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

References in corpus (1)

• Slice regular functions on real alternative algebras

Cited by in corpus (7)

• Geometric function theory over quaternionic slice domains
• Cauchy-Riemann operators and local slice analysis over real alternative algebras
• The harmonicity of slice regular functions
• A unified notion of regularity in one hypercomplex variable
• A unified theory of regular functions of a hypercomplex variable
• A manifold Fueter-Sce phenomenon in one hypercomplex variable
• A local Cauchy integral formula for slice-regular functions