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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sharp van der Corput estimates and minimal divided differences


Author: Keith M. Rogers
Journal: Proc. Amer. Math. Soc. 133 (2005), 3543-3550
MSC (2000): Primary 42A05; Secondary 65T40, 26D10
Published electronically: July 13, 2005
MathSciNet review: 2163589
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Abstract: We find the sharp constant in a sublevel set estimate which arises in connection with van der Corput's lemma. In order to do this, we find the nodes that minimise divided differences. We go on to find the sharp constant in the first instance of the van der Corput lemma. With these bounds we improve the constant in the general van der Corput lemma, so that it is asymptotically sharp.


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Additional Information

Keith M. Rogers
Affiliation: School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
Address at time of publication: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email: K.M.Rogers.99@cantab.net

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07918-9
PII: S 0002-9939(05)07918-9
Keywords: Van der Corput lemma, sharp constant, divided differences
Received by editor(s): July 8, 2004
Published electronically: July 13, 2005
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.