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Maximal and Variational Fourier Restriction Theory

Diogo Oliveira e Silva
Institution: 
University of Birmingham
Location: 
Luigi Stasi Seminar Room, ICTP
Schedule: 
Monday, December 17, 2018 - 11:00
Abstract: 

Müller, Ricci, and Wright recently established the first "maximal restriction theorem" for the Fourier transform. As a direct consequence, they clarified certain subtle measure theoretic aspects underlying Fourier restriction theory. In the first part of this talk, we will give a brief introduction to the restriction problem, and illustrate its importance in modern analysis. We will then focus on the endpoint Tomas-Stein inequality in 3-dimensional Euclidean space, together with its maximal and variational variants, for which especially simple proofs are available. Finally, we will describe a recent generalisation, and present some open problems.

This is partly based on joint work with Vjekoslav Kovac.

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