一类Moran测度的无穷正交指数

IF 0.6 4区数学 Q3 MATHEMATICS

International Journal of Mathematics Pub Date : 2023-10-11 DOI:10.1142/s0129167x23500908

Sha Wu, Jing-Cheng Liu

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引用次数: 0

摘要

对于一个用[公式:见文]展开矩阵的序列[公式:见文]和一个用[公式:见文]展开矩阵的序列[公式:见文]和一个用[公式:见文]展开有限数集的序列[公式:见文]，Moran测度[公式:见文]是由无穷卷积[公式:见文]定义的，收敛性是弱意义的。在一些附加的假设下，我们证明[公式:见文]包含一个无限正交的指数函数集，当且仅当[公式:见文]存在一个无限子序列[公式:见文]，使得[公式:见文]对于任何[公式:见文]，其中[公式:见文]。这扩展了[J]。李磊，有限的一个充要条件[公式:见文]-正交性，科学。中国数学，58(2015)2541-2548。

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Infinite Orthogonal Exponentials for a Class of Moran Measures

For a sequence [Formula: see text] of expanding matrices with [Formula: see text] and a sequence [Formula: see text] of finite digit sets with [Formula: see text], the Moran measure [Formula: see text] is defined by the infinite convolution [Formula: see text] and the convergence is in the weak sense. Under some additional assumptions, we show that [Formula: see text] contains an infinite orthogonal set of exponential functions if and only if there exists an infinite subsequence [Formula: see text] of [Formula: see text] such that [Formula: see text] for any [Formula: see text], where [Formula: see text]. This extends the results of [J. L. Li, A necessary and sufficient condition for the finite [Formula: see text]-orthogonality, Sci. China Math. 58 (2015) 2541–2548].

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来源期刊

International Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.