On the spectrality of a class of Moran measures

2024/04/29 by Yali Zheng, Zheng, Yali, Yingqing Xiao +1
Mathematics · #Mathematical Dynamics and Fractals #Analytic and geometric function theory #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2404.18690

Abstract

In this paper, we study the spectrality of a class of Moran measures μ_P,D on ℝ generated by \(p_n,D_n)\_n=1^∞, where P=\p_n\_n=1^∞ is a sequence of positive integers with p_n>1 and D=\D_n\_n=1^∞ is a sequence of digit sets of ℕ with the cardinality #D_n∈ \2,3,N_n\. We find a countable set Λ⊂ℝ such that the set \e^{-2πi λx}|λ∈Λ\ is a orthonormal basis of L²(μ_P,D) under some conditions. As an application, we show that when μ_P,D is absolutely continuous, μ_P,D not only is a spectral measure, but also its support set tiles ℝ with ℤ.

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