# On classical inequalities for autocorrelations and autoconvolutions

@inproceedings{Pont2021OnCI, title={On classical inequalities for autocorrelations and autoconvolutions}, author={Jaume de Dios Pont and Jos'e Madrid}, year={2021} }

In this paper we study an autocorrelation inequality proposed by Barnard and Steinerberger [1]. The study of these problems is motivated by a classical problem in additive combinatorics. We establish the existence of extremizers to this inequality, for a general class of weights, including Gaussian functions (as studied by the second author and Ramos) and characteristic function (as originally studied by Barnard and Steinerberger). Moreover, via a discretization argument and numerical analysis…

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