Integral Transform and Segal-Bargmann Representation Associated to q-Charlier Polynomials
Abstract
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.
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
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