Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions

Ricardo Abreu Blaya, Juan Bory Reyes, Richard Delanghe and Frank Sommen

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-19

Abstract:

Let be the space of -vectors in the Clifford algebra constructed over the quadratic vector space , let with , and , and let . Then, an -valued smooth function defined in an open subset is said to satisfy the generalized Moisil-Théodoresco system of type if in , where is the Dirac operator in . A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. Furthermore, if is bounded with boundary , where is an Ahlfors-David regular surface, and if is a -valued Hölder continuous function on , then necessary and sufficient conditions are given under which admits on a Cauchy integral decomposition .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:746946

DOI: 10.1155/2008/746946

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