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.

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

Ghiloni, Riccardo
Primo
;
Perotti, Alessandro
Ultimo
2013-01-01

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.
2013
12
Ghiloni, Riccardo; Perotti, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/92145
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