-valued differential forms on
A boundary value problem for Hermitian monogenic functions.
A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.
A generalization of a Cullen's integral theorem for the quaternions.
A generalization of Jørgensen's inequality to infinite dimension.
A generalization of the Schwarzian via Clifford numbers.
A hypercomplex method of calculating stresses in three-dimensional bodies
A new method for obtaining solutions of the Dirac equation.
Algebras of generalized analytic functions
Algèbres de Banach unitaire
An alternative definition of the Hermite polynomials related to the Dunkl Laplacian.
An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid
The Dirac equation for spinor-valued fields on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet of the hyperboloid. In particular, we derive an integral formula expressing the value of in a chosen point as an integral over a compact cycle given by the intersection of the null cone with in the Minkowski space .
Analysis in complex quaternions and its connections with mathematical physics
Analytic Cliffordian functions.
Applications of Quaternionic Holomorphic Geometry to minimal surfaces
In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface....
Arbitrary complex powers of the Dirac operator on the hyperbolic unit ball.
Basic sets of polynomials in Clifford analysis
Bemerkung zu der in No. 10 dieser Nachrichten abgedruckten Mittheilung des Herrn Weierstrass
Beweis eines von Herrn Dedekind angegebenen Satzes
Canonical bases for -modules of spherical monogenics in dimension 3
Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as -modules. As finite-dimensional irreducible -modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.