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arXiv · 2408.01186

Sign uncertainty and de Branges spaces

Emanuel Carneiro·Tolibjon Ismoilov·Antonio Pedro Ramos
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Abstract

We investigate here the sign uncertainty phenomenon for bandlimited functions, with a competing condition given by integration with respect to a general measure. Our main result provides a framework related to the theory of de Branges spaces of entire functions, that allows one to find the sharp constants and classify the extremizers in a broad range of situations. We discuss an application in number theory, in connection to bounds for zeros of $L$-functions.

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Emanuel Carneiro, Tolibjon Ismoilov, Antonio Pedro Ramos. 2024-08-02. Sign uncertainty and de Branges spaces. https://arxiv.org/abs/2408.01186

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