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Spectral properties of pattern sequences of general degrees

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Published 10 May 2021 • © 2021 IOP Publishing Ltd & London Mathematical Society
, , Citation Yu Zheng et al 2021 Nonlinearity 34 3411 DOI 10.1088/1361-6544/abe91a

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Author e-mails

zhengyu@yangtzeu.edu.cn

lpeng@hust.edu.cn

kamae@apost.plala.or.jp

Author affiliations

1 School of Information and Mathematics, Yangtze University, Jingzhou 434023, People's Republic of China

2 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China

3 Advanced Mathematical Institute, Osaka City University, 558-8585 Japan

Author notes

4 Author to whom any correspondence should be addressed.

Dates

  1. Received 23 July 2020
  2. Revised 21 February 2021
  3. Accepted 23 February 2021
  4. Published

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0951-7715/34/5/3411

Abstract

We study the spectral measures associated with pattern sequences of general degrees. They are either discrete, purely singular or absolutely continuous. We obtain a necessary and sufficient condition for the discreteness. We also obtain a sufficient condition to be absolutely continuous or to be the Lebesgue measure.

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10.1088/1361-6544/abe91a