Volume Cauchy formulas for slice functions on real associative *-algebras
Complex Variables
2018-07-02 v1 Rings and Algebras
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.
Cite
@article{arxiv.1205.6290,
title = {Volume Cauchy formulas for slice functions on real associative *-algebras},
author = {Riccardo Ghiloni and Alessandro Perotti},
journal= {arXiv preprint arXiv:1205.6290},
year = {2018}
}