Sharp van der Corput estimates and minimal divided differences
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arXiv
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| Format: | Preprint |
| Published: |
2003
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| _version_ | 1866909853425860608 |
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| author | Rogers, Keith |
| author_facet | Rogers, Keith |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0311013 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | Sharp van der Corput estimates and minimal divided differences Rogers, Keith Classical Analysis and ODEs Numerical Analysis 42A05; 65T40 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. |
| title | Sharp van der Corput estimates and minimal divided differences |
| topic | Classical Analysis and ODEs Numerical Analysis 42A05; 65T40 |
| url | https://arxiv.org/abs/math/0311013 |