一种快速收敛的采样算子

IF 1.1 Q1 MATHEMATICS

Constructive Mathematical Analysis Pub Date : 2022-12-01 DOI:10.33205/cma.1172005

B. Draganov

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引用次数: 4

摘要

我们构造了一个采样算子，其性质是函数越光滑，其逼近速度越快。我们利用光滑模和$K$-函数在一致范数中建立了其逼近率的直接估计和弱逆估计。还考虑了加权近似的情况。权重为正幂型，非正指数为无穷大。这个采样算子保留了每个代数多项式。

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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A fast converging sampling operator

We construct a sampling operator with the property that the smoother a function is, the faster its approximation is. We establish a direct estimate and a weak converse estimate of its rate of approximation in the uniform norm by means of a modulus of smoothness and a $K$-functional. The case of weighted approximation is also considered. The weights are positive and power-type with non-positive exponents at infinity. This sampling operator preserves every algebraic polynomial.

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来源期刊

Constructive Mathematical Analysis Mathematics-Analysis

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6 weeks