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Journal of Functional Analysis
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Preprint . 2006
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http://dx.doi.org/10.1016/j.jf...
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Journal of Functional Analysis
Article . 2006 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2006
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Free holomorphic functions on the unit ball ofB(H)n

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2006Embargo end date: 01 Jan 2006 English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 241, pages 268-333 (issn: 0022-1236, Copyright policy )
Authors: Popescu, Gelu;

doi: 10.1016/j.jfa.2006.07.004 , 10.48550/arxiv.math/0605237

arXiv: math/0605237

Free holomorphic functions on the unit ball ofB(H)n

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.

51 pages

Related Organizations
Keywords

Mathematics - Operator Algebras, 46T25, Hardy space, Analytic functional calculus, 47A60, Cauchy transform, 47A56; 47A13; 47A60; 46T25; 46E15, Fock space, Functional Analysis (math.FA), Mathematics - Functional Analysis, 47A56, 47A13, Poisson transform, FOS: Mathematics, Free holomorphic functions, Creation operators, 46E15, Multivariable operator theory, Hausdorff derivation, Operator Algebras (math.OA)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
101
Top 10%
Top 10%
Top 10%
Green
hybrid