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Free holomorphic functions on the unit ball of B(H)^n

Gelu Popescu
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Abstract

We develop a theory of holomorphic functions in several noncommuting (free) variables and thus provide a framework for the study of arbitrary n-tuples of operators. The main topics are the following: Free holomorphic functions and Hausdorff derivations; Cauchy, Liouville, and Schwartz type results for free holomorphic functions; Algebras of free holomorphic functions; Free analytic functional calculus and noncommutative Cauchy transforms; Weierstrass and Montel theorems for free holomorphic functions; Free pluriharmonic functions and noncommutative Poisson transforms; Hardy spaces of free holomorphic functions.

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BibTeXRIS

Gelu Popescu. 2007-11-19. Free holomorphic functions on the unit ball of B(H)^n. https://arxiv.org/abs/math/0605237

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