On optimal autocorrelation inequalities on the real line

José Madrid; João P. G. Ramos

doi:10.3934/cpaa.2020271

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2021, Volume 20, Issue 1: 369-388. Doi: 10.3934/cpaa.2020271

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On optimal autocorrelation inequalities on the real line

José Madrid^1, , and
João P. G. Ramos^2,

1.
Department of Mathematics, University of California, Los Angeles, Portola Plaza 520, Los Angeles, California, 90095, USA
2.
Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil

^*Corresponding author
^*Corresponding author

Received: July 31, 2020

Revised: August 31, 2020

Early access: November 2020

Published: January 2021

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Abstract

We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work [1]. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove existence of extremizers to these inequalities in certain specific settings. Our methods consist of relating the inequalities in question to other classical sharp inequalities in Fourier analysis, such as the sharp Hausdorff–Young inequality, and employing functional analysis as well as measure theory tools in connection to a suitable dual version of the problem to identify and impose conditions on extremizers.

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Mathematics Subject Classification: 42A05, 42A85, 28A12, 42A82.

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References

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