Segal-Bargmann Transforms of One-mode Interacting Fock Spaces Associated with Gaussian and Poisson Measures

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

Let ${\mu }_g$ and ${\mu }_p$ denote the Gaussian and Poisson measures on $\mathbb{R}$, respectively. We show that there exists a unique measure ${\tilde{\mu }}_g$ on $\mathbb{C}$ such that u…