Article

Arkiv för Matematik

, Volume 49, Issue 2, pp 277-294

Singularities of functions of one and several bicomplex variables

  • Fabrizio ColomboAffiliated withDipartimento di Matematica, Politecnico di Milano Email author 
  • , Irene SabadiniAffiliated withDipartimento di Matematica, Politecnico di Milano
  • , Daniele C. StruppaAffiliated withSchmid College of Science, Chapman University
  • , Adrian VajiacAffiliated withSchmid College of Science, Chapman University
  • , Mihaela B. VajiacAffiliated withSchmid College of Science, Chapman University

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Abstract

In this paper we study the singularities of holomorphic functions of bicomplex variables introduced by G. B. Price (An Introduction to Multicomplex Spaces and Functions, Dekker, New York, 1991). In particular, we use computational algebra techniques to show that even in the case of one bicomplex variable, there cannot be compact singularities. The same techniques allow us to prove a duality theorem for such functions.