Objective 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 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 by Bourgain, Wolff and Tao, among others. 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 this proposal is to improve the state of the art for the mixed norm analogues of these conjectures. Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2011-StG_20101014 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Address Calle serrano 117 28006 Madrid Spain See on map Region Comunidad de Madrid Comunidad de Madrid Madrid Activity type Research Organisations Administrative Contact Guillermo Sanjuanbenito García (Mr.) Principal investigator Keith Mckenzie Rogers (Dr.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Spain EU contribution € 950 000,00 Address Calle serrano 117 28006 Madrid See on map Region Comunidad de Madrid Comunidad de Madrid Madrid Activity type Research Organisations Administrative Contact Guillermo Sanjuanbenito García (Mr.) Principal investigator Keith Mckenzie Rogers (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
