Fourier transform and related integral transforms in superspace
arXiv:0805.1918 · doi:10.1016/j.jmaa.2008.03.047
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.
20 pages, accepted for publication in J. Math. Anal. Appl
References in corpus (5)
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- Orthogonality of Hermite polynomials in superspace and Mehler type formulae
- Orthosymplectically invariant functions in superspace
- A Cauchy integral formula in superspace
- Schrödinger equation with delta potential in superspace
- The orthosymplectic supergroup in harmonic analysis
- An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
- A minimal representation of the orthosymplectic Lie supergroup
- Hilbert space for quantum mechanics on superspace
- Quantum spectral analysis: frequency in time, with applications to signal and image processing
- Superfield equations in the Berezin-Kostant-Leites category
- Supersymmetric field equations from momentum space