Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 2 (2017), 177-189.
Generalized shift-invariant systems and approximately dual frames
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.
Ann. Funct. Anal., Volume 8, Number 2 (2017), 177-189.
Received: 25 May 2016
Accepted: 12 August 2016
First available in Project Euclid: 14 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42C15: General harmonic expansions, frames
Secondary: 46E40: Spaces of vector- and operator-valued functions
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