The Segal–Bargmann transform for Lévy white noise functionals associated with non-integrable Lévy processes

By using a method of truncation, we derive the closed form of the Segal–Bargmann transform of Lévy white noise functionals associated with a Lévy process with the Lévy spectrum without the moment condition. Besides, a sufficient and necessary condition to the existence of Lévy stochastic integrals is obtained.