Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 705-715.

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Multiple Spectra of Self-Similar Measures with Three Digits

Haixiong Li(),Xinlin Wu*,Daoxin Ding   

  1. School of Mathematics and Economics Bigdata Modeling and Intelligent Computing Institute, Hubei University of Education, Wuhan 430205
  • Received:2021-04-28 Online:2022-06-26 Published:2022-05-09
  • Contact: Xinlin Wu
  • Supported by:
    the NSFC(11401189);the NSF of Hubei(2019CFB782)


It is well known that the self-similar measure $\mu_{k, a, b}$ defined byis a spectral measure with a spectrumIn this paper, by applying the properties of congruences and the order of elements in the finite group, we obtain some conditions on the integer $p$ such that the set $p\Lambda(3k, C)$ is also a spectrum for $\mu_{k, a, b}$. Moreover, an example is given to explain our theory.

Key words: Self-similar measure, Spectral measures, Spectral eigenvalue, Multiple spectrum

CLC Number: 

  • O174.2