H2 Spaces of Non-commutative Functions

Mihai Popa; Victor Vinnikov

doi:10.1007/s11785-017-0747-4

H² Spaces of Non-commutative Functions

Mihai Popa, Victor Vinnikov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and asymptotic formulae for integration over the unitary group. The results are the first step in developing the general theory of free noncommutative bounded symmetric domains on the one hand and in studying the asymptotic free noncommutative analogues of classical spaces of analytic functions on the other.

Original language	English
Pages (from-to)	945-967
Number of pages	23
Journal	Complex Analysis and Operator Theory
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s11785-017-0747-4
State	Published - 1 Apr 2018

Keywords

Asymptotic free independence
Hardy H spaces
Non-commutative ball
Non-commutative functions
Non-commutative polydisc
Taylor–Taylor expansion for non-commutative functions

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1007/s11785-017-0747-4

Cite this

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abstract = "We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and asymptotic formulae for integration over the unitary group. The results are the first step in developing the general theory of free noncommutative bounded symmetric domains on the one hand and in studying the asymptotic free noncommutative analogues of classical spaces of analytic functions on the other.",

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AB - We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and asymptotic formulae for integration over the unitary group. The results are the first step in developing the general theory of free noncommutative bounded symmetric domains on the one hand and in studying the asymptotic free noncommutative analogues of classical spaces of analytic functions on the other.

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KW - Taylor–Taylor expansion for non-commutative functions

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