Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	On Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group
Publication Date:	2009
Authors:	- Luís Daniel Abreu
Abstract:	Gabor frames with Hermite functions are equivalent to Fock frames with monomials windows and to sampling sequences in true poly-Fock spaces. In the L² case, such an equivalence results from the unitarity of the so-called true poly-Bargmann transform. We will extend the equivalence to Banach spaces, applying Feichtinger-Grochenig coorbit theory to the Fock representation of the Heisenberg group. This task requires L^p estimates for the true poly-Bargmann transform which are obtained using the theory of modulation spaces. In the L² case we will also revisit the complex variables approach and obtain an explicit formula for the interpolation problem in true poly-Fock spaces, which yields Gabor frames with Hermite functions by a duality argument.
Institution:	DMUC 09-45
Online version:	http://www.mat.uc.pt...prints/eng_2009.html
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