On one result of J. Bourgain

  • S. V. Konyagin Мат. ин-т РАН, Москва, Россия
  • I. D. Shkredov Моск. ун-т им. М. В. Ломоносова, Россия

Abstract

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.
Published
25.03.2010
How to Cite
Konyagin, S. V., and I. D. Shkredov. “On One Result of J. Bourgain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 3, Mar. 2010, pp. 332–368, https://umj.imath.kiev.ua/index.php/umj/article/view/2872.
Section
Research articles