Global holomorphic functions in several non-commuting variables

Published 7 May 2013 in math.OA | (1305.1636v2)

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.

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