Том 71
№ 11

All Issues

Konyagin S. V.

Articles: 1
Article (Russian)

On one result of J. Bourgain

Konyagin S. V., Shkredov I. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 332–368

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.