Open AccessWeighted Paley-Wiener spaces
Author(s) -
Yurii Lyubarskii,
Kristian Seip
Publication year - 2002
Publication title -
journal of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.574
H-Index - 111
eISSN - 1088-6834
pISSN - 0894-0347
DOI - 10.1090/s0894-0347-02-00397-1
Subject(s) - mathematics , uniqueness , pure mathematics , unit sphere , interpolation space , hardy space , interpolation (computer graphics) , class (philosophy) , function space , ball (mathematics) , mathematical analysis , algebra over a field , functional analysis , artificial intelligence , motion (physics) , biochemistry , chemistry , computer science , gene
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.