Classification of spectral self-similar measures with four-digit elements

2022/09/12 by An, Li-Xiang, He, Xinggang, Lai, Chun-Kit
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2209.05619

Abstract

Let μ be a self-similar measure generated by iterated function system of four maps of equal contraction ratio 0<ρ<1. We study when μ is a spectral measure which means that it admits an exponential orthonormal basis \e^{2πi λx}\_λ∈Λ in L²(μ). By combining previous results of many authors and a careful study of some new cases, we completely classify all spectral self-similar measures with four maps. Moreover, the case allows us to propose a modified Łaba-Wang conjecture concerning when the self-similar measures are spectral in general cases.

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