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Some results related to the Logvinenko-Sereda theorem


Author: Oleg Kovrijkine
Journal: Proc. Amer. Math. Soc. 129 (2001), 3037-3047
MSC (2000): Primary 42A99, 42B99
DOI: https://doi.org/10.1090/S0002-9939-01-05926-3
Published electronically: April 2, 2001
MathSciNet review: 1840110
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Abstract:

We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial instead of exponential bound in this theorem, and we extend it to the case of functions with Fourier transforms supported in the union of a bounded number of intervals.


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

  • 1. R.P. Boas, Entire functions, Academic Press Inc., New York, 1954. MR 16:914f
  • 2. Peter Borwein and Tamás Erdélyi, Polynomials and polynomial inequalities, Graduate Texts in Mathematics, vol. 161, Springer-Verlag, New York, 1995. MR 1367960
  • 3. Victor Havin and Burglind Jöricke, The uncertainty principle in harmonic analysis, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 28, Springer-Verlag, Berlin, 1994. MR 1303780
  • 4. F. L. Nazarov, Local estimates of exponential polynomials and their application to inequalities of uncertainty principle type, St. Petersburg Math. J. 5(1994), 663-717.

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Additional Information

Oleg Kovrijkine
Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Address at time of publication: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Email: olegk@its.caltech.edu, olegk@ias.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05926-3
Received by editor(s): September 24, 1999
Received by editor(s) in revised form: March 3, 2000
Published electronically: April 2, 2001
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society