Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces
Regarding Hölder continuous circulant 2x2 matrix functions defined on the Ahlfors-David regular boundary \(\Gamma\) of a domain \(\Omega\) in \(R^n\), the authors study the question on its decomposition in a sum of two components, one of them extendable into the interior as a two-sided H-monogenic function and the other into the exterior, respectively, and vanishing at infinity. ''H-monogenicity is a concept from the framework of Hermitean Clifford analysis, a higher dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. H-monogenic functions then are the null solutions of a 2x2 matrix Dirac operator, having these Hermitean Dirac operators as its entries...''.
scientific article; zbMATH DE number 5538045
scientific article