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.

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