Annals of Functional Analysis

Generalized shift-invariant systems and approximately dual frames

Ana Benavente, Ole Christensen, and María I. Zakowicz

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Abstract

Dual pairs of frames yield a procedure for obtaining perfect reconstruction of elements in the underlying Hilbert space in terms of superpositions of the frame elements. However, practical constraints often force us to apply sequences that do not exactly form dual frames. In this article, we consider the important case of generalized shift-invariant systems and provide various ways of estimating the deviation from perfect reconstruction that occur when the systems do not form dual frames. The deviation from being dual frames will be measured either in terms of a perturbation condition or in terms of the deviation from equality in the duality conditions.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 2 (2017), 177-189.

Dates
Received: 25 May 2016
Accepted: 12 August 2016
First available in Project Euclid: 14 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1484363069

Digital Object Identifier
doi:10.1215/20088752-3784315

Mathematical Reviews number (MathSciNet)
MR3597156

Zentralblatt MATH identifier
1362.42060

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 46E40: Spaces of vector- and operator-valued functions

Keywords
approximately dual frames frames generalized shift-invariant systems

Citation

Benavente, Ana; Christensen, Ole; Zakowicz, María I. Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal. 8 (2017), no. 2, 177--189. doi:10.1215/20088752-3784315. https://projecteuclid.org/euclid.afa/1484363069


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