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Some results related to the Logvinenko-Sereda theorem

Author(s): Oleg Kovrijkine
Journal: Proc. Amer. Math. Soc. 129 (2001), 3037-3047.
MSC (2000): Primary 42A99, 42B99
Posted: April 2, 2001
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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:

1.: R.P. Boas, Entire functions, Academic Press Inc., New York, 1954. MR 16:914f
2.: P. Borwein, T. Erdelyi, Polynomials and polynomial inequalities, Springer-Verlag, New York, 1995. MR 97e:41001
3.: V. P. Havin, B. Joricke, The Uncertainty Principle in Harmonic Analysis, Springer-Verlag, Berlin Heidelberg, 1994. MR 96c:42001
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: 10.1090/S0002-9939-01-05926-3
PII: S 0002-9939(01)05926-3
Received by editor(s): September 24, 1999
Received by editor(s) in revised form: March 3, 2000
Posted: April 2, 2001
Communicated by: Albert Baernstein II
Copyright of article: Copyright 2001, American Mathematical Society


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