73 citations · 88 across the 3 of their papers we have counts for
4 papers
Reproducing kernels for polynomial null-solutions of Dirac operators
Hendrik De Bie, Frank Sommen, Michael Wutzig
It is well-known that the reproducing kernel of the space of spherical harmonics of fixed homogeneity is given by a Gegenbauer polynomial. By going over to complex variables and re…
The class of Clifford-Fourier transforms
H. De Bie, N. De Schepper, F. Sommen
Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general pr…
Hermite and Gegenbauer polynomials in superspace using Clifford analysis
Hendrik De Bie, Frank Sommen
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbo…
Spherical harmonics and integration in superspace
Hendrik De Bie, Frank Sommen
In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and stud…