Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces
نویسندگان
چکیده
We consider Hölder continuous circulant 2 × 2 matrix functions G2 defined on the AhlforsDavid regular boundary Γ of a domain Ω in R2n. The main goal is to study under which conditions such a function G2 can be decomposed as G 1 2 G 1 2 − G2 , where the components G2 ± are extendable to two-sided H-monogenic functions in the interior and the exterior of Ω, 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.
منابع مشابه
On Fundamental Solutions in Clifford Analysis
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued, rotation invariant, differential operator ∂ called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has ...
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