Random Variables and Positive Definite Kernels Associated with the Schroedinger Algebra

We show that the Feinsilver-Kocik-Schott (FKS) kernel for the Schroedinger algebra is not positive definite. We show how the FKS Schroedinger kernel can be reduced to a positive definite one through a restriction of the defining parameters of the exponential vectors. We define the Fock space associated with the reduced FKS Schroedinger kernel. We compute the characteristic functions of quantum random variables naturally associated with the FKS Schroedinger kernel and expressed in terms of the renormalized higher powers of white noise (or RHPWN) Lie algebra generators.