Noncommutative reproducing kernel Hilbert spaces

Ball, Joseph A.; Marx, Gregory; Vinnikov, Victor

doi:10.48550/arxiv.1602.00760

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2017

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“…This is related to the different (as opposed to the commutative case) convergence patterns for noncommutative power series, see [8,Section 8.3]. A general theory of noncommutative reproducing kernel Hilbert spaces and their multipliers is developed in the forthcoming paper [2]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

H${}^2$ Spaces of Non-Commutative Functions

Popa,

Vinnikov

2017

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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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Section: Introductionmentioning

confidence: 99%