Simultaneous approximation from PSI spaces
type: Item
instance of: scholarly article
title: Simultaneous approximation from PSI spaces
zbMATH Open document ID: 0821.41019
author: Kang Zhao
published in: Journal of Approximation Theory
publication date: 1995-05-18T00:00:00Z
review text: For a principal shift invariant space \(S (\varphi)\), generated by \(\varphi \in W_ 2^ m (\mathbb{R}^ s)\), a necessary and sufficient condition is found for determining whether \(S (\varphi)\) provides simultaneous approximation of order \((m,k)\). For a certain type of generating function \(\varphi\) it is proved that this necessary and sufficient condition is equivalent to the existence of a constant \(c\) such that \(| \widehat \varphi (\cdot + 2 \pi \beta) | \leq c | \cdot |^ k | \widehat \varphi |\) for all \(\beta \in \mathbb{Z}^ s \backslash \{0\}\) on a neighborhood of the origin.
Mathematics Subject Classification ID: 41A28
zbMATH DE Number: 756612
zbMATH Keywords: Strang-Fix conditions
zbMATH Keywords: principal shift invariant space
reviewed by: Herbert Stahl
MaRDI profile type: Publication
full work available at URL: jath.1995.1042
OpenAlex ID: W1983177734
DOI: 10.1006/JATH.1995.1042
description: scientific article; zbMATH DE number 756612