An extremal nonnegative sine polynomial
type: Item
instance of: scholarly article
title: An extremal nonnegative sine polynomial
zbMATH Open document ID: 1051.42001
author: R. Andreani
author: Dimitar K. Dimitrov
published in: Rocky Mountain Journal of Mathematics
publication date: 2004-05-27T00:00:00Z
review text: In this attractive paper the authors prove five pleasant theorems. Their synopsis is given in the abstract as follows: ``For any positive integer \(n\), the sine polynomials that are nonnegative in \([0,\pi]\) and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials \(K_n(\theta)\) are constructed in such a way that \(\{K_n (\theta)\}\) is a summability kernel. Thus, for each \(p\), \(1\leq p\leq \infty\), and for any \(2\pi\)-periodic function \(f\in L_p[-\pi,\pi]\), the sequence of convolutions \(K_n*f\) is proved to converge to \(f\) in \(L_p[-\pi,\pi]\). The pointwise and almost everywhere convergences are also consequences of our construction''.
reviewed by: László Leindler
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 26D05
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 2067048
zbMATH Keywords: convergence
zbMATH Keywords: sine polynomials
zbMATH Keywords: cosine polynomials
zbMATH Keywords: summability kernel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069926
OpenAlex ID: W2081032493
cites work: Special conformal mappings
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cites work: On multipliers preserving convergence of trigonometric series almost everywhere
DOI: 10.1216/RMJM/1181069926
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description: scientific article; zbMATH DE number 2067048