A local Cauchy integral formula for slice-regular functions

Abstract

We prove a Cauchy-type integral formula for slice-regular functions where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. In particular, we get a local Cauchy-type integral formula. As a step towards the proof, we provide a decomposition of a slice-regular function as a combination of two axially monogenic functions.

References in corpus (7)

• Slice regular functions on real alternative algebras
• The algebra of slice functions
• Slice regularity and harmonicity on Clifford algebras
• Volume Cauchy formulas for slice functions on real associative *-algebras
• Geometric function theory over quaternionic slice domains
• On a class of orientation-preserving maps of ${\mathbb{R}}^4$
• Eigenvalue problems for slice functions