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Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis

Min Ku, Uwe Kähler, Paula Cerejeiras (2012)

Archivum Mathematicum

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

Alberto P. Bergamasco, Abdelhamid Meziani (2005)

Annales de l’institut Fourier

We study the solvability of equations associated with a complex vector field L in ℝ 2 with C ∞ or C ω coefficients. We assume that L is elliptic everywhere except on a simple and closed curve Σ . We assume that, on Σ , L is of infinite type and that L ∧ L ¯ vanishes to a constant order. The equations considered are of the form L u = p u + f , with f satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of L ∧ L ¯ is > 1 , the equation L u = f is solvable in the C ∞ category but not in the C ω category....

Some initial boundary problems in electrodynamics for canonical domains in quaternions

Erhard V. Meister, L. Meister (2001)

Mathematica Bohemica

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...

Stone-Weierstrass theorem

Guy Laville, Ivan Ramadanoff (1996)

Banach Center Publications

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.

Strictly analytic functions on p-adic analytic open sets.

Kamal Boussaf (1999)

Publicacions Matemàtiques

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 fonctions finement holomorphes

Bent Fuglede (1981)

Annales de l'institut Fourier

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...

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