论区间 $$[-1,1]$$ 上广义 Lipschitz 类的傅立叶-邓克尔系数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-05 DOI:10.1007/s00009-024-02710-4

Othman Tyr

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引用次数: 0

摘要

在本文中，我们认为 $\mathcal {E}$ 是包含在区间 $I=[-1,1]$上的所有具有紧凑支持的无穷微分函数的集合。我们用 $\mathcal {E}$ 中的分布作为工具来证明邓克尔算子和邓克尔平移的连续性。我们还验证了与邓克尔算子相关的平滑模量的一些性质。通过 Dunkl-Sobolev 空间上的广义 Dunkl-Lipschitz 条件，作为特例推导出了 Younis 在环上的一个结果，它是 Titchmarsh 定理的类似物。此外，还根据傅里叶-敦克尔系数的行为推导出了 I 上 Dini-Lipschitz 类的某些条件和特征。

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On the Fourier–Dunkl Coefficients of Generalized Lipschitz Classes on the Interval $$[-1,1]$$

In this paper, we consider $\mathcal {E}$ the set of all infinitely differentiable functions with compact support included on the interval $I=[-1,1]$. We use the distributions in $\mathcal {E}$, as a tool to prove the continuity of the Dunkl operator and the Dunkl translation. Some properties of the modulus of smoothness related to the Dunkl operator are verified. By means of generalized Dunkl–Lipschitz conditions on Dunkl–Sobolev spaces, a result of Younis on the torus, which is an analog of Titchmarsh’s theorem, is deduced as a special case. In addition, certain conditions and a characterization of the Dini–Lipschitz classes on I in terms of the behavior of their Fourier–Dunkl coefficients are derived.

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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.