Average \(n\)-widths of the Wiener space in the \(L_ \infty\)-norm
type: Item
instance of: scholarly article
title: Average \(n\)-widths of the Wiener space in the \(L_ \infty\)-norm
zbMATH Open document ID: 0811.46039
published in: Journal of Complexity
publication date: 1993-08-24T00:00:00Z
review text: Let \(w\) denote the Wiener measure on \(C= C[ 0,1]\). The average \(n\)-width of \((C,w)\) in \(L_ q[ 0,1]\) \((1\leq q\leq\infty)\) is defined by \[ d_ n(C,w,L_ q)= \inf_ X \int_ C \inf_{y\in X} \| x-y\|_{L_ q} w(dx), \] where \(X\) runs through all linear subspaces of \(L_ q\) with \(\dim X\leq n\). For \(1\leq q<\infty\) the author proved in two earlier papers that \[ d_ n(C, w,L_ q) \asymp n^{-1/2}. \] In the present paper it is shown that this asymptotic formula is also valid for the case \(q=\infty\).
reviewed by: Egbert Dettweiler
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 370451
zbMATH Keywords: \(L_ p\)-space
zbMATH Keywords: Wiener measure
zbMATH Keywords: average \(n\)-width
zbMATH Keywords: asymptotic formula
author: Vitaly Maiorov
MaRDI profile type: Publication
full work available at URL: jcom.1993.1015
OpenAlex ID: W2022543427
DOI: 10.1006/JCOM.1993.1015
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description: scientific article; zbMATH DE number 370451