A local Cauchy integral formula for sliceregular functions
Abstract
We prove a Cauchytype integral formula for sliceregular 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 Cauchytype integral formula. As a step towards the proof, we provide a decomposition of a sliceregular function as a combination of two axially monogenic functions.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.07041
 Bibcode:
 2021arXiv210507041P
 Keywords:

 Mathematics  Complex Variables;
 Primary 30G35;
 Secondary 30E20;
 26B20