Localization of frames. II
type: Item
instance of: scholarly article
title: Localization of frames. II
zbMATH Open document ID: 1061.42016
author: Elena Cordero
author: Karlheinz Gröchenig
published in: Applied and Computational Harmonic Analysis
publication date: 2004-08-06T00:00:00Z
review text: In his paper [``Localization of frames, Banach frames, and the invertibility of the frame operator'', J. Fourier Anal. Appl. 10, No. 2, 105--132 (2004; Zbl 1055.42018)], \textit{K. Gröchenig} introduced the concept of localization of frames. One of the main features of this concept is that it leads to ``automatic expansion'' of the frame expansion in a Hilbert space to an expansion in a large class of associated Banach spaces. In the present paper, this theory is extended to certain quasi-Banach spaces (Besov spaces). This plays a role, e.g., in nonlinear approximation theory. It is proved that for localized frames, the iterative frame algorithm converges in the norm of the associated Banach spaces.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 46E99
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 2081609
zbMATH Keywords: frame
zbMATH Keywords: Banach frame
zbMATH Keywords: quasi-Banach space
zbMATH Keywords: Jaffard lemma
zbMATH Keywords: nonlinear approximation
zbMATH Keywords: shift-invariant space
zbMATH Keywords: wavelet frame
zbMATH Keywords: Besov space
MaRDI profile type: Publication
full work available at URL: j.acha.2004.02.002
OpenAlex ID: W2092260933
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DOI: 10.1016/J.ACHA.2004.02.002
description: scientific article; zbMATH DE number 2081609