Spectrality of certain Moran measures with three-element digit sets
Spectrality of certain Moran measures with three-element digit sets
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DOI：
10.1016/j.jmaa.2017.11.006
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发表时间：
2018-03
影响因子：
1.3
通讯作者：
Zhiyong Wang;Xin-Han Dong;ZONG-SHENG Liu
中科院分区：
文献类型：
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作者：
Zhiyong Wang;Xin-Han Dong;ZONG-SHENG Liu
摘要设dn ={0, a n, b n}={0, 1, 2}(m o D 3), p n∈3z +, n≥1，满足sup n≥1 (a, a, n, |,|, b, n, |) n<∞。众所周知，在弱收敛中存在一个唯一的Borel概率测度μ {p n}，{D n}由以下无限卷积积μ {p n}生成，{D n}= δ p 1−1 d1 δ (p 1 p2)−1 d2⋯。本文给出了指数函数系统{e 2 π i Λ x} Λ∈Λ形成l2 （μ {p n},{D n}）的标准正交基Λ的一些条件。
Abstract Let D n={0, a n, b n}={0, 1, 2}(m o d 3), p n∈ 3 Z+, n≥ 1, satisfy sup n≥ 1 max{| a n|,| b n|} p n<∞. It is well-known that there exists a unique Borel probability measure μ {p n},{D n} generated by the following infinite convolution product μ {p n},{D n}= δ p 1− 1 D 1⁎ δ (p 1 p 2)− 1 D 2⁎⋯ in the weak convergence. In this paper, we give some conditions to ensure that there exists a discrete set Λ such that the exponential function system {e 2 π i λ x} λ∈ Λ forms an orthonormal basis for L 2 (μ {p n},{D n}).