Wavelets and quasiasymptotics at a point
type: Item
instance of: scholarly article
title: Wavelets and quasiasymptotics at a point
zbMATH Open document ID: 0928.42021
author: Arpad Takači
author: Stevan Pilipović
author: Nenad Teofanov
published in: Journal of Approximation Theory
publication date: 1999-12-15T00:00:00Z
review text: Let \(\{V_j\), \(j \in {\mathbb Z}\}\) be a MRA of the space \(L^2({\mathbb R})\), \(h\) a tempered distribution, and \(h_j\) its projection to \(V_j\), \(j \in {\mathbb Z}\). The authors prove that if \(h\) has a quasiasymptotic behavior at zero related to a regularly varying function, then so does each \(h_j\), \(j \in {\mathbb Z}\), and also prove, with an additional condition, the converse statement.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1286387
zbMATH Keywords: wavelets
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: tempered distributions
zbMATH Keywords: quasiasymptotic behavior
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
full work available at URL: jath.1997.3242
OpenAlex ID: W1999409851
cites work: Orthonormal bases of compactly supported wavelets
cites work: Pointwise convergence of wavelet expansions
cites work: Sur la valeur et la limite d'une distribution en un point
cites work: Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
cites work: Q3135829
cites work: Q3995396
cites work: Q4379590
cites work: Regularly varying functions
cites work: Q4040022
cites work: Q4888818
DOI: 10.1006/JATH.1997.3242
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description: scientific article; zbMATH DE number 1286387