TY - JOUR UR - http://lib.ugent.be/catalog/pug01:977584 ID - pug01:977584 LA - eng TI - Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces PY - 2010 JO - (2010) BOUNDARY VALUE PROBLEMS SN - 1687-2762 PB - 2010 AU - Abreu-Balya, Ricardo AU - Bory-Reyes, Juan AU - Brackx, Fred TW16 801000224369 0000-0002-1849-8826 AU - De Schepper, Hennie TW16 801000937220 0000-0003-3708-4570 AB - We consider Holder continuous circulant (2 x 2) matrix functions G(2)(1) defined on the fractal boundary Gamma of a domain Omega in R-2n. 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 components G(2)(1 +/-) are extendable to H-monogenic functions in the interior and the exterior of Omega, 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 x 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 Teodorescu 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 977584 | ||
005 | 20161221154246.0 | ||
008 | 100613s2010------------------------eng-- | ||
022 | a 1687-2762 | ||
024 | a 000279735000001 2 wos | ||
024 | a 1854/LU-977584 2 handle | ||
024 | a 10.1155/2010/791358 2 doi | ||
040 | a UGent | ||
245 | a Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces | ||
260 | c 2010 | ||
520 | a We consider Holder continuous circulant (2 x 2) matrix functions G(2)(1) defined on the fractal boundary Gamma of a domain Omega in R-2n. 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 components G(2)(1 +/-) are extendable to H-monogenic functions in the interior and the exterior of Omega, 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 x 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 Teodorescu 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. | ||
598 | a A1 | ||
100 | a Abreu-Balya, Ricardo | ||
700 | a Bory-Reyes, Juan | ||
700 | a Brackx, Fred u TW16 0 801000224369 0 0000-0002-1849-8826 | ||
700 | a De Schepper, Hennie u TW16 0 801000937220 0 0000-0003-3708-4570 | ||
650 | a Mathematics and Statistics | ||
653 | a CLIFFORD ANALYSIS | ||
653 | a fractal hypersurface | ||
653 | a CAUCHY | ||
653 | a Hermitean Clifford analysis | ||
653 | a jump problem | ||
773 | t BOUNDARY VALUE PROBLEMS g Bound. Value Probl. 2010. q :< | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/977584/file/1016908 z [open] y AbreuBlaya_2010_BVP_a791358.pdf | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/977584/file/977588 z [no access] y | ||
920 | a article | ||
Z30 | x EA 1 TW16 | ||
922 | a UGENT-EA |
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