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.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Analysis
Reference23 articles.
1. Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory, Graduate Texts in Mathematics, vol. 137, 2nd edn. Springer, New York (2001)
2. Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis, Research Notes in Mathematics, vol. 76. Pitman (Advanced Publishing Program), Boston (1982)
3. Colombo, F., Gentili, G., Sabadini, I.: A Cauchy kernel for slice regular functions. Ann. Global Anal. Geom. 37, 361–378 (2010)
4. Colombo, F., Sabadini, I., Sommen, F.: The inverse Fueter mapping theorem. Commun. Pure Appl. Anal. 10(4), 1165–1181 (2011)
5. Cullen, C.G.: An integral theorem for analytic intrinsic functions on quaternions. Duke Math. J. 32, 139–148 (1965)