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\(\hbox {H}^2\) Spaces of Non-commutative Functions

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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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Authors and Affiliations

  1. Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA

    Mihai Popa

  2. Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Mihai Popa

  3. Department of Mathematics, Ben Gurion University of Negev, 84105, Be’er Sheva, Israel

    Victor Vinnikov

Authors
  1. Mihai Popa
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  2. Victor Vinnikov
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Correspondence to Mihai Popa.

Additional information

Communicated by Hari Bercovici.

This work was partially supported by a Grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, Project No. PN-II-ID-PCE-2011-3-0119 and Simmons Foundation Grant No. 360242.

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Popa, M., Vinnikov, V. \(\hbox {H}^2\) Spaces of Non-commutative Functions. Complex Anal. Oper. Theory 12, 945–967 (2018). https://doi.org/10.1007/s11785-017-0747-4

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