Weighted Paley-Wiener spaces

Lyubarskii, Yurii; Seip, Kristian

doi:10.1090/S0894-0347-02-00397-1

Weighted Paley-Wiener spaces
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by Yurii I. Lyubarskii and Kristian Seip

J. Amer. Math. Soc. 15 (2002), 979-1006

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

Published electronically: 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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