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

 

Sampling sets for Hardy spaces of the disk


Author: Pascal J. Thomas
Journal: Proc. Amer. Math. Soc. 126 (1998), 2927-2932
MSC (1991): Primary 30E10, 30D55, 30C15
MathSciNet review: 1452830
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Abstract: We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and Øyma about interpolating sequences in the same spaces, and it yields sampling sets which do not depend on the value of $p$ and correspond to the result proved for bounded functions ($p=\infty $) by Brown, Shields and Zeller. The second notion, while formally closer to the one used for weighted Bergman spaces, leads to trivial situations only, but raises a possibly interesting problem.


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Additional Information

Pascal J. Thomas
Affiliation: Laboratoire Emile Picard, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Email: pthomas@cict.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04411-6
PII: S 0002-9939(98)04411-6
Received by editor(s): October 14, 1996
Received by editor(s) in revised form: February 27, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society