Generalized shift-invariant systems and approximately dual frames

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Generalized shift-invariant systems and approximately dual frames. / Benavente, Ana; Christensen, Ole; Zakowicz, Maria I.

In: Annals of Functional Analysis, Vol. 8, No. 2, 2017, p. 177-189.

Research output: Contribution to journalJournal article – Annual report year: 2017Researchpeer-review

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Benavente, Ana ; Christensen, Ole ; Zakowicz, Maria I. / Generalized shift-invariant systems and approximately dual frames. In: Annals of Functional Analysis. 2017 ; Vol. 8, No. 2. pp. 177-189.

Bibtex

@article{23ce3de019584ef29d9be8b7a437f3e9,
title = "Generalized shift-invariant systems and approximately dual frames",
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.",
author = "Ana Benavente and Ole Christensen and Zakowicz, {Maria I.}",
year = "2017",
doi = "10.1215/20088752-3784315",
language = "English",
volume = "8",
pages = "177--189",
journal = "Annals of Functional Analysis",
issn = "2008-8752",
publisher = "Tusi Mathematical Research Group",
number = "2",

}

RIS

TY - JOUR

T1 - Generalized shift-invariant systems and approximately dual frames

AU - Benavente, Ana

AU - Christensen, Ole

AU - Zakowicz, Maria I.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

U2 - 10.1215/20088752-3784315

DO - 10.1215/20088752-3784315

M3 - Journal article

VL - 8

SP - 177

EP - 189

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

SN - 2008-8752

IS - 2

ER -