Discretization of linear operators on \(L^p(\mathbb{R}^N)\)
type: Item
instance of: scholarly article
title: Discretization of linear operators on \(L^p(\mathbb{R}^N)\)
zbMATH Open document ID: 0904.47019
published in: Illinois Journal of Mathematics
publication date: 1999-01-19T00:00:00Z
review text: We study conditions on a pair of functions \(\varphi\) and \(\phi\) in \(L^2(\mathbb{R}^N)\) so that the following condition holds: Any linear operator \(T\) is bounded on \(L^p(\mathbb{R}^N)\) if and only if the operators \(\widetilde T_k\) associated to the matrices \[ (\langle 2^{kN/p}T(\varphi(2^k\cdot- n)), 2^{kN/p'}\phi(2^k\cdot- m)\rangle)_{n,m}, \] are bounded on \(\ell^p(\mathbb{Z}^N)\) uniformly in \(k\in\mathbb{Z}\). We work under the restriction \(\text{supp }\widehat\varphi\) and \(\text{supp }\widehat\phi\subset (-1,1)^N\) and \(1< p<\infty\). We will also study some connections with multiresolution analysis on \(L^p(\mathbb{R}^N)\).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 1190783
zbMATH Keywords: discretization
zbMATH Keywords: multiresolution analysis
author: María J. Carro
reviewed by: María J. Carro
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1190783