Complex Analysis and Operator Theory

, Volume 7, Issue 5, pp 1675–1711

Complex Laplacian and Derivatives of Bicomplex Functions

  • M. E. Luna-Elizarrarás
  • M. Shapiro
  • D. C. Struppa
  • A. Vajiac
Article

DOI: 10.1007/s11785-013-0284-8

Cite this article as:
Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C. et al. Complex Anal. Oper. Theory (2013) 7: 1675. doi:10.1007/s11785-013-0284-8

Abstract

In this paper we study in detail the theory of bicomplex holomorphy, in the context of the several ways in which bicomplex numbers can be considered. In particular we will show how the notions of bicomplex derivability and bicomplex holomorphy can be interpreted in these different ways, and the consequences that can be derived.

Keywords

Bicomplex derivability Bicomplex differentiability Bicomplex holomorphic functions Complex and hyperbolic Laplacians 

Mathematics Subject Classification (2010)

30G35 32A30 32A10 

Copyright information

© Springer Basel 2013

Authors and Affiliations

  • M. E. Luna-Elizarrarás
    • 1
  • M. Shapiro
    • 1
  • D. C. Struppa
    • 2
  • A. Vajiac
    • 2
  1. 1.Escuela Superior de Fisica y MatemáticasInstituto Politécnico NacionalMéxico CityMexico
  2. 2.Schmid College of Science and TechnologyChapman UniversityOrangeUSA

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