Sharp van der Corput estimates and minimal divided differences

2003/11/03 by Keith M. Rogers, Rogers, Keith
Mathematics · #42A05 #65T40 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0311013

openalex publication_date 2003/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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