Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions
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 passa...
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| Veröffentlicht in: | Siberian mathematical journal 2017-03, Vol.58 (2), p.190-204 |
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| container_title | Siberian mathematical journal |
| container_volume | 58 |
| creator | Vinogradov, O. L. |
| description | 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. |
| doi_str_mv | 10.1134/S0037446617020021 |
| format | Article |
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L.</creatorcontrib><title>Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions</title><title>Siberian mathematical journal</title><addtitle>Sib Math J</addtitle><description>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. 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L.</creatorcontrib><collection>CrossRef</collection><jtitle>Siberian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vinogradov, O. L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions</atitle><jtitle>Siberian mathematical journal</jtitle><stitle>Sib Math J</stitle><date>2017-03-01</date><risdate>2017</risdate><volume>58</volume><issue>2</issue><spage>190</spage><epage>204</epage><pages>190-204</pages><issn>0037-4466</issn><eissn>1573-9260</eissn><abstract>We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. 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| ispartof | Siberian mathematical journal, 2017-03, Vol.58 (2), p.190-204 |
| issn | 0037-4466 1573-9260 |
| language | eng |
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| subjects | Convolution Entire functions Estimates Inequalities Kernels Mathematics Mathematics and Statistics Test procedures |
| title | Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions |
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