Radial Bargmann representation for the Fock space of type B

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Abstract

Let ν<_α,_q >be the probability and orthogonality measure for the q-Meixner-Pollaczek orthogonal polynomials, which has appeared in the work of Bożejko, Ejsmont, and Hasebe [J. Funct. Anal. 269, 1769–1795 (2015)] as the distribution of the (α,q)-Gaussian process (the Gaussian process of type B) over the (α,q)-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of ν<_α,_q>. Our main results cover not only the representation of q-Gaussian distribution by van Leeuwen and Maassen [J. Math. Phys. 36, 4743–4756 (1995)] but also of q^2-Gaussian and symmetric free Meixner distributions on R. In addition, non-trivial commutation relations satisfied by (α,q)-operators are presented.

Journal

  • Journal of Mathematical Physics

    Journal of Mathematical Physics 57(2), 021702, 2016-02

    AIP Publishing LLC

Codes

  • NII Article ID (NAID)
    120005985259
  • NII NACSIS-CAT ID (NCID)
    AA00701758
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0022-2488
  • Data Source
    IR 
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