Global Holomorphic Functions in Several Noncommuting Variables

被引：52
|
作者：
Agler, Jim [1 ]
McCarthy, John E. [2 ]
机构：
[1] Univ Calif San Diego, La Jolla, CA 92093 USA
[2] Washington Univ, St Louis, MO 63130 USA
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2015年 / 67卷 / 02期
基金：
美国国家科学基金会;
关键词：
noncommutative analysis; free holomorphic functions; UNIT BALL; INTERPOLATION; DOMAINS;
D O I：
10.4153/CJM-2014-024-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.
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页码：241 / 285
页数：45
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