Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
The initial boundary-transmission problems for electromagnetic fields in homogeneous and anisotropic media for canonical semi-infinite domains, like halfspaces, wedges and the exterior of half- and quarter-plane obstacles are formulated with the use of complex quaternions. The time-harmonic case was studied by A. Passow in his Darmstadt thesis 1998 in which he treated also the case of an homogeneous and isotropic layer in free space and above an ideally conducting plane. For thin layers and free...
It will be shown that the Stone-Weierstrass theorem for Clifford-valued functions is true for the case of even dimension. It remains valid for the odd dimension if we add a stability condition by principal automorphism.