The restriction of the Fourier transform to surfaces: the hyperbolic case
Analysis and Geometry Seminar
12th June 2018, 2:00 pm – 3:00 pm
Howard House, TBA - maybe 4th floor?
The problem of restriction of the Fourier transform to hypersurfaces (or more generally to submanifolds in R^n) was posed by Stein in the seventies. This operator, in its adjoint form, gives the solution of dispersive equations (Schrödinger, wave, etc) in terms of the Fourier transform of the initial data. There are many open problems about dispersive equations for which it can be a powerful tool. Also, the restriction operator can be thought as a model case for more complicated oscillatory integral operators, for instance, the spherical summation operators.
We will make a review of this problem, which is still open. We will present some new results for the case of surfaces with negative curvature. That part is joint work with Stefan Buschenhenke and Detlef Müller.