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

Research paper by Tom Sanders

Indexed on: 31 Mar '10Published on: 31 Mar '10Published in: Mathematics - Classical Analysis and ODEs



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.