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

DOI:
https://doi.org/10.1090/S0894-0347-02-00397-1

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:
https://doi.org/10.1090/S0894-0347-02-00397-1

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