Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	Wavelet frames, Bergman spaces and Fourier transforms of Laguerre functions
Publication Date:	2006
Authors:	- Luís Daniel Abreu
Abstract:	The Fourier transforms of Laguerre functions play the same canonical role in Wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as mother wavelets in a similar way as the Hermite functions were recently used as windows in Gabor frames by Grochenig and Lyubarskii. Using results due to K. Seip concerning lattice sampling sequences on weighted Bergman spaces, we find a sufficient condition for the discretization of the resulting wavelet transform to be a frame. As in Grochenig-Lyubarskii theorem, the density increases with n, when considering frames generated by translations and dilations of the Fourier transform of the nth Laguerre function.
Institution:	DMUC 06-41
Online version:	http://www.mat.uc.pt...prints/eng_2006.html
Download:	Not available