The l^1-norm of the Fourier transform on compact vector spaces

Details The l^1-norm of the Fourier transform on compact vector spaces The l^1-norm of the Fourier transform on compact vector spaces

2006-05-18

arxiv.org/abs/math/0605519v2

Bull. Lond. Math. Soc. 39 (2007), no. 3, 509--521

Mathematics

Classical Analysis and ODEs

13 pp. Corrected typos. Updated references.

Scientific paper

10.1112/blms/bdm010

Suppose that A is a subset of F_2^n of density as close to 1/3 as possible.
We show that the A(F_2^n)-norm (that is the sum of the absolute values of the
Fourier transform) of the characterstic function of A is bounded below by an
absolute constant times log n as n tends to infinity.

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