Free holomorphic functions on the unit ball of B(H)^n
Functional Analysis
2007-11-19 v2 Operator Algebras
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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Cite
@article{arxiv.math/0605237,
title = {Free holomorphic functions on the unit ball of B(H)^n},
author = {Gelu Popescu},
journal= {arXiv preprint arXiv:math/0605237},
year = {2007}
}
Comments
51 pages