Application of signal analysis to the embedding problem of Zk -actions

Yonatan Gutman, Yixiao Qiao, Masaki Tsukamoto

研究成果: ジャーナルへの寄稿記事

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We study the problem of embedding arbitrary Zk-actions into the shift action on the infinite dimensional cube ([0,1]D)Zk. We prove that if a Zk-action X satisfies the marker property (in particular if X is a minimal system without periodic points) and if its mean dimension is smaller than D / 2 then we can embed it in the shift on ([0,1]D)Zk. The value D / 2 here is optimal. The proof goes through signal analysis. We develop the theory of encoding Zk-actions into band-limited signals and apply it to proving the above statement. Main technical difficulties come from higher dimensional phenomena in signal analysis. We overcome them by exploring analytic techniques tailored to our dynamical settings. The most important new idea is to encode the information of a tiling of Rk into a band-limited function which is constructed from another tiling.

元の言語英語
ページ(範囲)1440-1502
ページ数63
ジャーナルGeometric and Functional Analysis
29
発行部数5
DOI
出版物ステータス出版済み - 10 1 2019

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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