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arXiv · 1205.6290

Volume Cauchy formulas for slice functions on real associative *-algebras

Riccardo Ghiloni·Alessandro Perotti
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Abstract

We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case, we get a volume Cauchy formula. In the Clifford algebra case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy formula for slice monogenic functions.

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Riccardo Ghiloni, Alessandro Perotti. 2012-05-29. Volume Cauchy formulas for slice functions on real associative *-algebras. https://doi.org/10.1080/17476933.2012.709851

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