On the hyperderivatives of moisil-Théodoresco hyperholomorphic functions

M. Elena Luna-Elizarrarás, Marco A. Macías-Cedeño, Michael Shapiro

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

Any Moisil-Théodoresco-hyperholomorphic function is also Fueterhyperholomorphic, but its hyperderivative is always zero, so these functions can be thought of as "constants" for the Fueter operator. It turns out that it is pobible to give another kind of hyperderivatives "consistent" with the Moisil-Théodoresco operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of two-dimensional directional hyperderivative along a plane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.

Original languageEnglish
Title of host publicationHypercomplex Analysis and Applications
EditorsIrene Sabadini, Frank Sommen
PublisherSpringer International Publishing
Pages181-193
Number of pages13
ISBN (Print)9783034602457
DOIs
StatePublished - 2011
Event7th ISAAC Conference on Hypercomplex Analysis and Applications, 2009 - London, United Kingdom
Duration: 13 Jul 200918 Jul 2009

Publication series

NameTrends in Mathematics
Volume53
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

Conference7th ISAAC Conference on Hypercomplex Analysis and Applications, 2009
Country/TerritoryUnited Kingdom
CityLondon
Period13/07/0918/07/09

Keywords

  • Cauchy-Type Integrals
  • Hyperderivative
  • Two-Dimensional Directional Hyperderivative

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