Cyclic Vectors in Korenblum Type Spaces

Abstract

In this paper we use the technique of premeasures, introduced by Korenblum in the 1970's, to give a characterization of cyclic functions in the Korenblum type spaces $\mathscr{A}_{\Lambda}^{-\infty}$. In particular, we give a positive answer to a conjecture by Deninger [7, Conjecture 42].