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Radial Bargmann representation for the Fock space of type B

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タイトル: Radial Bargmann representation for the Fock space of type B
著者: Asai, Nobuhiro 著作を一覧する
Bozejko, Marek 著作を一覧する
Hasebe, Takahiro 著作を一覧する
発行日: 2016年 2月
出版者: American Institute of Physics (AIP)
誌名: Journal of mathematical physics
巻: 57
号: 2
開始ページ: 021702
出版社 DOI: 10.1063/1.4939748
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.
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 長谷部 高広


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