-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.
-harmonic equations and the Dirac operator.
A homogeneous Dirichlet problem for a nonlinear partial differential equation in an anisotropic Sobolec space.
A hypercomplex method of calculating stresses in three-dimensional bodies
A new method for obtaining solutions of the Dirac equation.
A new proof of a theorem of Saxer
A representation for the derivative of a meta-analytic function
A uniqueness theorem for monogenic functions.
Algebras of generalized analytic functions
Algèbres de Banach unitaire
An alternative definition of the Hermite polynomials related to the Dunkl Laplacian.
An initial and boundary value problem for nonlinear composite type systems of three equations.
An integral formula for the derivatives of solutions of certain elliptic systems
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 .
An ultrametric Nevanlinna’s second main theorem for small functions of a special type
In ultrametric Nevanlinna theory, the Nevanlinna’s second main theorem for small functions has only been proved in the case of at most three small functions. In this paper, we prove a second main theorem for small functions of a special type when the residue characteristic of the field is zero.