Algebraic Properties of the Module of Slice Regular Functions in Several Quaternionic Variables

被引：15

作者：

Colombo, Fabrizio ^{[1
]}

Sabadini, Irene ^{[1
]}

Struppa, Daniele C. ^{[2
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Chapman Univ, Schmid Coll Sci, Orange, CA 92866 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2012年 / 61卷 / 04期

关键词：

algebraic analysis; slice regular functions; quaternions; MONOGENIC FUNCTIONS; CALCULUS; FORMULA; THEOREM; KERNEL;

D O I：

10.1512/iumj.2012.61.4978

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we define the notion of slice regularity for several quaternionic variables by employing the recent definition due to Ghiloni and Perotti in one variable [25]. We show that in the case of several variables slice regularity is equivalent to being solutions of intertwined Cauchy-Riemann type operators, and we give an algebraic treatment of these functions. We also sketch how to extend our ideas to the case of higher dimension.

引用

页码：1581 / 1602

页数：22

共 34 条

[11] The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators
Colombo, Fabrizio
Sabadini, Irene
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 373 (02) : 655 - 679
[12] Duality theorems for slice hyperholomorphic functions
Colombo, Fabrizio
Sabadini, Irene
Struppa, Daniele C.
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2010, 645 : 85 - 104
[13] An extension theorem for slice monogenic functions and some of its consequences
Colombo, Fabrizio
Sabadini, Irene
Struppa, Daniele C.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2010, 177 (01) : 369 - 389
[14] On the formulations of the quaternionic functional calculus
Colombo, Fabrizio
Sabadini, Irene
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2010, 60 (10) : 1490 - 1508
[15] A Cauchy kernel for slice regular functions
Colombo, Fabrizio
Gentili, Graziano
Sabadini, Irene
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2010, 37 (04) : 361 - 378
[16] Extension results for slice regular functions of a quaternionic variable
Colombo, Fabrizio
Gentili, Graziano
Sabadini, Irene
Struppa, Daniele
[J]. ADVANCES IN MATHEMATICS, 2009, 222 (05) : 1793 - 1808
[17] Slice monogenic functions
Colombo, Fabrizio
Sabadini, Irene
Struppa, Daniele C.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2009, 171 (01) : 385 - 403
[18] Non Commutative Functional Calculus: Bounded Operators
Colombo, Fabrizio
Gentili, Graziano
Sabadini, Irene
Struppa, Daniele C.
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2010, 4 (04) : 821 - 843
[19] On Some Properties of the Quaternionic Functional Calculus
Colombo, Fabrizio
Sabadini, Irene
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2009, 19 (03) : 601 - 627
[20] Colombo F, 2009, TRENDS MATH, P101

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