Continuous Gabor transform for semi-direct product of locally compact groups

Details Continuous Gabor transform for semi-direct product of locally compact groups Continuous Gabor transform for semi-direct product of locally compact groups

2012-03-07

arxiv.org/abs/1203.1517v1

Mathematics

Functional Analysis

Scientific paper

Let $H$ be a locally compact group, $K$ be an LCA group, $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\tau$. In this article we introduce the $\tau\times\hat{\tau}$-time frequency group $G_{\tau\times\hat{\tau}}$. We define the $\tau\times\hat{\tau}$-continuous Gabor transform of $f\in L^2(G_\tau)$ with respect to a window function $u\in L^2(K)$ as a function defined on $G_{\tau\times\hat{\tau}}$. It is also shown that the $\tau\times\hat{\tau}$-continuous Gabor transform satisfies the Plancherel Theorem and reconstruction formula. This approach is tailored for choosing elements of $L^2(G_\tau)$ as a window function. Finally, we illustrate application of these methods in the case of some well-known semi-direct product groups.

Affiliated with

Also associated with

No associations

Rating

Continuous Gabor transform for semi-direct product of locally compact 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 Continuous Gabor transform for semi-direct product of locally compact groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous Gabor transform for semi-direct product of locally compact groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-394532