Spectrality of Moran measures with finite arithmetic digit sets

2019/11/13 by Zong-Sheng Liu, Xin-Han Dong, Xin-han Dong
Mathematics · #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical functions and polynomials

paper · doi:10.1142/s0129167x20500081

openalex publication_date 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

Let [Formula: see text] be a prime and [Formula: see text] be a sequence of finite arithmetic digit sets in [Formula: see text] with [Formula: see text] uniformly bounded, and let [Formula: see text] be the discrete probability measure on the finite set [Formula: see text] with equal distribution. For [Formula: see text], the infinite Bernoulli convolution [Formula: see text] converges weakly to a Borel probability measure (Moran measure). In this paper, we study the existence of exponential orthonormal basis for [Formula: see text].

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