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Hyperderivatives in Clifford Analysis and Some Applications to the Cliffordian Cauchy-type Integrals

  • M.E. Luna-Elizarrarás
  • M.A. Macías-Cedeño
  • M. Shapiro
Part of the Trends in Mathematics book series (TM)

Abstract

We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the “increments” of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in ℝm+1 for a Clifford algebra Cl o,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.

Keywords

Hyperderivative m-dimensional directional hyperderivative Cliffordian Cauchy-type integrals 

Mathematics Subject Classification (2000)

Primary 30G35 Secondary 32A10 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • M.E. Luna-Elizarrarás
    • 1
  • M.A. Macías-Cedeño
    • 1
  • M. Shapiro
    • 1
  1. 1.Departamento MatemáticasE.S.F.M. del I.P.N.México, D.F.México

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