Combinatorics Seminar

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.