Improved bounds on the supremum of autoconvolutions

Details Improved bounds on the supremum of autoconvolutions Improved bounds on the supremum of autoconvolutions

2009-07-08

arxiv.org/abs/0907.1379v2

Mathematics

Classical Analysis and ODEs

15 pages. Some typos have been corrected, the best examples have been slightly improved, two plots of them have been included

Scientific paper

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.

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