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Slice regular functions on real alternative algebras

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
226
Issue
2
Identifiers
DOI: 10.1016/j.aim.2010.08.015
Keywords
  • Functions Of A Hypercomplex Variable
  • Quaternions
  • Octonions
  • Clifford Algebras
  • Fundamental Theorem Of Algebra
  • Cauchy Integral Formula
Disciplines
  • Mathematics

Abstract

Abstract In this paper we develop a theory of slice regular functions on a real alternative algebra A. Our approach is based on a well-known Fueter's construction. Two recent function theories can be included in our general theory: the one of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits to extend the range of these function theories and to obtain new results. In particular, we get a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in A and we prove a Cauchy integral formula for slice functions of class C 1 .

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