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Local interpolation in Hilbert spaces of Dirichlet series

Authors:	Jan-Fredrik Olsen Kristian Seip

Institution:	Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130 ; Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway

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