A Seidel-Walsh theorem with linear differential operators

Abstract

Assume that {Sn}∞1 is a sequence of automorphisms of the open unit disk D and that {Tn}∞1 is a sequence of linear differential operators with constant coefficients, both of them satisfying suitable conditions. We prove that for certain spaces X of holomorphic functions in the open unit disk, the set of functions f ∈ X such that {(Tnf) ◦ Sn : n ∈ N} is dense in H(D) is residual in X. This extends the Seidel-Walsh theorem together with some subsequent results.