Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis |
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Authors: | Ricardo Abreu-Blaya Juan Bory-Reyes Fred Brackx Hennie De Schepper Frank Sommen |
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Institution: | 1. Facultad de Inform??tica y Matem??tica, Universidad de Holgu??n, Holgu??n, 80100, Cuba 2. Departamento de Matem??tica, Universidad de Oriente, Santiago de Cuba, 90500, Cuba 3. Department of Mathematical Analysis, Faculty of Engineering and Architecture, Ghent University, Galglaan 2, 9000, Ghent, Belgium 4. Department of Mathematical Analysis, Faculty of Sciences, Ghent University, Galglaan 2, 9000, Ghent, Belgium
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Abstract: | The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel?CPompeiu and the Clifford?CCauchy formula have been obtained by using a (2 ×?2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford?CCauchy integral formula, by following a (4?× 4) circulant matrix approach. |
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