Local interpolation in Hilbert spaces of Dirichlet series
Authors:
JanFredrik Olsen and Kristian Seip
Journal:
Proc. Amer. Math. Soc. 136 (2008), 203212
MSC (2000):
Primary 30B50; Secondary 30E05, 30H05, 42B30, 46E20
Published electronically:
October 18, 2007
MathSciNet review:
2350405
Fulltext PDF Free Access
Abstract 
References 
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Abstract: We denote by the Hilbert space of ordinary Dirichlet series with squaresummable coefficients. The main result is that a bounded sequence of points in the halfplane is an interpolating sequence for if and only if it is an interpolating sequence for the Hardy space of the same halfplane. Similar local results are obtained for Hilbert spaces of ordinary Dirichlet series that relate to Bergman and Dirichlet spaces of the halfplane .
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Interpolating sequences for the Dirichlet space and its multipliers, Preprint, 1994.
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Duke Math. J. 86, 137 (1997). MR 1427844 (99i:42033)
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Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, volume 84 of CBMS Regional Conference Series in Mathematics, AMS, 1994.
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 K. Seip, Beurling type density theorems in the unit disk,
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 H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions,
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An Introduction to Nonharmonic Fourier Series, Academic Press, New York, Revised First Edition, 2001. MR 1836633 (2002b:42001)
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Additional Information
JanFredrik 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), NO7491 Trondheim, Norway
Email:
seip@math.ntnu.no
DOI:
http://dx.doi.org/10.1090/S0002993907089551
PII:
S 00029939(07)089551
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.
