SPECTRAL EIGENVALUE PROBLEMS OF SELF-SIMILAR MEASURES WITH CONSECUTIVE DIGITS

Hai-Xiong Li () and Qian Li
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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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-10

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.

Keywords: Self-Similar Measure; Spectral Measures; Spectral Eigenvalue Problems; Consecutive Digits (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502005

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