Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions

被引：0
作者：
O. L. Vinogradov
机构：
[1] St. Petersburg State University,
来源：
Siberian Mathematical Journal | 2017年 / 58卷
关键词：
inequalities of Akhiezer–Kreĭn–Favard type; entire function of exponential type; convolution;
D O I：
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中图分类号：
学科分类号：
摘要：
We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol’skiĭ-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.
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页码：190 / 204
页数：14
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