改良高斯-魏尔斯特拉斯奇异积分在加权空间中的逼近特性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.1186/s13660-024-03171-9

Abhay Pratap Singh, Uaday Singh

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引用次数: 0

摘要

奇异积分算子在近似理论和谐波分析中发挥着重要作用。在本文中，我们考虑了一个加权的 Lebesgue 空间 $L^{p,w}$，在其上定义了一个修正的高斯-韦尔斯特拉斯奇异积分，并研究了该算子的直接和反向逼近性质，随后针对函数 $f\in L^{p,w}$ 提出了一个 Korovkin 型逼近定理。我们使用函数的连续性模量来衡量收敛速度。

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Approximation properties of a modified Gauss–Weierstrass singular integral in a weighted space

Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $f\in L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.

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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.