Combinatorica

, Volume 14, Issue 1, pp 35–50 | Cite as

Spectral properties of threshold functions

  • Craig Gotsman
  • Nathan Linial
Article

Abstract

We examine the spectra of boolean functions obtained as the sign of a real polynomial of degreed. A tight lower bound on various norms of the lowerd levels of the function's Fourier transform is established. The result is applied to derive best possible lower bounds on the influences of variables on linear threshold functions. Some conjectures are posed concerning upper and lower bounds on influences of variables in higher order threshold functions.

AMS subject classification codes (1991)

68 Q 15 68 R 05 

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Copyright information

© Akadémiai Kiadó - Springer-Verlag 1994

Authors and Affiliations

  • Craig Gotsman
    • 1
  • Nathan Linial
    • 2
  1. 1.Department of Computer ScienceTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Computer ScienceThe Hebrew UniversityJerusalemIsrael

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