Schwarz-sche Randwertaufgabe fur eine Klasse der verallgemeinerten analytischen Funktionen
Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation
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.
Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
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...
Solvability near the characteristic set for a class of planar vector fields of infinite type
We study the solvability of equations associated with a complex vector field in with or coefficients. We assume that is elliptic everywhere except on a simple and closed curve . We assume that, on , is of infinite type and that vanishes to a constant order. The equations considered are of the form , with satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of is , the equation is solvable in the category but not in the category....
Solvability of a Riemann linear conjugation problem on a fractal surface.
Some initial boundary problems in electrodynamics for canonical domains in quaternions
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...
Some integral formulas in complex Clifford analysis
Stochastic Holomorphy.
Stone-Weierstrass theorem
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.
Strict topologies in non-archimedean function spaces.
Strictly analytic functions on p-adic analytic open sets.
Let K be an algebraically closed complete ultrametric field. M. Krasner and P. Robba defined theories of analytic functions in K, but when K is not spherically complete both theories have the disadvantage of containing functions that may not be expanded in Taylor series in some disks. On other hand, affinoid theories are only defined in a small class of sets (union of affinoid sets) [2], [13] and [17]. Here, we suppose the field K topologically separable (example Cp). Then, we give a new definition...
Sur les automorphismes d'extensions transcendantes de corps valués
Sur les fonctions finement holomorphes
Ces fonctions sont définies dans des ouverts pour la topologie fine de Brelot-Cartan dans le plan complexe. Elles généralisent les fonctions holomorphes ordinaires. L’étude des fonctions finement holomorphes est fondée ici sur les fonctions Beppo Levi comme précisées par Deny. En utilisant la transformée de Cauchy-Pompeiu on retrouve et étend de façon non-probabiliste les résultats de Debiard, Gaveau et Lyons. On montre en outre que toute fonction finement holomorphe est déterminée par sa série...
Systeme von Differentialgleichungen Erster Ordnung vom Elliptischen Typus mit Analytischen Koeffizienten und Methode der Verallgemeinerten Areolaren Reihen
Szegő projections for Hardy spaces of monogenic functions and applications.