Hilbert spaces of Dirichlet series and their multipliers

Abstract

We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted ℓ 2 \ell ^2 norms of the Dirichlet coefficients. We describe the multiplier algebras of these spaces. The functions in the multiplier algebra may or may not extend to be analytic on a larger half-plane than the functions in the Hilbert space.