Generalized Fourier transforms arising from the enveloping algebras of sl(2) and osp(1|2)

H. De Bie, R. Oste, J. Van der Jeugt

The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen…