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2 results

  • A refined nc Oka–Weil theorem

  • Part of
  • Kenta Kojin
  • Journal:
    Canadian Mathematical Bulletin / Volume 66 / Issue 1 / March 2023
    Published online by Cambridge University Press:
    02 November 2021, pp. 218-224
    Print publication:
    March 2023
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  • This short note refines a noncommutative (nc) Oka–Weil theorem by using a characterization of free compact nc sets based on the notion of dilation hulls. A consequence of it is that any free holomorphic function can be represented as a free polynomial on each free compact nc set.

  • Global Holomorphic Functions in Several Noncommuting Variables

  • Jim Agler, John E. McCarthy
  • Journal:
    Canadian Journal of Mathematics / Volume 67 / Issue 2 / April 2015
    Published online by Cambridge University Press:
    20 November 2018, pp. 241-285
    Print publication:
    April 2015
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  • 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.