Wavelets of Y. Meyer. -- An optimal basis in \(C(0,1)\)
type: Item
instance of: scholarly article
title: Wavelets of Y. Meyer. -- An optimal basis in \(C(0,1)\)
zbMATH Open document ID: 0807.42022
DOI: 10.1007/BF01236624
published in: Mathematical Notes
publication date: 1994-07-21T00:00:00Z
review text: Let \(k\) be a non-negative integer. The basis in the space \(C(0,1)\) of continuous 1-periodic functions is called \(k\)-optimal if for any \(m\in N\) and any \(f\in C(0,1)\), \[ \| f- S_ m(f)\|_ C\leq A_ k \omega_{k+1}\left(\textstyle{{1\over m}},f\right). \] Here \(S_ m(f)\) is the \(m\)-partial sum, \(\omega_ \ell(\delta,f)\) is the \(\ell\)th modulus of continuity. The author has proved that the system of Meyer wavelets is a \(k\)-optimal basis for all \(k\) simultaneously.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 578694
zbMATH Keywords: optimal basis
zbMATH Keywords: Meyer wavelets
author: I. Ya. Novikov
MaRDI profile type: Publication
cites work: Q3276774
cites work: Q3257254
cites work: On Schauder system series
cites work: Constructive function theory and spline systems
cites work: Q5644548
cites work: Q3254471
full work available at URL: https://doi.org/10.1007/bf01236624
OpenAlex ID: W2015229276
description: scientific article; zbMATH DE number 578694