English

On the Radon transform and the Dirac delta distribution in superspace

Mathematical Physics 2021-07-13 v1 math.MP

Abstract

In this manuscript, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon transform in these cases. Moreover, we prove a more general Radon inversion formula valid for all possible integer values of the superdimension. The proof of this result comes along with the study of fractional powers of the super Laplacian, their fundamental solutions, and the plane wave decompositions of super Riesz kernels.

Keywords

Cite

@article{arxiv.2107.05551,
  title  = {On the Radon transform and the Dirac delta distribution in superspace},
  author = {Alí Guzmán Adán and Irene Sabadini and Frank Sommen},
  journal= {arXiv preprint arXiv:2107.05551},
  year   = {2021}
}

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38 pages