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

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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.




Dykema, K., & Yan, C. (2003). Generating functions for moments of the quasi-nilpotent DT-operator. Advances in Applied Mathematics, 30(3), 545–561.

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