Generating functions for moments of the quasi-nilpotent DT-operator

Abstract

We prove a recursion formula for generating functions of certain renormalizations of *-moments of the DT(δ0, 1 -operator T, involving an operation ⊙ on formal power series and a transformation E 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. © 2003 Elsevier Science (USA). All rights reserved.