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Global holomorphic functions in several noncommuting variables

  • Jim Agler,
    U.C. San Diego , La Jolla, CA 92093, USA
  • McCarthy,
    Washington University , St. Louis, MO 63130, USA
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Abstract

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.
Keywords: noncommutative analysis, free holomorphic functions noncommutative analysis, free holomorphic functions
MSC Classifications: 15A54 show english descriptions Matrices over function rings in one or more variables 15A54 - Matrices over function rings in one or more variables
 

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