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 | References | Similar Articles | Additional Information

Abstract: We denote by 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 is an interpolating sequence for 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 .

**[Bis94]**C. Bishop,

Interpolating sequences for the Dirichlet space and its multipliers,

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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

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.