TY - JOUR
T1 - Global holomorphic functions in several noncommuting variables
AU - Agler, Jim
AU - McCarthy, John E.
N1 - 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 -