Weighted Paley–Wiener spaces sharing a majorant-weight
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- by Philippe Poulin PDF
- Proc. Amer. Math. Soc. 140 (2012), 941-949 Request permission
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
- Yurii I. Lyubarskii and Kristian Seip, Weighted Paley-Wiener spaces, J. Amer. Math. Soc. 15 (2002), no. 4, 979–1006. MR 1915824, DOI 10.1090/S0894-0347-02-00397-1
- Louis de Branges, Hilbert spaces of entire functions, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1968. MR 0229011
- Thomas Ransford, Potential theory in the complex plane, London Mathematical Society Student Texts, vol. 28, Cambridge University Press, Cambridge, 1995. MR 1334766, DOI 10.1017/CBO9780511623776
Additional Information
- Philippe Poulin
- Affiliation: Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, Al Ain, Abu Dhabi, United Arab Emirates
- Email: PhilippePoulin@uaeu.ac.ae
- Received by editor(s): December 16, 2010
- Published electronically: July 15, 2011
- Communicated by: Richard Rochberg
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 941-949
- MSC (2010): Primary 30H99
- DOI: https://doi.org/10.1090/S0002-9939-2011-10978-X
- MathSciNet review: 2869078