Slice regular functions on real alternative algebras

2010/08/25 by Riccardo Ghiloni, Alessandro Perotti · 2 citations
Mathematics · #math.CV #math.RA #msc:17D05 #msc:30C15 #msc:30G35 #msc:32A30

paper · pdf · doi:10.1016/j.aim.2010.08.015

published as Advances in Mathematics 226 (2011) pp.1662-1691 · 32 pages - accepted for publication in Advances in Mathematics

arxiv created 2010/08/25 · arxiv updated 2018/07/02

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 C¹.

Cited by

• Slice regular functions of several octonionic variables
• Some properties for quaternionic slice-regular functions on domains without real points

Related

• Generalized partial-slice monogenic functions: the octonionic case
• A unified theory of regular functions of a hypercomplex variable
• Algebra of slice regular functions on non-symmetric domains in several quaternionic variables
• Noncommutative Cauchy integral formula
• Entire slice regular functions