2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127257The 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 analyzing wavelets in a similar way the Hermite functions were recently by K. Groechenig and Y. Lyubarskii in "Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007)". Building on the work of K. Seip, "Beurling type density theorems in the unit disc, Invent. Math., 113, 21-39 (1993)", concerning sampling sequences on weighted Bergman spaces, we find a sufficient density condition for constructing frames by translations and dilations of the Fourier transform of the nth Laguerre function. As in Groechenig-Lyubarskii theorem, the density increases with n, and in the special case of the hyperbolic lattice in the upper half plane it is given by b\log a<\frac{4π}{2n+α}, where alpha is the parameter of the Laguerre function.15 pagesClassical Analysis and ODEsComplex Variables33C45; 42C15; 30H05; 42C40text