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–Pompeiu and the Clifford–Cauchy 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–Cauchy integral formula, by following a (4 × 4) circulant matrix approach.
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Communicated by Irene Sabadini.
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Abreu-Blaya, R., Bory-Reyes, J., Brackx, F. et al. Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis. Complex Anal. Oper. Theory 6, 971–985 (2012). https://doi.org/10.1007/s11785-011-0168-8
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DOI: https://doi.org/10.1007/s11785-011-0168-8