Global holomorphic functions in several non-commuting variables
classification
🧮 math.OA
keywords
freefunctionsholomorphicfunctionlocallyproveanalyticapproximable
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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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