Gabor-type Frames from Generalized Weyl-Heisenberg Groups

Details Gabor-type Frames from Generalized Weyl-Heisenberg Groups Gabor-type Frames from Generalized Weyl-Heisenberg Groups

2005-10-15

arxiv.org/abs/math-ph/0510053v1

Physics

Mathematical Physics

22 pages

Scientific paper

We present in this paper a construction for Gabor-type frames built out of generalized Weyl-Heisenberg groups. These latter are obtained via central extensions of groups which are direct products of locally compact abelian groups and their duals. Our results generalize many of the results, appearing in the literature, on frames built out of the Schr\"odinger representation of the standard Weyl-Heisenberg group. In particular, we obtain a generalization of the result in \cite{PO}, in which the product $ab$ determines whether it is possible for the Gabor system $\{E_{mb}T_{na}g \}_{m,n\in \mathbb Z}$ to be a frame for $L^2(\mathbb R)$. As a particular example of the theory, we study in some detail the case of the generalized Weyl-Heisenberg group built out of the $d$-dimensional torus. In the same spirit we also construct generalized shift-invariant systems.

Affiliated with

Also associated with

No associations

Rating

Gabor-type Frames from Generalized Weyl-Heisenberg Groups 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 Gabor-type Frames from Generalized Weyl-Heisenberg Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gabor-type Frames from Generalized Weyl-Heisenberg Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688260