In recent work a radial deformation of the Fourier transform in the setting of Clifford analysis was introduced. The key idea behind this deformation is a family of new realizations of the Lie superalgebra \({\mathfrak {osp}}(1|2)\) in terms of a so-called radially deformed Dirac operator \({\mathbf {D}}\) depending on a deformation parameter c such that for \(c=0\) the classical Dirac operator is reobtained. In this paper, several versions of the Paley–Wiener theorems for this radially deformed Fourier transform are investigated, which characterize the supports of functions associated to this generalized Fourier transform in Clifford analysis.

中文翻译：

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关于径向变形傅立叶变换的函数的支持

在最近的工作中，介绍了在Clifford分析中设置的Fourier变换的径向变形。这种变形背后的关键思想是李超代数\（{\ mathfrak {osp}}（1 | 2）\）的一系列新实现，即所谓的径向变形Dirac算子\（{\ mathbf {D }} \）取决于变形参数c，以便对于\（c = 0 \）重新获得经典Dirac算子。在本文中，研究了此径向变形傅立叶变换的几种Paley-Wiener定理，这些定理表征了Clifford分析中与该广义傅立叶变换相关的函数的支持。