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arXiv · 2009.01402

The spectral theory of regular sequences

Michael Coons·James Evans·Neil Manibo
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Abstract

Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we study the limiting asymptotics of regular sequences by constructing a systematic measure-theoretic framework surrounding them. The constructed measures are generalisations of mass distributions supported on attractors of iterated function systems.

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Michael Coons, James Evans, Neil Manibo. 2020-09-03. The spectral theory of regular sequences. https://arxiv.org/abs/2009.01402

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