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Singularities of functions of one and several bicomplex variables

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, IT-20133, Milano, Italy

    Fabrizio Colombo & Irene Sabadini

  2. Schmid College of Science, Chapman University, One University Drive, Orange, CA, 92866, U.S.A.

    Daniele C. Struppa, Adrian Vajiac & Mihaela B. Vajiac

Authors
  1. Fabrizio Colombo
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  2. Irene Sabadini
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  3. Daniele C. Struppa
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  4. Adrian Vajiac
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  5. Mihaela B. Vajiac
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Correspondence to Fabrizio Colombo.

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Colombo, F., Sabadini, I., Struppa, D.C. et al. Singularities of functions of one and several bicomplex variables. Ark Mat 49, 277–294 (2011). https://doi.org/10.1007/s11512-010-0126-0

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  • DOI: https://doi.org/10.1007/s11512-010-0126-0

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