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On one result of J. Bourgain

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    S. V. Konyagin

  2. Lomonosov Moscow State University, Moscow, Russia

    I. D. Shkredov

Authors
  1. S. V. Konyagin
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  2. I. D. Shkredov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 332–368, March, 2010.

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Konyagin, S.V., Shkredov, I.D. On one result of J. Bourgain. Ukr Math J 62, 380–419 (2010). https://doi.org/10.1007/s11253-010-0361-3

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  • DOI: https://doi.org/10.1007/s11253-010-0361-3

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