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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Weighted Paley-Wiener spaces


Authors: Yurii I. Lyubarskii and Kristian Seip
Journal: J. Amer. Math. Soc. 15 (2002), 979-1006
MSC (2000): Primary 46E22; Secondary 30E05, 42A99
Published electronically: June 21, 2002
MathSciNet review: 1915824
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Abstract: We study problems of sampling and interpolation in a wide class of weighted spaces of entire functions. These weights are characterized by the property that their natural regularization as the envelop of the unit ball of the corresponding space is equivalent to the original weight. We give an independent description of such weights and also show that, in a sense, this is the widest class of weights and associated spaces for which results on sets of uniqueness, sampling, and interpolation related to the classical Paley-Wiener spaces can be extended in a direct and natural way, keeping the basic features of the theory intact. One of the basic tools for our study is the De Brange theory of spaces of entire functions.


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Additional Information

Yurii I. Lyubarskii
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N–7491 Trondheim, Norway
Email: yura@math.ntnu.no

Kristian Seip
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N–7491 Trondheim, Norway
Email: seip@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00397-1
PII: S 0894-0347(02)00397-1
Keywords: De Branges spaces, Paley-Wiener spaces, interpolation, sampling
Received by editor(s): March 7, 2002
Published electronically: June 21, 2002
Article copyright: © Copyright 2002 American Mathematical Society