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.

引用

页码：241 / 285

页数：45

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