TY - JOUR
T1 - Global holomorphic functions in several noncommuting variables
AU - Agler, Jim
AU - McCarthy, John E.
N1 - Funding Information:
The first author was partially supported by National Science Foundation Grant DMS 1068830. The second author was partially supported by National Science Foundation Grants DMS 0966845 and DMS 1300280.
Publisher Copyright:
© Canadian Mathematical Society 2014.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Free holomorphic functions
KW - Noncommutative analysis
UR - http://www.scopus.com/inward/record.url?scp=84983353025&partnerID=8YFLogxK
U2 - 10.4153/CJM-2014-024-1
DO - 10.4153/CJM-2014-024-1
M3 - Article
AN - SCOPUS:84983353025
SN - 0008-414X
VL - 67
SP - 241
EP - 285
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 2
ER -