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Hilbert spaces of Dirichlet series and their multipliers


Author: John E. McCarthy
Journal: Trans. Amer. Math. Soc. 356 (2004), 881-893
MSC (2000): Primary 30B50, 46E20
Published electronically: October 9, 2003
MathSciNet review: 1984460
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted $\ell^2$ norms of the Dirichlet coefficients. We describe the multiplier algebras of these spaces. The functions in the multiplier algebra may or may not extend to be analytic on a larger half-plane than the functions in the Hilbert space.


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Additional Information

John E. McCarthy
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: mccarthy@wustl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03452-4
Received by editor(s): December 7, 2001
Published electronically: October 9, 2003
Additional Notes: The author was partially supported by National Science Foundation Grant DMS 0070639
Article copyright: © Copyright 2003 by the author