Beurling dimension and a class of Moran measures

Cong Wang and Min-Min Zhang

Chaos, Solitons & Fractals, 2023, vol. 166, issue C

Abstract: In this paper, we will study the Beurling dimension of spectra for Moran measures defined by infinite convolution of discrete measures μb,D,{nj}=δb−n1D∗δb−(n1+n2)D∗δb−(n1+n2+n3)D∗⋯. We obtain the upper and lower bounds of the dimension. More precisely, the upper bound is the Hausdorff dimension of the compact support of μb,D,{nj} and the lower bound is 0. The bounds are attained in special cases and some examples are given to explain our theory.

Keywords: Beurling dimension; Moran measure; Spectrum; Hausdorff dimension (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011055

DOI: 10.1016/j.chaos.2022.112926

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