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arXiv · 1111.3990

Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance

Romain Tessera·Haichao Wang
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Abstract

We consider finitely generated shift-invariant spaces (SIS) with additional invariance in $L^2(\R^d)$. 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 $L^2(\R)$ whose generator and its translates form a Riesz basis.

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Romain Tessera, Haichao Wang. 2011-11-16. Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance. https://arxiv.org/abs/1111.3990

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