Compact composition operators with non-linear symbols on the $H^2$ space of Dirichlet series

Abstract

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $\phi (s)=c_{0}s+{\phi }_0(s)$, where ${\phi }_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic $c_0$ of $\phi$ and, when $c_0=0$, on both the degree of ${\phi }_0$ and its local behaviour near a boundary point. We also study the approximation numbers for some of these operators. Our methods involve geometric estimates of Carleson measures and tools from differential geometry.

Cited by in corpus (4)

• A mean counting function for Dirichlet series and compact composition operators
• Composition operators and embedding theorems for some function spaces of Dirichlet series
• Counting functions for Dirichlet series and compactness of composition operators
• Orthogonal decomposition of composition operators on the $H^2$ space of Dirichlet series