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Spectral Eigenvalue Problems Of Self-Similar Measures With Consecutive Digits

Author

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  • HAI-XIONG LI

    (School of Mathematics and Statistics, HuBei University of Education, Wuhan, 430205, P. R. China)

  • QIAN LI

    (School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079 P. R. China)

Abstract

Let k,b ≥ 2 be two positive integers. For D = k{0, 1,…,b − 1}, it is well known that the self-similar measure μk,b defined by μk,b(⋅) = 1 b∑i=0b−1μ k,b(kb(⋅) − ki) is a spectral measure with a spectrum Λ(kb,C) = ∑j=0finite(kb)jc j : cj ∈ C = {0, 1,…,b − 1}. In 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 pΛ(kb,C) is also a spectrum for μk,b. Moreover, an example is given to explain our theory.

Suggested Citation

  • Hai-Xiong Li & Qian Li, 2021. "Spectral Eigenvalue Problems Of Self-Similar Measures With Consecutive Digits," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-10, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502005
    DOI: 10.1142/S0218348X21502005
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