Scaling of spectra of a class of self‐similar measures on R

Zhi‐Min Wang, Xin‐Han Dong and Wen‐Hui Ai

Mathematische Nachrichten, 2019, vol. 292, issue 10, 2300-2307

Abstract: Let n,b≥2 be two positive integers. For D={0,1,⋯,b−1}, let the self‐similar measure μbn,D be defined by μbn,D=1b∑d∈Dμbn,D(bnx−d). It is known [18] that μbn,D is a spectral measure with a spectrum Λ(bn,C)=∑j=0finiteajbnj:aj∈C,where C=bn−1{0,1,⋯,b−1}. In this paper, we give some conditions on τ∈Z under which the scaling set τΛ(bn,C) is also a spectrum of μbn,D.

Date: 2019
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