Slice regular functions on real alternative algebras
Riccardo Ghiloni, Alessandro Perotti

TL;DR
This paper develops a comprehensive theory of slice regular functions on real alternative algebras, unifying and extending existing theories for quaternions, octonions, and Clifford algebras, with new algebraic and integral results.
Contribution
It introduces a unified framework for slice regular functions on real alternative algebras, extending previous theories and establishing new fundamental algebraic and integral formulas.
Findings
A strong fundamental theorem of algebra for polynomials over real alternative algebras.
A Cauchy integral formula for slice functions of class C^1.
Extension of existing function theories to broader algebraic contexts.
Abstract
In this paper we develop a theory of slice regular functions on a real alternative algebra . 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 and we prove a Cauchy integral formula for slice functions of class .
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