Seminario: On the root uncertainty principle

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dalle 11:30 alle 13:00


Aula 10 - Dipartimento di Matematica e Infomartica - via Machiavelli, 30 - Ferrara

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Speaker: prof. Diogo Oliveira e Silva (Università di Bonn)

Title: On the root uncertainty principle.


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.


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