Optimal recovery of derivatives of Hardy class functions

Author:

Ovchintsev Mikhail

Abstract

The paper considers the best linear method for approximating the values of derivatives of Hardy class functions in the unit circle at zero according to the information about the values of functions at a finite number of points z1,...,zn that form a regular polygon, and also the error of the best method is obtained. The introduction provides the necessary concepts and results from the papers of K.Yu. Osipenko. Some results of the studies of S.Ya. Khavinson and other authors are also mentioned here. The main section consists of two parts. In the first part of the second section, the research method is disclosed, namely, the error of the best method for approximating the derivatives at zero according to the information about the values of functions at the points z1,...,zn is calculated; the corresponding extremal function is written out. It is established that for p>1, the corresponding extremal function is unique up to a constant factor that is equal to one in modulus. For p=1, the corresponding extremal function is not unique. All such corresponding extremal functions are determined here. In the second part of the second section, it is proved that for all p (1≤p<∞), the best linear approximation method is unique, and the coefficients of the best linear recovery method are calculated. The expressions used to calculate the coefficients are greatly simplified. At the end of the paper, the obtained results are described, and possible areas for further research are indicated.

Publisher

EDP Sciences

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3