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Title: Wavelet frames, Bergman spaces and Fourier transforms of Laguerre functions
Authors: Abreu, Luís Daniel 
Keywords: Wavelets; Frames; Laguerre functions; Bergman spaces
Issue Date: 2006
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 06-41 (2006)
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 Gr¨ochenig 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 Gr¨ochenig-Lyubarskii theorem, the density increases with n, when considering frames generated by translations and dilations of the Fourier transform of the nth Laguerre function.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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