Seminar Analysis: Julien Sabin (University of Paris-Sud)

Optimal trace ideals properties of the Fourier restriction operator and applications

We study the trace ideals properties of the Fourier restriction operator to hypersurfaces. Equivalently, we generalize the theorems of Stein-Tomas and Strichartz to systems of orthonormal functions, with an optimal dependence on the number of such functions. As an application, we deduce new Strichartz inequalities describing the dispersive behaviour of the free evolution of quantum systems with an infinite number of particles. This is a joint work with Rupert Frank.

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