English

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}
}