On the Fourier orthonormal bases of Cantor-Moran measures

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• 作者：Liu He ^{heliu_2014@163.com} ; Xing-Gang He ; ^{xingganghe@163.com}
• 关键词：28A80 ; 42A16 ; 42A85 ; 42C05
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：272
• 期：5
• 页码：1980-2004
• 全文大小：439 K
• 卷排序：272

文摘

Let {dn,pn}n=1∞ be a sequence of integers so that 0<dn<pn0<dn<pn for n≥1n≥1. The infinite convolution of probability measures with finite support and equal distributionμ{pn},{dn}:=δp1−1{0,d1}⁎δ(p1p2)−1{0,d2}⁎⋯ is a Borel probability measure (Cantor–Moran measure). In this paper we study the existence of Fourier basis for L2(μ{pn},{dn})L2(μ{pn},{dn}), i.e., find a discrete set Λ such that EΛ={e−2πiλx:λ∈Λ}EΛ={e−2πiλx:λ∈Λ} is an orthonormal basis for L2(μ{pn},{dn})L2(μ{pn},{dn}). We give some sufficient conditions for this aim and some examples to explain the theory.