期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 260, 期 5, 页码 1476-1490出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2010.11.007
关键词
Non-commutative set and function; Analytic map; Proper map; Rigidity; Linear matrix inequality; Several complex variables; Free analysis; Free real algebraic geometry
类别
资金
- NSF [DMS-0700758, DMS-0757212, DMS-0758306]
- Ford Motor Co.
- Slovenian Research Agency [P1-0222, P1-0288]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0757212, 0758306] Funding Source: National Science Foundation
This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations they are free variables. Analytic free maps include vector-valued polynomials in free (non-commuting) variables and form a canonical class of mappings from one non-commutative domain D in say g variables to another non-commutative domain (D) over tilde in (g) over tilde variables. As a natural extension of the usual notion, an analytic free map is proper if it maps the boundary of D into the boundary of (D) over tilde. Assuming that both domains contain 0, we show that if f : D -> (D) over tilde is a proper analytic free map, and f(0) = 0, then f is one-to-one. Moreover, if also g = (g) over tilde, then f is invertible and f(-1) is also an analytic free map. These conclusions on the map f are the strongest possible without additional assumptions on the domains D and (D) over tilde. (C) 2010 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据