  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 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{4\pi}{2n+\alpha}, where alpha is the parameter of the Laguerre
function.
