某些二维矩形沃尔什-傅里叶级数的矩阵变换手段的后继逼近

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-05 DOI:10.1007/s00041-024-10106-x

István Blahota, György Gát

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引用次数: 0

摘要

本文讨论了在\(L^p(G^{2})\)空间(\(1\le p <\infty \))和\(C(G^{2})\)中通过矩阵变换逼近某些二维矩形（对角线递减）沃什-傅里叶级数的特殊部分和的速率。在某些特殊情况下，它意味着规范收敛。我们还展示了我们的结果在 Lipschitz 函数中的应用。在本文的最后，我们展示了最重要的结果，即几乎无处不在的收敛定理。我们注意到 T 求和是以下已知求和方法的通用概括：Cesàro、Weierstrass、Riesz 和 Picar 以及 Bessel 方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series

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Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series

In the present paper we discuss the rate of the approximation by the matrix transform of special partial sums of some two-dimensional rectangle (decreasing diagonal) Walsh-Fourier series in \(L^p(G^{2})\) space (\(1\le p <\infty \)) and in \(C(G^{2})\). It implies in some special case

norm convergence. We also show an application of our results for Lipschitz functions. At the end of the paper we show the most important result, the almost everywhere convergence theorem. We note that T summation is a common generalization of the following known summation methods Cesàro, Weierstrass, Riesz and Picar and Bessel methods.

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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.