LAUSR

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 $${\mathfrak {osp}}(1|2)$$ osp ( 1 | 2 ) in terms of a so-called radially deformed Dirac operator $${\mathbf {D}}$$ D depending on a deformation parameter c such that for $$c=0$$ 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.