New characterizations of Riesz bases
type: Item
instance of: scholarly article
title: New characterizations of Riesz bases
zbMATH Open document ID: 0902.42015
author: Hong Oh Kim
author: Jae Kun Lim
published in: Applied and Computational Harmonic Analysis
publication date: 1998-11-29T00:00:00Z
review text: Using the projection method for frames [\textit{O. Christensen}, Appl. Comput. Harmon. Anal. 1, No. 1, 50-53 (1993; Zbl 0849.42025)] this paper gives two equivalent conditions for a frame to be a Riesz basis in a separable Hilbert space. These conditions emerge from taking the limit in a sequence of nested finite dimensional subspaces. As a bonus, expressions for the Riesz bounds are obtained by taking the limit for the Riesz bounds of the finite dimensional subspaces. These can be expressed in terms of the largest and smallest eigenvalues of the Gram matrix of these subspaces.
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1038811
zbMATH Keywords: frames
zbMATH Keywords: Riesz basis
zbMATH Keywords: Riesz bounds
zbMATH Keywords: projection method
zbMATH Keywords: eigenvalues
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
OpenAlex ID: W2084899942
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cites work: Q4340096
cites work: Q3955832
DOI: 10.1006/ACHA.1997.0210
description: scientific article; zbMATH DE number 1038811