Boolean functions whose Fourier transform is concentrated on the first two levels

Ehud Friedgut; Gil Kalai; Assaf Naor

doi:10.1016/S0196-8858(02)00024-6

Boolean functions whose Fourier transform is concentrated on the first two levels

Ehud Friedgut
, Gil Kalai^*
, Assaf Naor

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

71 Scopus citations

Abstract

In this note we describe Boolean functions f ( x₁, x₂,..., x_n ) whose Fourier coefficients are concentrated on the lowest two levels. We show that such a function is close to a constant function or to a function of the form f = x_k or f = 1 - x_k. This result implies a "stability" version of a classical discrete isoperimetric result and has an application in the study of neutral social choice functions. The proofs touch on interesting harmonic analysis issues.

Original language	English
Pages (from-to)	427-437
Number of pages	11
Journal	Advances in Applied Mathematics
Volume	29
Issue number	3
DOIs	https://doi.org/10.1016/S0196-8858(02)00024-6
State	Published - Oct 2002

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Boolean functions whose Fourier transform is concentrated on the first two levels

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