Radial Bargmann representation for the Fock space of type B

Asai, Nobuhiro; Bozejko, Marek; Hasebe, Takahiro

Journal of mathematical physics, 2016, 57(2), 021702

Permalink : https://hdl.handle.net/2115/64421

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アクセス権	open access
URI	https://hdl.handle.net/2115/64421
タイトル	Radial Bargmann representation for the Fock space of type B
著者	Asai, Nobuhiro ; Bozejko, Marek ; Hasebe, Takahiro
著者名 Asai, Nobuhiro
著者名 Bozejko, Marek
著者名 Hasebe, Takahiro
言語	英語
発行日	2016-02
出版者	American Institute of Physics (AIP)
収録物名	Journal of mathematical physics
巻(号)	57(2)
ページ	021702
抄録	Let nu(alpha,q) be the probability and orthogonality measure for the q-Meixner-Pollaczek orthogonal polynomials, which has appeared in the work of Bozejko, Ejsmont, and Hasebe [J. Funct. Anal. 269, 1769-1795 (2015)] as the distribution of the (alpha,q)-Gaussian process (the Gaussian process of type B) over the (alpha,q)-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of nu(alpha,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 (alpha,q)-operators are presented. (C) 2016 AIP Publishing LLC.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	0022-2488
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1063/1.4939748