Article

Complex Analysis and Operator Theory

, Volume 7, Issue 5, pp 1675-1711

Complex Laplacian and Derivatives of Bicomplex Functions

  • M. E. Luna-ElizarrarásAffiliated withEscuela Superior de Fisica y Matemáticas, Instituto Politécnico Nacional
  • , M. ShapiroAffiliated withEscuela Superior de Fisica y Matemáticas, Instituto Politécnico Nacional
  • , D. C. StruppaAffiliated withSchmid College of Science and Technology, Chapman University Email author 
  • , A. VajiacAffiliated withSchmid College of Science and Technology, Chapman University

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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