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Global Holomorphic Functions in Several Noncommuting Variables

Published online by Cambridge University Press:  20 November 2018

Jim Agler  and
John E. McCarthy
Jim Agler
Affiliation:
U.C. San Diego, La Jolla, CA 92093. e-mail: jagler@san.rr.com
John E. McCarthy
Affiliation:
Washington University, St. Louis, MO 63130. e-mail: mccarthy@math.wustl.edu
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Abstract

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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.

Keywords

15A54noncommutative analysisfree holomorphic functions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 2 , April 2015 , pp. 241 - 285
Copyright
Copyright © Canadian Mathematical Society 2015

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