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arxiv: 2408.01186 · v1 · pith:OTEYJKZ2 · submitted 2024-08-02 · math.CA · math.CV· math.NT

Sign uncertainty and de Branges spaces

Emanuel Carneiro , Tolibjon Ismoilov , Antonio Pedro Ramos This is my paper

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classification math.CA math.CVmath.NT
keywords functionsbrangessignspacestheoryuncertaintyallowsapplication
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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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  1. Sharp sign uncertainty for trigonometric polynomials

    math.CA 2026-06 unverdicted novelty 7.0

    For each symmetric Borel measure μ on the circle, the smallest radius of the last sign change is determined for trigonometric polynomials of degree N with non-positive μ-integral; the result reduces to the one-dimensi...