Hermitean Cauchy Integral Decomposition of Continuous Functions on Hypersurfaces
We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the Ahlfors-David regular boundary Γ of a domain Ω in â„Â2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+-G21-, where the components G21± are extendabl...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-12-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2008/425256 |
| Summary: | We consider Hölder continuous circulant (2×2) matrix functions G21 defined on the Ahlfors-David regular boundary Γ of a domain Ω in â„Â2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+-G21-, where the components G21± 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. |
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| ISSN: | 1687-2762 1687-2770 |