An algebraic structure for Faber polynomials

Let Σ be the set of functions, convergent for all |z|>1, with a Laurent series of the form f(z)=z+∑n⩾0anz-n. In this paper, we prove that the set of Faber polynomial sequences over Σ and the set of their normalized kth derivative sequences form groups which are isomorphic to the hitting time subgroup and the Bell(k) subgroup of the Riordan group, respectively. Further, a relationship between such Faber polynomial sequences and Lucas and Sheffer polynomial sequences is derived.