Uncertainty principles in finitely generated shift-invariant spaces with additional invariance

Romain Tessera; Haichao Wang

doi:10.1016/j.jmaa.2013.07.077

Uncertainty principles in finitely generated shift-invariant spaces with additional invariance

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Abstract

We consider finitely generated shift-invariant spaces (SIS) with additional invariance in L2(Rd). We prove that if the generators and their translates form a frame, then they must satisfy some stringent restrictions on their behavior at infinity. Part of this work (non-trivially) generalizes recent results obtained in the special case of a principal shift-invariant spaces in L2(R) whose generator and its translates form a Riesz basis.

Original language	English
Pages (from-to)	134-143
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	410
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.07.077
Publication status	Published - 1 Feb 2014
Externally published	Yes

Keywords

Additional invariance
Finitely generated shift-invariant spaces
Frame
Uncertainty principle

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10.1016/j.jmaa.2013.07.077

Cite this

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AB - We consider finitely generated shift-invariant spaces (SIS) with additional invariance in L2(Rd). We prove that if the generators and their translates form a frame, then they must satisfy some stringent restrictions on their behavior at infinity. Part of this work (non-trivially) generalizes recent results obtained in the special case of a principal shift-invariant spaces in L2(R) whose generator and its translates form a Riesz basis.

KW - Additional invariance

KW - Finitely generated shift-invariant spaces

KW - Frame

KW - Uncertainty principle

U2 - 10.1016/j.jmaa.2013.07.077

DO - 10.1016/j.jmaa.2013.07.077

M3 - Article

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SP - 134

EP - 143

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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Uncertainty principles in finitely generated shift-invariant spaces with additional invariance

Abstract

Keywords

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