Franciscus Sommen

Details der Publikationsliste

Zeitraum

1981 - 2009

Anzahl

184

Co-Autoren

Discrete Clifford analysis : a germ of function theory (2009)

Brackx, Fred, De Schepper, Hennie, Sommen, Franciscus, Van De Voorde, Liesbet

We develop a discrete version of Clifford analysis, i.e., a higher-dimensional discrete function theory in a Clifford algebra context. On the simplest of all graphs, the rectangular Z(m) grid, the...

On the CK-extension for a Special Overdetermined System in Complex Clifford Analysis (2009)

De Knock, Bram, Pena Pena, Dixan, Sommen, Franciscus

In this paper we investigate a new overdetermined system in Rm+1, called RicSom system, arising from adding one extra real dimension to the Hermitian Dirac system in R-m, m = 2n, that uses the...

On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis (2009)

Brackx, Fred, De Knock, Bram, De Schepper, Hennie, Sommen, Franciscus

Euclidean Clifford analysis is a higher dimensional function theory, refining harmonic analysis, centered around the concept of monogenic functions, i.e.\ null solutions of a first order vector...

The Cylindrical Fourier Spectrum of an L-2-basis consisting of Generalized Clifford-Hermite Functions (2008)

Brackx, Fred, De Schepper, Nele, Sommen, Franciscus

In this paper we devise a new so-called cylindrical Fourier transform within the Clifford analysis setting by substituting for the standard inner product in the classical exponential Fourier kernel a...

Fourier-Borel Transforms in Clifford Analysis and the Dual Fischer Decomposition (2008)

Sommen, Franciscus

In this presentation we introduce several generalizations to Clifford analysis of the classical Fourier-Borel transform for analytic of holomorphic functionals. We also prove that every analytic or...

Orthogonality of the generalized Hermitean Clifford-Hermite polynomials (2008)

Brackx, Fred, De Schepper, Hennie, De Schepper, Nele, Eelbode, David, Sommen, Franciscus

Clifford analysis is a higher-dimensional function theory offering a refinement of classical harmonic analysis. It is centred around monogenic functions, i.e. null solutions of the rotation invariant...

The Hermitian Clifford analysis toolbox (2008)

Brackx, Fred, De Schepper, Hennie, Sommen, Franciscus

Hermitian Clifford analysis focusses on monogenic functions taking values in a complex Clifford algebra, or in a complex spinor space. Here monogenicity is expressed by means of two complex mutually...

Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces (2008)

Abreu Blaya, Ricardo, Bory Reyes, Juan, Brackx, Fred, De Knock, Bram, De Schepper, Hennie, Pena Pena, Dixan, ...

We consider Holder continuous circulant (2 x 2) matrix functions G(2)(1) defined on the Ahlfors-David regular boundary Gamma of a domain Omega in R-2n. The main goal is to study under which...

Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space (2007)

Brackx, Fred, De Schepper, Nele, Sommen, Franciscus

Specific wavelet kernel functions for a continuous wavelet transform in Euclidean space are presented within the framework of Clifford analysis. These multi-dimensional wavelets are constructed by...