Thorin classes of Lévy processes and their transforms

We define and characterize Thorin classes {ie294-01}, of infinitely divisible distributions on R+. We investigate Poisson, Karlin, and Bessel transforms of Thorin classes and also consider extended Thorin classes {ie294-02}. Canonical representation and self-decomposability properties of Thorin subordinated Gaussian Lévy processes are discussed. As an example, a subordinated Cauchy process is considered in detail.