Geodesic
Global Holomorphic Functions in Several Noncommuting Variables
Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 241-285

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DOI

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.
DOI : 10.4153/CJM-2014-024-1
Mots-clés : 15A54, noncommutative analysis, free holomorphic functions 
Agler, Jim; McCarthy, John E. Global Holomorphic Functions in Several Noncommuting Variables. Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 241-285. doi: 10.4153/CJM-2014-024-1
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     title = {Global {Holomorphic} {Functions} in {Several} {Noncommuting} {Variables}},
     journal = {Canadian journal of mathematics},
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     year = {2015},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-024-1/}
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