On the root uncertainty principle

06/10/2016, ore 11:30, aula 10

This talk will focus on a recent result of Bourgain, Clozel and Kahane. One of its versions states that a real-valued function which equals its Fourier transform and vanishes at the origin necessarily has a root which is larger than c>0, where the best constant c satisfies 0.41<c<0.64. A similar result holds in higher dimensions. I will show how to improve the one-dimensional result to 0.45<c<0.60, and the lower bound in higher dimensions. I will also argue that extremizers for this problem exist, and necessarily possess infinitely many double roots. Time permitting, I will make the connection to several related problems. This is joint work with Felipe Gonçalves and Stefan Steinerberger.