Journal article
Weighted stationary phase of higher orders
Frontiers of Mathematics in China, Vol.12(3), pp.675-702
06/2017
DOI: 10.1007/s11464-016-0615-y
Abstract
The subject matter of this paper is an integral with exponential oscillation of phase f(x) weighted by g(x) on a finite interval [α β]: When the phase f(x) has a single stationary point in (α β), an nth-order asymptotic expansion of this integral is proved for n ≥ 2: This asymptotic expansion sharpens the classical result for n = 1 by M. N. Huxley. A similar asymptotic expansion was proved by V. Blomer, R. Khan and M. Young under the assumptions that f(x) and g(x) are smooth and g(x) is compactly supported on R: In the present paper, however, these functions are only assumed to be continuously differentiable on [α β] 2n + 3 and 2n + 1 times, respectively. Because there are no requirements on the vanishing of g(x) and its derivatives at the endpoints α and β, the present asymptotic expansion contains explicit boundary terms in the main and error terms. The asymptotic expansion in this paper is thus applicable to a wider class of problems in analysis, analytic number theory, and other fields.
Details
- Title: Subtitle
- Weighted stationary phase of higher orders
- Creators
- Mark McKee - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USAHaiwei Sun - School of Mathematics and Statistics Shandong University Weihai 264209 ChinaYangbo Ye - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Frontiers of Mathematics in China, Vol.12(3), pp.675-702
- Publisher
- Higher Education Press; Beijing
- DOI
- 10.1007/s11464-016-0615-y
- ISSN
- 1673-3452
- eISSN
- 1673-3576
- Language
- English
- Date published
- 06/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9983985861602771
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