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Computational Methods and Function Theory
Article . 2023 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2021
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A Local Cauchy Integral Formula for Slice-Regular Functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 30 May 2023Embargo end date: 01 Jan 2021 Italy Publisher:Springer Science and Business Media LLCJournal:Computational Methods and Function Theory, volume 24, pages 185-203 (issn: 1617-9447, eissn: 2195-3724, Copyright policy )
Authors: Perotti, Alessandro;

doi: 10.1007/s40315-023-00485-5 , 10.48550/arxiv.2105.07041

arXiv: http://arxiv.org/abs/2105.07041

handle: 11572/306471

A Local Cauchy Integral Formula for Slice-Regular Functions

Abstract

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

Country
Italy
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Keywords

Mathematics - Complex Variables, Primary 30G35, Secondary 30E20, 26B20, FOS: Mathematics, Slice-regular functions; Axially monogenic functions; Cauchy-Riemann operator; Cauchy integral formula, Complex Variables (math.CV)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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