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https://hdl.handle.net/10316/11333
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. | URI: | https://hdl.handle.net/10316/11333 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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Wavelet frames, Bergman spaces and Fourier transforms.pdf | 155.43 kB | Adobe PDF | View/Open |
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