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 symbolic way. This means… (More)

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we… (More)

Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an… (More)

The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given… (More)

The fundamental solutions of the super Dirac and Laplace operators and their natural powers are determined within the framework of Clifford analysis. MSC 2000 : 30G35, 35A08, 58C50

A new framework for studying superspace is given, based on methods from Clifford analysis. This leads to the introduction of both orthogonal and symplectic Clifford algebra generators, allowing for… (More)

In this paper we introduce an abstract algebra of vector variables that generalizes both polynomial algebra and Clifford algebra. This abstractly defined algebra and its endomorphisms contains all… (More)

We consider Hölder continuous circulant 2 × 2 matrix functions G2 defined on the AhlforsDavid regular boundary Γ of a domain Ω in R2n. The main goal is to study under which conditions such a function… (More)

Hermitian Clifford analysis deals with the simultaneous null solutions of the orthogonal Dirac operators ∂x and its twisted counterpart ∂x|, introduced below. For a thorough treatment of this… (More)

In this paper we construct the main ingredients of a discrete function theory in higher dimensions by means of a new “skew” type of Weyl relations. We will show that this new type overcomes the… (More)