\(n\)-widths of \(H^ p\)-spaces in \(L_ p(-1,1)\)
type: Item
instance of: scholarly article
title: \(n\)-widths of \(H^ p\)-spaces in \(L_ p(-1,1)\)
zbMATH Open document ID: 0803.46056
DOI: 10.1016/0885-064X(92)90029-B
author: Klaus Wilderotter
published in: Journal of Complexity
publication date: 1993-01-17T00:00:00Z
review text: Kolmogorov \(n\)-widths \(d_ n\), Gel'fand \(n\)-widths \(d^ n\), and linear \(n\)-widths \(\delta_ n\) of the Hardy spaces \(H^ p\) in \(L_ q(-1,1)\) are estimated. For \(1\leq q< p\leq \infty\) and some constants \(k_ 1\), \(k_ 2\) the inequality \[ \begin{aligned} k_ 1 & n^{(1/2)(1/q-1/p)}\exp\left(- \pi\sqrt{{n\over 2}\Bigl({1\over q}-{1\over p}\Bigr)}\right)\\ & \leq d_ n(H^ p,L_ q(-1, 1)),\;d^ n(H^ p, L_ q(-1,1)),\;\delta_ n(H^ p, L_ q(-1,1))\\ & \leq k_ 2 n^{1/2q} \exp\left(- \pi \sqrt{{n\over 2}\Bigl({1\over q}- {1\over p}\Bigr)}\right).\end{aligned} \] is shown among others.
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 97385
zbMATH Keywords: Kolmogorov \(n\)-widths
zbMATH Keywords: Gel'fand \(n\)-widths
zbMATH Keywords: linear \(n\)-widths
zbMATH Keywords: Hardy spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97385