Ghiloni, Riccardo and Perotti, Alessandro (2011) *Slice regular functions on real alternative algebras.* In «Advances in Mathematics», vol. 226, n. 2 Elsevier, pp. 1662-1691. ISBN 0001-8708

## 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 $C^1$.

Item Type: | Article in journal |

Department or Research center: | Mathematics |

Subjects: | Q Science > QA Mathematics > QA299.6 Analysis |

Uncontrolled Keywords: | Functions of a hypercomplex variable, Quaternions, Octonions, Fundamental theorem of algebra, Cauchy integral formula |

Repository staff approval on: | 13 Jan 2011 |
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