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Diogo Oliveira e Silva : Towards a sharp restriction inequality on the circle (Mar 16, 2015 4:25 PM)

The geometric notion of curvature is closely related to the analytic concept of Fourier decay. This will be our starting point to explore some restriction inequalities on spheres sitting in d-dimensional Euclidean space. The case d=2 is of special interest as it can be approached with a variety of tools ranging from elementary combinatorics and planar geometry to Fourier analysis and special function theory. Among other things, we shall see how new convexity estimates for certain integrals involving six-fold products of Bessel functions allow for partial progress in this tantalizing problem.

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