GENERATING FUNCTIONS FOR MOMENTS OF THE QUASI-NILPOTENT DT-OPERATOR

KEN DYKEMA CATHERINE YAN

Abstract. We prove a recursion formula for generating functions of certain renormalizations of ∗-moments of the DT(δ_{0}, 1)-operator T, involving an operation ⊙ on formal power series and a transformation U that converts ⊙ to usual multiplication. This recursion formula is used to prove that all of these generating functions are rational functions, and to find a few of them explicitly.