Open Access
May 2017 Generalized shift-invariant systems and approximately dual frames
Ana Benavente, Ole Christensen, María I. Zakowicz
Ann. Funct. Anal. 8(2): 177-189 (May 2017). DOI: 10.1215/20088752-3784315


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.


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Ana Benavente. Ole Christensen. María I. Zakowicz. "Generalized shift-invariant systems and approximately dual frames." Ann. Funct. Anal. 8 (2) 177 - 189, May 2017.


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

zbMATH: 1362.42060
MathSciNet: MR3597156
Digital Object Identifier: 10.1215/20088752-3784315

Primary: 42C15
Secondary: 46E40

Keywords: approximately dual frames , frames , generalized shift-invariant systems

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.8 • No. 2 • May 2017
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