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arXiv · 2105.07041

A local Cauchy integral formula for slice-regular functions

Alessandro Perotti
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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.

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Alessandro Perotti. 2021-05-14. A local Cauchy integral formula for slice-regular functions. https://doi.org/10.1007/s40315-023-00485-5

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