Linear combinations of frames and frame packets
type: Item
instance of: scholarly article
title: Linear combinations of frames and frame packets
zbMATH Open document ID: 0999.42024
DOI: 10.4171/ZAA/1046
author: R. Smith
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-11-21T00:00:00Z
review text: The author finds coefficients \(c_{mn}\) (\(m, n \in Z\)) such that for an arbitrary frame \(\{f_n\}_{n \in Z}\) the set of vectors \(\{\varphi_m\}_{m \in Z} = \{\sum_{n \in Z} c_{mn}f_n\}_{m \in Z}\) will again be a frame. Appropriate coefficients can always be chosen as function values \(c_{mn} = g({n \over \beta}-m\alpha)\), where \(g\) belongs to a broad class of functions generating a Gabor frame \(\{E_{\beta m}T_{\alpha n}g\}_{m, n \in Z}\) for \(L^2(R)\). He also proves a version of the splitting trick, which allows for the construction of a large family of frames based on a single (wavelet or Gabor) frame.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1747391
zbMATH Keywords: wavelets
zbMATH Keywords: frame packets
zbMATH Keywords: Gabor frames
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1046
OpenAlex ID: W2007844963
description: scientific article; zbMATH DE number 1747391