Variations on Fefferman's Ball Multiplier Theorem

What happens to an Lp function when one truncates its Fourier transform to a domain? This question is now rather well understood, thanks to famous results by Marcel Riesz and Charles Fefferman, and the answer depends on the domain: if it is a polytope, the function remains Lp integrable. But not necessarily when the domain is curved, such as a Euclidean ball. The lecture will be devoted to another question of the same flavour: What happens to a matrix and its singular values when some of its entries are set to zero? My goal will be to explain unexpected relations betweeen the two questions, which lead to a satisfactory answer to the second.

Based on a joint work with Javier Parcet and Eduardo Tablate.