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

Tom Sanders
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Abstract

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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Tom Sanders. 2010-03-31. The l^1-norm of the Fourier transform on compact vector spaces. https://doi.org/10.1112/blms%2Fbdm010

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