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On the Hyperderivatives of Moisil–Théodoresco Hyperholomorphic Functions

  • M. Elena Luna-ElizarrarásEmail author
  • Marco A. Macías-Cedeño
  • Michael Shapiro
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Any Moisil-Th´eodoresco-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 possible to give another kind of hyperderivatives “consistent” with the Moisil- Th´eodoresco 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.

Keywords

Hyperderivative two-dimensional directional hyperderivative Cauchy-type integrals 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • M. Elena Luna-Elizarrarás
    • 1
    Email author
  • Marco A. Macías-Cedeño
    • 1
  • Michael Shapiro
    • 1
  1. 1.Departamento de Matemáticas Escuela Superior de Fĺsica y MatemáticasInstituto Politécnico NacionalMéxico CityMéxico

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