Radial Bargmann representation for the Fock space of type B
| Autor: | Asai, Nobuhiro, Bożejko, Marek, Hasebe, Takahiro |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics, Vol.57, Issue 2, 021702, 2016 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4939748 |
| Popis: | Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} 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 \cite{LM95}, but also of $q^2$-Gaussian and symmetric free Meixner distributions on $\mathbb R$. In addition, non-trivial commutation relations satisfied by $(\alpha,q)$-operators are presented. Comment: 13 pages, minor changes have been made |
| Databáze: | arXiv |
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