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Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional
invariance
Published Web Location
https://arxiv.org/pdf/1111.3990.pdfNo data is associated with this publication.
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.