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arXiv:0907.1379math.CA

Improved bounds on the supremum of autoconvolutions

Mate Matolcsi, Carlos Vinuesa

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Abstract

We give a slight improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval. Also, by means of explicit examples we disprove a long standing natural conjecture of Schinzel and Schmidt concerning the extremal function for such autoconvolutions.

arXiv comments
15 pages. Some typos have been corrected, the best examples have been slightly improved, two plots of them have been included and some remarks have been added
Journal reference
DOI
Subjects
math.CAClassical Analysis and ODEs math.NTNumber Theory

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    • This is great. But how incremental are these advancements? I picked one at random (B.2 -- the second autocorrelation inequality). Then, I looked up the paper that produced the previous state of the art (https://arxiv.org/pdf/0907.1379). It turns out that the authors had…

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