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.
A local Cauchy integral formula for slice-regular functions / Perotti, Alessandro. - In: COMPUTATIONAL METHODS AND FUNCTION THEORY. - ISSN 1617-9447. - 24:1(2024), pp. 185-203. [10.1007/s40315-023-00485-5]
A local Cauchy integral formula for slice-regular functions
Alessandro Perotti
2024-01-01
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.File in questo prodotto:
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