Israel Journal of Mathematics

, Volume 171, Issue 1, pp 385–403 | Cite as

Slice monogenic functions

  • Fabrizio Colombo
  • Irene Sabadini
  • Daniele C. Struppa
Article

Abstract

In this paper we offer a new definition of monogenicity for functions defined on ℝn+1 with values in the Clifford algebra ℝn following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra ℝn. We will prove a Cauchy integral formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials and power series.

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Copyright information

© Hebrew University Magnes Press 2009

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Irene Sabadini
    • 1
  • Daniele C. Struppa
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Department of Mathematics and Computer SciencesChapman UniversityOrangeUSA

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