In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.

The algebra of slice functions / Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 369:(2017), pp. 4725-4762. [10.1090/tran/6816]

The algebra of slice functions

STOPPATO, CATERINA
2017

Abstract

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.
2017
369
4725
4762
Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1083330
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