Cauchy formulas for slice functions on real associative ∗ - algebras
نویسنده
چکیده
We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For every suitable choice of a real 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 gives a volume Cauchy formula for slice monogenic functions.
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