Local interpolation in Hilbert spaces of Dirichlet series

Olsen, Jan-Fredrik; Seip, Kristian

doi:10.1090/S0002-9939-07-08955-1

Local interpolation in Hilbert spaces of Dirichlet series
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by Jan-Fredrik Olsen and Kristian Seip

Proc. Amer. Math. Soc. 136 (2008), 203-212

DOI: https://doi.org/10.1090/S0002-9939-07-08955-1

Published electronically: October 18, 2007

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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 $H^2$ 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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