On the ℓ4:ℓ2 ratio of functions with restricted Fourier support

Naomi Kirshner, Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-review


Given a subset A⊆{0,1}n, let μ(A) be the maximal ratio between ℓ4 and ℓ2 norms of a function whose Fourier support is a subset of A.1 We make some simple observations about the connections between μ(A) and the additive properties of A on one hand, and between μ(A) and the uncertainty principle for A on the other hand. One application obtained by combining these observations with results in additive number theory is a stability result for the uncertainty principle on the discrete cube. Our more technical contribution is determining μ(A) rather precisely, when A is a Hamming sphere S(n,k) for all 0≤k≤n.

Original languageEnglish
Article number105202
JournalJournal of Combinatorial Theory - Series A
StatePublished - May 2020


  • Additive combinatorics
  • Fourier spectrum
  • Hypercontractivity
  • Krawchouk polynomials
  • Uncertainty principle

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


Dive into the research topics of 'On the ℓ4:ℓ2 ratio of functions with restricted Fourier support'. Together they form a unique fingerprint.

Cite this