Abstract
It is observed that a certain isometric mapping between Hardy–Szegö and Bergman–Selberg spaces, studied by D-W Byun, generalizes a transformation arising from a family of special wavelet transforms studied by Grossman et al. in one of the early papers on wavelet theory. Furthermore, we will see that, when mapped under such transforms, the Fourier transforms of Laguerre functions play the same canonical role as do the Hermite functions when mapped via the Bargmann–Fock transform. As a byproduct we obtain an integral representation, with respect to area measure in the upper half plane, of the Fourier transforms of the Laguerre functions.
Acknowledgements
Partial financial assistance by the FCT grant SFRH/BPD/26078/2005 and the CMUC.