Integral Transform and Segal-Bargmann Representation Associated to q-Charlier Polynomials
| dc.creator | Asai, Nobuhiro | |
| dc.date | 2001-04-27 | |
| dc.date | 2001-11-30 | |
| dc.date.accessioned | 2026-07-07T04:41:29Z | |
| dc.date.available | 2026-07-07T04:41:29Z | |
| dc.description | Let $μ_p^{(q)}$ be the q-deformed Poisson measure in the sense of Saitoh Yoshida and $ν_p$ be the measure given by Equation \eqref{eq:nu-q}. In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform associated with $μ_p^{(q)}$. We prove that our Segal-Bargmann transform is a unitary map of $L^2(μ_p^{(q)})$ onto the q-deformed Hardy space ${\cal H}^2(ν_q)$. Moreover, we give the Segal-Bargmann representation of the multiplication operator by $x$ in $L^2(μ_p^{(q)})$, which is a linear combination of the q-creation, q-annihilation, q-number, and scalar operators. | |
| dc.description | Accepted for the publication in "Quantum Information IV", T. Hida and K. Saito (eds.), World Scientific. Minor misprints have been fixed. Reference information has been updated | |
| dc.identifier | https://arxiv.org/abs/math/0104260 | |
| dc.identifier | http://arxiv.org/abs/math/0104260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61376 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Representation Theory | |
| dc.subject | 33D45, 44A20,81S25,81R30 | |
| dc.title | Integral Transform and Segal-Bargmann Representation Associated to q-Charlier Polynomials | |
| dc.type | text |