Local interpolation in Hilbert spaces of Dirichlet series

Details Local interpolation in Hilbert spaces of Dirichlet series Local interpolation in Hilbert spaces of Dirichlet series

2006-08-21

arxiv.org/abs/math/0608506v1

Mathematics

Complex Variables

Scientific paper

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 $\sigma >1/2$.

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