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Slice Regular Functions: Analysis

  • Fabrizio Colombo
  • Irene SabadiniEmail author
  • Daniele C. Struppa
Chapter
  • 267 Downloads
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we study the analytic properties of slice regular functions. We start by illustrating the Cauchy and Schwarz integral formulas as well as some consequences. Then we prove a version of the Riemann mapping theorem, we discuss the properties of the zeros of slice regular functions and the Ehrenpreis-Malgrange lemma. Finally we prove a quaternionic version of Cartan theorem.

Keywords

Slice Regular Functions Schwarz Integral Formula Cartan's Theorem Riemann Mapping Theorem Quaternionic Polynomials 
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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Irene Sabadini
    • 1
    Email author
  • Daniele C. Struppa
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Schmid College of Science and TechnologyChapman UniversityOrangeUSA

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