Spectrality of Moran-Type Bernoulli Convolutions
Spectrality of Moran-Type Bernoulli Convolutions
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DOI：
10.1007/s40840-023-01532-z
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发表时间：
2023-06
影响因子：
1.2
通讯作者：
Qi-Rong Deng;Mingtian Li
中科院分区：
文献类型：
--
作者：
Qi-Rong Deng;Mingtian Li
Letbe integers such thatandis bounded. It is proven that the Moran-type Bernoulli convolution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mu :=\delta _{p_1^{-1}\{0,d_1\}}*\delta _{p_1^{-1}p_2^{-1} \{0,d_2\}}*\dots *\delta _{p_1^{-1}\dots p_n^{-1}\{0,d_n\}}*\dots \end{aligned}$$\end{document}is a spectral measure if and only if the numbers of factor 2 in the sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\big \{\frac{p_1p_2\dots p_n}{2d_n}\big \}_{n\ge 1}$$\end{document} are different from each other.
Letbe integers such thatandis bounded. It is proven that the Moran-type Bernoulli convolution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mu :=\delta _{p_1^{-1}\{0,d_1\}}*\delta _{p_1^{-1}p_2^{-1} \{0,d_2\}}*\dots *\delta _{p_1^{-1}\dots p_n^{-1}\{0,d_n\}}*\dots \end{aligned}$$\end{document}is a spectral measure if and only if the numbers of factor 2 in the sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\big \{\frac{p_1p_2\dots p_n}{2d_n}\big \}_{n\ge 1}$$\end{document} are different from each other.