Seminario de Análisis y Aplicaciones

Lugar: Aula 520, Módulo 17, Ciencias

Día y hora: Viernes 21 de Junio, 11:30-12:30

Ponente: Itamar Oliveira (U. of Birmingham)

Título: A phase-space approach to weighted Fourier extension inequalities
Abstract: The goal of the talk is to present and investigate a set of problems about weighted Fourier extension inequalities from a phase-space perspective involving the Wigner transform, an object that appears naturally in quantum mechanics and in quantum optics. In joint work with Bennett, Gutierrez and Nakamura, we show how Sobolev estimates for the Wigner transform can be converted into certain tomographic bounds for the Fourier extension operator to the paraboloid, which imply weaker variants of the classical Mizohata-Takeuchi and Stein's conjectures for this manifold. We are also able to extend this analysis to a wide class of hypersurfaces, which requires finding and understanding a good "geometric" replacement for the classical Wigner transform. Our results do not depend on lower bounds for the Gaussian curvature of these manifolds, which contrasts the intuition behind the classical Fourier restriction conjecture.