Local interpolation in Hilbert spaces of Dirichlet series

Abstract

We denote by H \mathscr {H} 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 σ > 1 / 2 \sigma >1/2 is an interpolating sequence for H \mathscr {H} if and only if it is an interpolating sequence for the Hardy space H 2 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 σ > 1 / 2 \sigma >1/2 .