Ukrainian Mathematical Journal

, Volume 62, Issue 3, pp 380–419 | Cite as

On one result of J. Bourgain

  • S. V. Konyagin
  • I. D. Shkredov

In a linear space of dimension n over the field \( {\mathbb{F}_2} \), we construct a set A of given density such that the Fourier transform of A is large on a large set, and the intersection of A with any subspace of small dimension is small. The results obtained show, in a certain sense, the sharpness of one theorem of J. Bourgain.


Abelian Group Natural Number Nonnegative Integer Chebyshev Polynomial Linear Span 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • S. V. Konyagin
    • 1
  • I. D. Shkredov
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

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