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

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

2011-11-16

arxiv.org/abs/1111.3990v1

Mathematics

Functional Analysis

12 pages

Scientific paper

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. For instance, if the finitely generated SIS is translation-invariant then at least one of its generators is non-integrable. On the other hand we show that at least a portion of the generators can be chosen in $L^1(\R^d)$. Pointwise estimate and other weighted norm estimates are also shown. 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.

Affiliated with

Also associated with

No associations

Rating

Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-349062