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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local interpolation in Hilbert spaces of Dirichlet series


Authors: Jan-Fredrik Olsen and Kristian Seip
Journal: Proc. Amer. Math. Soc. 136 (2008), 203-212
MSC (2000): Primary 30B50; Secondary 30E05, 30H05, 42B30, 46E20
Published electronically: October 18, 2007
MathSciNet review: 2350405
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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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Additional Information

Jan-Fredrik Olsen
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
Email: janfreol@math.ntnu.no

Kristian Seip
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
Email: seip@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08955-1
PII: S 0002-9939(07)08955-1
Received by editor(s): July 17, 2006
Received by editor(s) in revised form: October 12, 2006
Published electronically: October 18, 2007
Additional Notes: The authors are supported by the Research Council of Norway grant 160192/V30.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.