On a certain norm and related applications
type: Item
instance of: scholarly article
title: On a certain norm and related applications
zbMATH Open document ID: 0955.42002
DOI: 10.1007/BF02314638
published in: Mathematical Notes
publication date: 2000-08-17T00:00:00Z
review text: Let \(QC(\mathbb{T})\) be the closure of trigonometrical polynomials with respect to the norm \[ \|f\|_{QC}:= \int^1_0 \Biggl\|\sum^\infty_{k=0} r_k(\omega) \sum_{2^{k-1}\leq |n|< 2^k}\widehat f(n)e^{inx}\Biggr\|_{L_\infty(\mathbb{T})}d\omega, \] where \(\{r_k(\omega)\}^\infty_{k= 0}\) is the Rademacher system. Using this and norms closed to it, the authors accounce several inequalities for trigonometric polynomials and their applications to in order sharp estimates of entropy numbers and Kolmogorov width.
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 1294965
zbMATH Keywords: quasicontinuous functions
zbMATH Keywords: closure
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: Rademacher system
zbMATH Keywords: entropy
zbMATH Keywords: Kolmogorov width
author: B. S. Kashin
author: V. N. Temlyakov
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
cites work: An inequality for trigonometric polynomials and its application for estimating the entropy numbers
cites work: Metric entropy and approximation
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description: scientific article; zbMATH DE number 1294965