Approximation by Modified Generalized Sampling Series

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-30 DOI:10.1007/s00009-024-02653-w

Metin Turgay, Tuncer Acar

引用次数: 0

Abstract

In the present paper, we introduce a new family of sampling operators, so-called “modified sampling operators”, by taking a function \(\rho \) that satisfies the suitable conditions, and we study pointwise and uniform convergence of the family of newly introduced operators. We give the rate of convergence of the family of operators via classical modulus of continuity. We also obtain an asymptotic formula in the sense of Voronovskaja. Moreover, we investigate the approximation properties of modified sampling operators in weighted spaces of continuous functions characterized by \(\rho \) function. Finally, we present examples of some kernels that satisfy the appropriate assumptions. At the end, we present some graphical and numerical representations by comparing the modified sampling operators and the classical sampling operators.

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修正广义抽样序列的近似值

在本文中，我们通过取满足适当条件的函数 \(\rho \) 引入了一个新的采样算子族，即所谓的 "修正采样算子"，并研究了新引入算子族的点收敛性和均匀收敛性。我们通过经典的连续性模数给出了算子族的收敛率。我们还得到了沃罗诺夫斯卡娅意义上的渐近公式。此外，我们还研究了连续函数加权空间中以 \(\rho \) 函数为特征的修正采样算子的近似性质。最后，我们举例说明了一些满足相应假设的核。最后，我们通过比较修正采样算子和经典采样算子，给出了一些图形和数值表示。

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.