When: Sunday, March 18, 10am
Where: Schreiber 309
Speaker: Alex Samorodnitsky, Hebrew University
Title: On norm ratio of functions with restricted Fourier support
Given a subset A of the
discrete cube, let mu(A) be the maximal ratio between the fourth and the second
norms of a function whose Fourier support is a subset of A. We describe simple
connections between mu(A) and the additive properties
of A on one hand, and between mu(A) and the uncertainty principle for A on the
other hand, and discuss some applications. One application obtained by
combining our observations with results in additive number theory is a
stability result for the uncertainty principle in the discrete cube.
We also determine mu(A) rather precisely when A is a Hamming sphere or a Hamming ball of any radius between zero and the dimension of the cube, and discuss some applications of this, in particular connections to hypercontractivity, and some conjectures.
Joint work with Naomi Kirshner.