``Compactly'' supported frames for spaces of distributions on the ball
type: Item
instance of: scholarly article
title: ``Compactly'' supported frames for spaces of distributions on the ball
zbMATH Open document ID: 1239.42024
published in: Monatshefte für Mathematik
publication date: 2012-03-23T00:00:00Z
review text: The authors study the problem of the construction of multiscale frames on the unit ball \(B^d\) in \(\mathbb R^d\) consisting of the \(C^{\infty}\) functions with small supports which shrink at higher scales. The construction relies on a general scheme for construction of frames from [the authors, J. Funct. Anal. 257, No. 7, 2159--2187 (2009; Zbl 1179.42025)] and frames called ``needlets'' for weighted Triebel-Lizorkin and Besov spaces on \(B^d\) developed by the authors and \textit{Y. Xu} [Proc. Lond. Math. Soc. (3) 97, No. 2, 477--513 (2008; Zbl 1153.41004)] and \textit{P. Petrushev} and \textit{Y. Xu} [Constr. Approx. 27, No. 2, 121--148 (2008; Zbl 1213.42153)]. The authors construct frames that can be used to decompose weighted Triebel-Lizorkin and Besov spaces on \(B^d\) with weight \(w_{\mu}(x) := (1-|x|^2)^{\mu - 1/2}\), \(\mu\) half integer and nonnegative.
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6018282
zbMATH Keywords: weighted Triebel-Lizorkin spaces
zbMATH Keywords: Besov spaces
zbMATH Keywords: frames
zbMATH Keywords: needlets
zbMATH Keywords: decomposition
author: G. Kyriazis
author: Pencho Petrushev
MaRDI profile type: Publication
full work available at URL: s00605-011-0291-7
OpenAlex ID: W2094778136
cites work: Q5824493
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DOI: 10.1007/S00605-011-0291-7
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description: scientific article; zbMATH DE number 6018282