On Eigenmeasures Under Fourier Transform

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1007/s00041-023-10045-z

Michael Baake, Timo Spindeler, Nicolae Strungaru

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Abstract

Abstract Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $$\mathbb {R}\hspace{0.5pt}^d$$ R d . In particular, we classify all periodic eigenmeasures on $$\mathbb {R}\hspace{0.5pt}$$ R , which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on $$\mathbb {R}\hspace{0.5pt}$$ R with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodic Meyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around 0.

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傅里叶变换下的特征测度

摘要:本文描述了几类调质测度，它们是傅里叶变换的特征测度，后者被看作是$$\mathbb {R}\hspace{0.5pt}^d$$ R d上Radon测度(通常是无界的)的线性算子。特别地，我们对$$\mathbb {R}\hspace{0.5pt}$$ R上的所有周期特征测度进行了分类，它给出了与离散傅里叶变换及其特征向量的有趣联系，以及具有一致离散支持的$$\mathbb {R}\hspace{0.5pt}$$ R上的所有特征测度。后者的一个有趣的子类出现在非周期Meyer集的经典切割和投影方法中。最后，我们构造了一大类具有局部有限支持的特征测度，它不是一致离散的，并且在0附近有很大的间隙。

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.