Existence of Exponential Orthonormal Bases for Infinite Convolutions on $${{\mathbb {R}}}^n$$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-07 DOI:10.1007/s00041-024-10088-w

Yan-Song Fu, Min-Wei Tang

引用次数: 0

Abstract

In this paper we investigate the harmonic analysis of infinite convolutions generated by admissible pairs on Euclidean space ${{\mathbb {R}}}^n$. Our main results give several sufficient conditions so that the infinite convolution $\mu $ to be a spectral measure, that is, its Hilbert space $L^2(\mu )$ admits a family of orthonormal basis of exponentials. As a concrete application, we give a complete characterization on the spectral property for certain infinite convolution on the plane ${{\mathbb {R}}}^2$ in terms of admissible pairs.

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$${{mathbb {R}}^n$ 上无限卷积的指数正则基的存在性

在本文中，我们研究了欧几里得空间 ${{\mathbb {R}}^n$ 上的可容许对产生的无限卷积的谐波分析。）我们的主要结果给出了几个充分条件，使得无限卷积（\mu \）成为一个谱度量，即它的希尔伯特空间（L^2(\mu )\）承认一个正交指数基的族。作为一个具体的应用，我们给出了平面 ${{\mathbb {R}}^2$ 上某些无限卷积在可容许对上的谱性质的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.