Improved bounds on the supremum of autoconvolutions
Classical Analysis and ODEs
2009-09-04 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.0907.1379,
title = {Improved bounds on the supremum of autoconvolutions},
author = {Mate Matolcsi and Carlos Vinuesa},
journal= {arXiv preprint arXiv:0907.1379},
year = {2009}
}
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