%0 Journal Article
%T Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance
%A Romain Tessera
%A Haichao Wang
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1111.3990v2