On one result of J. Bourgain

• Date: 2010
• Main Authors: Konyagin, S. V., Shkredov, I. D., Конягин, С. В., Шкредов, И. Д.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2872
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 shar...