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arXiv · 2006.00959

Generalized sign Fourier uncertainty

Emanuel Carneiro·Emily Quesada-Herrera
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Abstract

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 Gon\c{c}alves in 2019. 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 $P \equiv 1$. Surprisingly, even in such a rough setup, we are able to identify sharp constants in some cases.

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Emanuel Carneiro, Emily Quesada-Herrera. 2020-06-01. Generalized sign Fourier uncertainty. https://arxiv.org/abs/2006.00959

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