Journal
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume 67, Issue 2, Pages 241-285Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.4153/CJM-2014-024-1
Keywords
noncommutative analysis; free holomorphic functions
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Funding
- National Science Foundation Grant [DMS 1068830, DMS 0966845, DMS 1300280]
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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.
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