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Caltech/UCLA Joint Analysis Seminar

Tuesday, December 15, 2020
10:00am to 10:50am
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Uncertain signs
Emanuel Carneiro, Mathematics Section, ICTP,


We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gonçalves in 2019, in connection to the sphere packing problem. In our setup, the signs of a function and its Fourier transform resonate with a generic given function P outside of a ball. One essentially wants to know if and how soon this resonance can happen, when facing a suitable competing weighted integral condition. The original version of the problem corresponds to the case P=1. Surprisingly, even in such a rough setup, we are able to identify sharp constants in some cases. This is a joint work with Oscar Quesada-Herrera (IMPA - Rio de Janeiro).

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].