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

Bei Zhang; Daxiong Piao

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arXiv · 2502.17532

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

Bei Zhang·Daxiong Piao

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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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Bei Zhang, Daxiong Piao. 2025-02-24. The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals. https://arxiv.org/abs/2502.17532

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