Global holomorphic functions in several non-commuting variables
Operator Algebras
2013-07-03 v2
Abstract
We define a free holomorphic function to be a function that is locally 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.
Cite
@article{arxiv.1305.1636,
title = {Global holomorphic functions in several non-commuting variables},
author = {Jim Agler and John E. McCarthy},
journal= {arXiv preprint arXiv:1305.1636},
year = {2013}
}