dimensional torus play a critical role in defining the Verblunsky coefficients for these matrices.
Understanding this structure may have implications for further studies in mathematical physics and operator theory.

Implication

Analysis reveals intervals in the spectrum of CMV matrices, governed by Lyapunov exponents and Diophantine conditions.

Abstract

We investigate the spectral structure of multi-frequency quasi-periodic CMV matrices with Verblunsky coefficients defined by shifts on the d-dimensional torus. Under the positive Lyapunov exponent regime and standard Diophantine frequency conditions, we establish that the spectrum of these operators contains intervals on the unit circle.

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Cite This Study

Zhang et al. (2025) studied this question.

synapsesocial.com/papers/68f0d5eb105731330a2b1f39 https://doi.org/10.48550/arxiv.2502.17532

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Implication

Analysis reveals intervals in the spectrum of CMV matrices, governed by Lyapunov exponents and Diophantine conditions.

The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals

Key Points

Implication

Abstract

Discussion

Cite This Study

The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals

Key Points

Implication

Abstract

Discussion

Cite This Study

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