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arXiv · 1305.1636

Global holomorphic functions in several non-commuting variables

Jim Agler·John E. McCarthy
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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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Jim Agler, John E. McCarthy. 2013-05-07. Global holomorphic functions in several non-commuting variables. https://arxiv.org/abs/1305.1636

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