A Seidel-Walsh theorem with linear differential operators

Abstract.

Assume that $\{S_n\}_1^\infty$ is a sequence of automorphisms of the open unit disk ${\Bbb D}$ and that $\{T_n\}_1^\infty$ 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 $f \in X$ such that $\{(T_n\,f) \circ S_n: \, n \in {\Bbb N}\}$ is dense in $H({\Bbb D})$ is residual in X. This extends the Seidel-Walsh theorem together with some subsequent results.