Global Holomorphic Functions in Several Noncommuting Variables

Authors

Jim Agler, University of California - San Diego
John E. McCarthy, Washington University in St LouisFollow

Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

4-2015

Originally Published In

Canad. J. Math. 67(2015), 241-285

Abstract

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.

Comments

Preprint version of article copyright 2014 Canadian Mathematical Society published in Canad. J. Math. 67 (2015), 241-285 and available at http://dx.doi.org/10.4153/CJM-2014-024-1

Recommended Citation

Agler, Jim and McCarthy, John E., "Global Holomorphic Functions in Several Noncommuting Variables" (2015). Mathematics Faculty Publications. 17.
https://openscholarship.wustl.edu/math_facpubs/17