Global Holomorphic Functions in Several Noncommuting Variables
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 the...
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Veröffentlicht in: | Canadian journal of mathematics 2015-04, Vol.67 (2), p.241-285 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | 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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ISSN: | 0008-414X 1496-4279 |
DOI: | 10.4153/CJM-2014-024-1 |