Global Holomorphic Functions in Several Noncommuting Variables

Agler, Jim ; McCarthy, John E.

Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 241-285

Résumé

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.

Détail

DOI : 10.4153/CJM-2014-024-1

Mots-clés : 15A54, noncommutative analysis, free holomorphic functions

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