Compact composition operators with non-linear symbols on the H2 space of Dirichlet series

Abstract

We investigate compactness of composition operators on the Hardy space of Dirichlet series induced by a map φ(s)=c0s+φ0(s), where φ0 is a Dirichlet polynomial. Our results depend heavily on the characteristic c0 of φ and, whenc0=0, on both the degree of φ0 and its local behavior 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.