Frames and pseudo-inverses
type: Item
instance of: scholarly article
title: Frames and pseudo-inverses
zbMATH Open document ID: 0845.47002
author: Ole Christensen
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-03-31T00:00:00Z
review text: A family \(\{f_i \}_{i\in I}\) in an infinite-dimensional Hilbert space \({\mathcal H}\) is called a Bessel sequence if \(\forall_{f\in {\mathcal H}} \sum_{i\in I} |\langle f,f_i \rangle|^2< \infty\). A Bessel sequence \(\{f_i \}_{i\in I}\) is called a frame if \[ \exists A>0:\;A|f|^2\leq \sum_{i\in I}|\langle f,f_i \rangle|^2, \qquad \forall f\in {\mathcal H}. \] There are studied connections between the frame theory and the theory of pseudo-inverse operators (i.e. Moore-Penrose inverses). According to the author, the frame theory is now a very useful tool in the wavelet theory.
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 861771
zbMATH Keywords: Bessel sequence
zbMATH Keywords: frame
zbMATH Keywords: pseudo-inverse operators
zbMATH Keywords: Moore-Penrose inverses
zbMATH Keywords: wavelet theory
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1363
OpenAlex ID: W2057935334
DOI: 10.1006/JMAA.1995.1363
description: scientific article; zbMATH DE number 861771