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March 2015 The multidimensional van der Corput transformation
Patrick Sargos
Funct. Approx. Comment. Math. 52(1): 133-176 (March 2015). DOI: 10.7169/facm/2015.52.1.11

Abstract

We make a systematic study of van der Corput's $B$-process for multiple exponential sums. We study directly the important case where the determinant of the Hessian $H_{f}(\mathbf{x})$ of the phase $f$ may be abnormally small. This requires a work on multidimensional stationary phase integrals uniform in $\delta$, the lower bound for $||\det H_{f}(\mathbf{x})||$. In passing, we obtain an independent result on the asymptotic behaviour of the stationary phase integral when the critical point of the phase is also a singular point of the boundary of the domain of integration. The whole paper is self-contained.

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Patrick Sargos. "The multidimensional van der Corput transformation." Funct. Approx. Comment. Math. 52 (1) 133 - 176, March 2015. https://doi.org/10.7169/facm/2015.52.1.11

Information

Published: March 2015
First available in Project Euclid: 20 March 2015

MathSciNet: MR3326130
zbMATH: 06425019
Digital Object Identifier: 10.7169/facm/2015.52.1.11

Subjects:
Primary: 11L07

Rights: Copyright © 2015 Adam Mickiewicz University

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Vol.52 • No. 1 • March 2015
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