Let $\{b_n\}_{n=1}^{\infty }$ be a sequence of integers larger than 1. We will study the harmonic analysis of the equal-weighted Moran measures $\mu _{\{b_n\},\{{\mathcal D}_n\}}$ with ${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$, where $q_n$ divides $b_n$ for all $n\geq 1.$ In this paper, we first characterize all the maximal orthogonal sets of $L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$ via a tree mapping. By this characterization, we give some sufficient conditions for the maximal orthogonal set to be an orthonormal basis.

中文翻译：

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具有连续数字的谱莫兰测度谱的树结构

令$\{b_n\}_{n=1}^{\infty }$为大于 1 的整数序列。我们将研究等权莫兰测度$\mu _{\{b_n\的调和分析},\{{\mathcal D}_n\}}$与${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$，其中$q_n$除以$b_n$为所有$n\geq 1.$在本文中，我们首先通过以下方式表征$L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$的所有最大正交集树映射。通过这个表征，我们给出了最大正交集作为正交基的一些充分条件。