JournalsdmVol. 27pp. 629–653

Spectral theory of regular sequences

  • Michael Coons

    Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

  • James Evans

    School of Information and Physical Sciences, University of Newcastle, 130 University Drive, Callaghan NSW 2308, Australia

  • Neil Mañibo

    Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
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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.

Cite this article

Michael Coons, James Evans, Neil Mañibo, Spectral theory of regular sequences. Doc. Math. 27 (2022), pp. 629–653

DOI 10.4171/DM/880