Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces. (16th November 2008)

• Record Type: Journal Article
• Authors: Blaya, Ricardo Abreu; Reyes, Juan Bory; Brackx, Fred; De Knock, Bram; De Schepper, Hennie; Peña, Dixan Peña; Sommen, Frank
• Other Names: Rogers Colin Academic Editor.
• Is Part Of: Boundary value problems. Volume 2008(2008)
• Publication Date: 2008-11-16
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2008/425256
• Languages: English
• ISSNs: 1687-2762

Abstract

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.