Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces
type: Item
instance of: scholarly article
title: Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces
zbMATH Open document ID: 1180.30052
DOI: 10.1155/2008/425256
author: Ricardo Abreu-Blaya
author: Juan Bory-Reyes
author: F. Brackx
author: Bram De Knock
author: H. De Schepper
author: Dixan Peña Peña
author: Frank Sommen
published in: Boundary Value Problems
publication date: 2009-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/45427
review text: 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...''.
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 5538045
zbMATH Keywords: Ahlfors-David regular boundary
zbMATH Keywords: \(H\)-monogenic function
MaRDI profile type: Publication
OpenAlex ID: W2154104798
Wikidata QID: Q59216546
cites work: Q3337727
cites work: Q4003806
cites work: Q4382291
cites work: Q3995205
cites work: Complexified clifford analysis
cites work: Integral theorems for functions and differential forms in \(C^m\)
cites work: Hermitian Clifford analysis and resolutions
cites work: Analysis of Dirac systems and computational algebra.
cites work: The Hermitian Clifford analysis toolbox
cites work: Fundaments of Hermitean Clifford analysis. I: Complex structure
cites work: Fundaments of Hermitean Clifford analysis part II: splitting ofh-monogenic equations
cites work: Q3504669
cites work: A Martinelli–Bochner formula for the Hermitian Dirac equation
cites work: On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis
cites work: Jump problem and removable singularities for monogenic functions
cites work: A matrix Hilbert transform in Hermitean Clifford analysis
cites work: Q4278678
cites work: Q5565773
cites work: Clifford Cauchy type integrals on Ahlfors-David regular surfaces in \(\mathbb R^{m+1}\)
cites work: The Clifford–Cauchy transform with a continuous density: N. Davydov's theorem
cites work: Minkowski dimension and Cauchy transform in Clifford analysis
cites work: Cauchy transform on nonrectifiable surfaces in Clifford analysis
cites work: Cauchy transform and rectifiability in Clifford analysis
cites work: A boundary value problem for Hermitian monogenic functions
cites work: Cauchy integral decomposition of multi-vector valued functions on hypersurfaces
description: scientific article; zbMATH DE number 5538045