P. Van Lancker

Symmetric Analogues of Rarita-Schwinger Equations

In this paper a generalization of the classicalRarita–Schwinger equations for spin 3/2 fields to the case of spin fieldswith values in irreducible representation spaces with weight k+1/2 isgiven. It corresponds to the study of serie of first orderconformal invariant operators, which are constructed from twisted Diracoperators. The representation character of polynomial solutions of the equations onflat space and their relations are described in details.

Models for irreducible representations ofSpin(m)

In this paper we consider harmonic and monogenic polynomials of simplicial type. It is proved that these polynomials provide explicit realizations of all irreducible representations ofSpin(m).

Clifford Analysis on the Sphere

In this paper we give some basic integral formulas related to spherical monogenics of complex degree. These monogenics, locally defined on the sphere S m−1, are eigenfunctions of the Γ-operator corresponding to complex eigenvalues and generalise the classical spherical monogenics.

Rarita–Schwinger fields in the half space

This article deals with the Hardy space related to solutions of generalized Rarita–Schwinger operators in the ball and the half space. These operators generalize the Rarita–Schwinger operator for spin -fields to the case of functions taking values in irreducible representation spaces with weight . †Dedicated to Richard Delanghe on the occasion of his 65th birthday.This article deals with the Hardy space related to solutions of generalized Rarita–Schwinger operators in the ball and the half space. These operators generalize the Rarita–Schwinger operator for spin -fields to the case of functions taking values in irreducible representation spaces with weight . †Dedicated to Richard Delanghe on the occasion of his 65th birthday.

Evaluation of some enzymatic methods to measure the bio-activity of aquatic environments

Methods have been evaluated and standardised to measure the phosphatase, saccharase, amylase and lipase enzymatic activities in aquatic environments. The analytical reproducibility, the ecological applicability and the etiology of these activities have been investigated. The usefulness of the various enzymatic assays for routine analyses and for fundamental research of aquatic environments is discussed.

Homogeneous monogenic functions in euclidean space

This paper illustrates that the theory of monogenic functions satisfying a fixed homogeneity condition leads to a new function theory, parallel to but different from the standard theory of monogenic functions. The function theory thus obtained includes the theory of the Dirac operator on the unit sphere.

Gegenbauer polynomials and the Fueter theorem

The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator. In this paper we interpret this theorem on the level of representation theory, as an intertwining map between certain -modules.

Taylor and Laurent series on the sphere

Spherical monogenics of complex degree correspond to local eigenfunctions of the (Atiyah-Singer) Dirac operator on the unit sphere Sm-1 of R m. In this paper we will given explicit formulae for the Taylor and Laurent series for this class of functions. This leads to an explicity residue theory for spherical monogenics having point singularities.

The Monogenic Fischer Decomposition: Two Vector Variables

In this paper we will present two proofs of the monogenic Fischer decomposition in two vector variables. The first one is based on the so-called “Harmonic Separation of Variables Theorem” while the second one relies on some simple dimension arguments. We also show that these decomposition are still valid under milder assumptions than the usual stable range condition. In the process, we derive explicit formula for the summands in the monogenic Fischer decomposition of harmonics.

The kerzman-stein theorem on the sphere

Spherical monogenics of complex degree correspond to local eigenfunctions of the (Atiyah-Singer) Dirac operator on the unit sphere. Sm−1 of . In this paper we will consider the L2 -boundary value theory for this class of functions. The main Theorem is a higher dimensional version of the Kerzman-Stein Theorem of complex analysis in the plane.Spherical monogenics of complex degree correspond to local eigenfunctions of the (Atiyah-Singer) Dirac operator on the unit sphere. Sm−1 of . In this paper we will consider the L2 -boundary value theory for this class of functions. The main Theorem is a higher dimensional version of the Kerzman-Stein Theorem of complex analysis in the plane.