Local interpolation in Hilbert spaces of Dirichlet series

Abstract

We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if it is an interpolating sequence for the Hardy space $H^2$ of the same half-plane. Similar local results are obtained for Hilbert spaces of ordinary Dirichlet series that relate to Bergman and Dirichlet spaces of the half-plane $\sigma >1/2$.

Cited by in corpus (4)

• Approximation numbers of composition operators on the $H^2$ space of Dirichlet series
• Interpolating sequences in spaces with the complete Pick property
• Composition operators on weighted Hilbert spaces of Dirichlet series
• Almost periodicity and boundary values of Dirichlet series