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

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI:10.1007/s00041-024-10106-x

István Blahota, György Gát

引用次数: 0

Abstract

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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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

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。

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来源期刊

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications

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