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Cyclic extensions of odometer transformations and spectral disjointness

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Abstract

We discuss spectral properties of cyclic extensions of the odometer transformations. We prove that continuous power spectral measures corresponding to two of them with multiplicatively independent bases are mutually singular. These measures can be used to distinguish sets of normal numbers to multiplicatively independent bases.

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  1. Department of Mathematics, Osaka City University, Sugimoto-cho, 558, Osaka, Japan

    Teturo Kamae

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  1. Teturo Kamae
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Kamae, T. Cyclic extensions of odometer transformations and spectral disjointness. Israel J. Math. 59, 41–63 (1987). https://doi.org/10.1007/BF02779666

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  • DOI: https://doi.org/10.1007/BF02779666

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