Restriction of the Fourier transform with applications to the Schrödinger and wave equations
Principal investigator: Keith Rogers
Project reference: 277778
Start Date: 2011-09-01
End Date: 2017-08-31
Abstract: In 1967, Stein proved that the Fourier transform of functions in L^p could be meaningfully restricted to the sphere for certain p>1. The restriction conjecture, which asserts the maximal range of such p, was solved by Fefferman and Stein in two dimensions, but the conjecture remains open in higher dimensions. Strichartz considered the same question but with the sphere replaced by the paraboloid or the cone, and a great deal of progress has been made in the last two decades. Due to the fact that the adjoint operators of the restriction operators to the paraboloid and cone correspond to the Schrödinger and wave evolution operators, respectively, this work has been hugely influential. The main goal of the project is to improve the state of the art for the mixed norm analogues of these conjectures.
This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 277778. Area PE1.