Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces. (16th November 2008) - Blaya, Ricardo Abreu; Reyes, Juan Bory; Brackx, Fred; De Knock, Bram; De Schepper, Hennie; Peña, Dixan Peña; Sommen, Frank
Abstract : We consider Hölder continuous circulant( 2 × 2 ) matrix functionsG 2 1 defined on the Ahlfors-David regular boundaryΓ of a domainΩ inℝ 2 n . The main goal is to study under which conditions such a functionG 2 1 can be decomposed asG 2 1 = G 2 1 + _ G 2 1 _, where the componentsG 2 1 _ are extendable to two-sidedH -monogenic functions in the interior and the exterior ofΩ, respectively.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( 2 × 2 ) matrix Dirac operator, having these Hermitean Dirac operators as its entries; such functions have been crucial for the development of function theoretic results in the Hermitean Clifford context.