University of Birmingham > Talks@bham > Analysis seminar > Local maximizers for Fourier adjoint restriction estimates

Local maximizers for Fourier adjoint restriction estimates

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Restricting the Fourier transform to curved hypersurfaces improves its continuity properties in Lebesgue spaces. We consider the estimates obtained by such restriction to the paraboloid, to the cone and to the sphere, which are due to Strichartz, Tomas and Stein. These involve a multiplicative constant, whose exact value has been computed only in a few cases, corresponding to low spatial dimension. There is a conjecture, due to Foschi, concerning what the constant and the functions that attain it should be, in arbitrary dimension. We prove that there is an open set of functions on which this conjecture does hold. This is joint work with Felipe Gonçalves (Univ. Bonn).

This talk is part of the Analysis seminar series.

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