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Weighted Paley-Wiener spaces
Author(s):
Yurii
I.
Lyubarskii;
Kristian
Seip
Journal:
J. Amer. Math. Soc.
15
(2002),
979-1006.
MSC (2000):
Primary 46E22;
Secondary 30E05, 42A99
Posted:
June 21, 2002
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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:
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
Posted:
June 21, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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