We define a free holomorphic function to be a function
that is locally, with respect to the free topology, a bounded
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.
noncommutative analysis, free holomorphic functions
15A54 - Matrices over function rings in one or more variables