Investigation reveals purely singular continuous spectrum in CMV matrices, suggesting refined spectral analysis techniques.
In this paper, we investigate the spectral properties of extended Cantero-Moral-Velázquez matrices Eω generated by the product dynamical system Ω(p)=X×Zp, where X is the period doubling subshift. We prove purely singular continuous spectrum by excluding eigenvalues via combinatorial structure and Gordon’s lemma, and establishing the absence of absolutely continuous spectrum through Kotani theory and Boshernitzan conditions.
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Fang et al. (2026) studied this question.
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