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

Ehud Friedgut, Gil Kalai, Assaf Naor

Research output: Contribution to journalArticlepeer-review

Abstract

In this note we describe Boolean functions f ( x1, x2,..., xn ) 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 = xk or f = 1 - xk. 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 languageEnglish (US)
Pages (from-to)427-437
Number of pages11
JournalAdvances in Applied Mathematics
Volume29
Issue number3
DOIs
StatePublished - Oct 2002

ASJC Scopus subject areas

  • Applied Mathematics

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