Spectrality of homogeneous Moran measures on the plane

Zong-Sheng Liu

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

Abstract: LetM=ρ1−1a0ρ2−1 be a real upper triangular expanding matrix and D=00,d10,d2d3 be a three-element real digit set with d1d3≠0 , and let {nk}k=1∞ be a sequence of positive integers with upper bound. The infinite convolutions μM,D,{nk}=δM−n1D∗δM−(n1+n2)D∗⋯∗δM−(n1+⋯+nk)D∗⋯ converges weakly to a Borel probability measure (homogeneous Moran measure). In this paper, we study the existence of exponential orthonormal basis for L2(μM,D,{nk}). A necessary and sufficient condition for μM,D,{nk} to be a spectral measure is established.

Keywords: Moran measures; Spectral measure; Orthonormal basis; Fourier transform (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004788

DOI: 10.1016/j.chaos.2024.114926

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