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タイトル: Radial Bargmann representation for the Fock space of type B
著者: Asai, Nobuhiro
Bożejko, Marek
Hasebe, Takahiro
著者(訳): 淺井, 暢宏
出典: Journal of Mathematical Physics. 2016, 57(2), 021702
出版者: AIP Publishing LLC
抄録: 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.
URI: http://hdl.handle.net/10424/6957
関連URI: http://dx.doi.org/10.1063/1.4939748
言語: en
NII資源タイプ: Journal Article
DOI: info:doi/10.1063/1.4939748
権利情報: Copyright 2016 AIP Publishing LLC. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Mathematical Physics. 2016, 57(2), 021702 and may be found at http://dx.doi.org/10.1063/1.4939748.
著者版フラグ: publisher
出現コレクション:022 外国雑誌


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