TY - JOUR
T1 - Hermitean téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Brackx, Fred
AU - De Schepper, Hennie
N1 - Funding Information:
This paper was written during a scientific stay of the first author at the Clifford Research Group of the Department of Mathematical Analysis of Ghent University, supported by a "Visiting Postdoctoral Fellowship" of the Flemish Research Foundation. He wishes to thank the members of the Clifford Research Group for their kind hospitality during this stay.
PY - 2010
Y1 - 2010
N2 - We consider Hölder continuous circulant (2 × 2) matrix functions G 2 1 defined on the fractal boundary Γ of a domain ω in ℝ2n. The main goal is to study under which conditions such a function G 2 1 can be decomposed as G 2 1 = G 2 1+ - G 2 1-, where the componentsG 2 1± are extendable to H -monogenic functions in the interior and the exterior of ω,respectively. H -monogenicity are 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 matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.
AB - We consider Hölder continuous circulant (2 × 2) matrix functions G 2 1 defined on the fractal boundary Γ of a domain ω in ℝ2n. The main goal is to study under which conditions such a function G 2 1 can be decomposed as G 2 1 = G 2 1+ - G 2 1-, where the componentsG 2 1± are extendable to H -monogenic functions in the interior and the exterior of ω,respectively. H -monogenicity are 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 matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.
UR - http://www.scopus.com/inward/record.url?scp=77954617654&partnerID=8YFLogxK
U2 - 10.1155/2010/791358
DO - 10.1155/2010/791358
M3 - Artículo
SN - 1687-2762
VL - 2010
JO - Boundary Value Problems
JF - Boundary Value Problems
M1 - 791358
ER -