Sharp van der Corput estimates and minimal divided differences
Classical Analysis and ODEs
2025-10-20 v1 Numerical Analysis
Numerical Analysis
Abstract
We find the nodes that minimise divided differences and use them to find the sharp constant in a sublevel set estimate. We also find the sharp constant in the first instance of the van der Corput Lemma using a complex mean value theorem for integrals. With these sharp bounds we improve the constant in the general van der Corput Lemma, so that it is asymptotically sharp.
Keywords
Cite
@article{arxiv.math/0311013,
title = {Sharp van der Corput estimates and minimal divided differences},
author = {Keith Rogers},
journal= {arXiv preprint arXiv:math/0311013},
year = {2025}
}