# 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
- Disciplines

## 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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