On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis |
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Authors: | F Brackx B De Knock H De Schepper F Sommen |
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Institution: | 1.Clifford Research Group Department of Mathematical Analysis Faculty of Engineering,Ghent University,Gent,Belgium |
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Abstract: | Euclidean Clifford analysis is a higher dimensional function theory, refining harmonic analysis, centred around the concept
of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator, called
the Dirac operator. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis,
offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions of two Hermitean Dirac operators,
invariant under the action of the unitary group. In this paper, a Cauchy integral formula is established by means of a matrix
approach, allowing the recovering of the traditional Martinelli-Bochner formula for holomorphic functions of several complex
variables as a special case. |
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Keywords: | |
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