THE ALGEBRA OF SLICE FUNCTIONS

被引：38

作者：

Ghiloni, Riccardo ^{[1
]}

Perotti, Alessandro ^{[1
]}

Stoppato, Caterina ^{[2
]}

机构：

[1] Univ Trento, Dipartimento Matemat, Via Sommarive 14, I-38123 Povo, Italy

[2] Univ Florence, Ist Nazl Alta Matemat, Unita Ric Firenze DiMaI U DINI, Viale Morgagni 67-A, I-50134 Florence, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 07期

关键词：

REGULAR FUNCTIONS; SINGULARITIES; ZEROS;

D O I：

10.1090/tran/6816

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：4725 / 4762

页数：38

共 27 条

[1] Some properties for quaternionic slice regular functions on domains without real points [J].