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Remarks on Holomorphicity in Three Settings: Complex, Quaternionic, and Bicomplex

  • Daniele C. StruppaEmail author
  • Adrian Vajiac
  • Mihaela B. Vajiac
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We compare holomorphicity in three distinct settings: complex, quaternionic, and bicomplex variables. We show how the analysis in the complex case can be extended in substantially different directions when dealing with quaternions or bicomplex numbers. In particular, we highlight the different dimensionality of hyperfunctions in the three settings.

Keywords

Bicomplex numbers hyperfunction theory quaternions 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Daniele C. Struppa
    • 1
    Email author
  • Adrian Vajiac
    • 1
  • Mihaela B. Vajiac
    • 1
  1. 1.Schmid College of ScienceChapman UniversityOrangeUSA

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