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Weighted Paley-Wiener spaces sharing a majorant-weight

Author: Philippe Poulin
Journal: Proc. Amer. Math. Soc. 140 (2012), 941-949
MSC (2010): Primary 30H99
Published electronically: July 15, 2011
MathSciNet review: 2869078
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Abstract: We point out a need to slightly modify the statement of Theorem 2 in Yurii Lyubarskii and Kristian Seip's work Weighted Paley-Wiener spaces. This last theorem lists all weighted Paley-Wiener spaces (in reduced form) sharing a prescribed majorant-weight. Attention is called to a part of its proof that requires an additional argument. Such an argument, based on a new characterization of Beurling's lower uniform density, is then presented.

References [Enhancements On Off] (What's this?)

  • 1. Y. Lyubarskii and K. Seip, Weighted Paley-Wiener spaces, J. Amer. Math. Soc. 5 (2002), 979-1006. MR 1915824 (2003m:46039)
  • 2. L. de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, 1968. MR 0229011 (37:4590)
  • 3. T. Ransford, Potential Theory in the Complex Plane, London Math. Soc. Student Texts 28, Cambridge University Press, 1995. MR 1334766 (96e:31001)

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Additional Information

Philippe Poulin
Affiliation: Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, Al Ain, Abu Dhabi, United Arab Emirates

Keywords: de Branges space, weighted Paley-Wiener space, majorant-weight
Received by editor(s): December 16, 2010
Published electronically: July 15, 2011
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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