Fourier transform and related integral transforms in superspace

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dc.creatorDe Bie, Hendrik
dc.date2008-05-13
dc.date.accessioned2026-07-07T09:38:39Z
dc.date.available2026-07-07T09:38:39Z
dc.descriptionIn 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.
dc.description20 pages, accepted for publication in J. Math. Anal. Appl
dc.identifierhttps://arxiv.org/abs/0805.1918
dc.identifierhttp://arxiv.org/abs/0805.1918
dc.identifierdoi:10.1016/j.jmaa.2008.03.047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160881
dc.subjectClassical Analysis and ODEs
dc.subjectMathematical Physics
dc.subject30G35, 58C50, 42B10, 44A12
dc.titleFourier transform and related integral transforms in superspace
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