Abstract :
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to
superspace are studied. Previously, a Fourier transform in superspace was already studied,
but with a different kernel. In this work, the fermionic part of the Fourier kernel has
a natural symplectic structure, derived using a Clifford analysis approach. Several basic
properties of these three transforms are studied. Using suitable generalizations of the
Hermite polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer
polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007) 10441–10456]) an
eigenfunction basis for the Fourier transform is constructed.
