|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Radial Bargmann representation for the Fock space of type B
| Title: | Radial Bargmann representation for the Fock space of type B |
| Authors: | Asai, Nobuhiro Browse this author | | Bozejko, Marek Browse this author | | Hasebe, Takahiro Browse this author |
| Issue Date: | Feb-2016 |
| Publisher: | American Institute of Physics (AIP) |
| Journal Title: | Journal of mathematical physics |
| Volume: | 57 |
| Issue: | 2 |
| Start Page: | 021702 |
| Publisher DOI: | 10.1063/1.4939748 |
| Abstract: | 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. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/64421 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 長谷部 高広
|
