Fourier transform and related integral transforms in superspace
Classical Analysis and ODEs
2008-05-14 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0805.1918,
title = {Fourier transform and related integral transforms in superspace},
author = {Hendrik De Bie},
journal= {arXiv preprint arXiv:0805.1918},
year = {2008}
}
Comments
20 pages, accepted for publication in J. Math. Anal. Appl