Boolean functions with small spectral norm

Details Boolean functions with small spectral norm Boolean functions with small spectral norm

2006-05-18

arxiv.org/abs/math/0605524v2

Geom. Funct. Anal. 18 (2008), no. 1, 144-162

Mathematics

Classical Analysis and ODEs

17 pp. Updated references.

Scientific paper

10.1007/s00039-008-0654-y

Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm
(that is the sum of the absolute values of its Fourier coefficients) at most M.
We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))
indicator functions of subgroups of F_2^n.

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