2021/06/25 by Jaume de Dios Pont, José Madrid, Pont, Jaume de Dios +1
Computer Science · Mathematics · #39A12 #42A05 #42A85 #70H03 #Applied mathematics #Argument (complex analysis) #Autocorrelation #Class (philosophy) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Computer science #Constant (computer programming) #Discretization #Epistemology #FOS: Mathematics #Gaussian #Inequality #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Mathematical analysis #Mathematical economics #Mathematics #Number Theory (math.NT) #Philosophy #Physics #Pure mathematics #Statistics #math.CA #math.CO #math.NT #msc:39A12 #msc:42A05 #msc:42A85 #msc:70H03
paper · pdf · doi:10.48550/arxiv.2106.13873
published in arXiv (Cornell University) (Cornell University) · 14 pages, 1 table, 1 figure
arxiv created 2021/06/25 · openalex publication_date 2021/06/25 · arxiv updated 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study an autocorrelation inequality proposed by Barnard and Steinerberger. 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, we find some almost optimal approximation for the best constant allowed in this inequality. We also discuss some other related problem about autoconvolutions.