Mathematics – Functional Analysis
Scientific paper
2008-04-29
Math. Ann. 345(2) (2009), 267 -- 286
Mathematics
Functional Analysis
Scientific paper
We investigate vector-valued Gabor frames (sometimes called Gabor superframes) based on Hermite functions $H_n$. Let $h= (H_0, H_1, ..., H_n)$ be the vector of the first $n+1$ Hermite functions. We give a complete characterization of all lattices $\Lambda \subseteq \bR ^2$ such that the Gabor system $\{e^{2\pi i \lambda_2 t} \boh (t-\lambda_1): \lambda = (\lambda_1, \lambda_2) \in \Lambda \}$ is a frame for $L^2 (\bR, \bC ^{n+1})$. As a corollary we obtain sufficient conditions for a single Hermite function to generate a Gabor frame and a new estimate for the lower frame bound. The main tools are growth estimates for the Weierstrass $\sigma $-function, a new type of interpolation problem for entire functions on the Bargmann-Fock space, and structural results about vector-valued Gabor frames.
Gröchenig Karlheinz
Lyubarskii Yurii
No associations
LandOfFree
Gabor (Super)Frames with Hermite Functions 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 (Super)Frames with Hermite Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gabor (Super)Frames with Hermite Functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-209917