Cyclic vectors in Korenblum type spaces

TL;DR

This paper characterizes cyclic functions in Korenblum type spaces using premeasure techniques, confirming a conjecture by Deninger and advancing understanding of these function spaces.

Contribution

It provides a new characterization of cyclic functions in Korenblum spaces and confirms Deninger's conjecture using premeasure methods.

Findings

Characterization of cyclic functions in Korenblum spaces

Positive resolution of Deninger's conjecture

Application of premeasure techniques to function space analysis

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 $\mathcal{A}_{\Lambda}^{-\infty}$. In particular, we give a positive answer to a conjecture by Deninger (arXiv:1111.6416).