Abstract
Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article McClure J. P. and Wong R. 1997Justification of the stationary phase approximation in time–domain asymptoticsProc. R. Soc. Lond. A.4531019–1031http://doi.org/10.1098/rspa.1997.0057SectionRestricted accessJustification of the stationary phase approximation in time–domain asymptotics J. P. McClure J. P. McClure Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada Google Scholar Find this author on PubMed Search for more papers by this author and R. Wong R. Wong Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong Google Scholar Find this author on PubMed Search for more papers by this author J. P. McClure J. P. McClure Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada Google Scholar Find this author on PubMed Search for more papers by this author and R. Wong R. Wong Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong Google Scholar Find this author on PubMed Search for more papers by this author Published:08 May 1997https://doi.org/10.1098/rspa.1997.0057AbstractA rigorous proof is supplied for the validity of an asymptotic approximation to the integralI(λ)=∫ab g(κ)p {λ f(x)},dx,where f(x) and g(x) are sufficiently smooth functions on [a,b] and p(x) is a piece–wise smooth periodic function with mean zero. In addition, a two–dimensional generalization is given. Problems concerning coalescence of two stationary points and a stationary point near an end point are also considered. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Chen C, Hansen H, Hendriks G, Menssen J, Lu J and de Korte C Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 10.1109/TUFFC.2019.2944191, 67:2, (296-307) Carteret H, Richmond B and Temme N (2005) Evanescence in coined quantum walks, Journal of Physics A: Mathematical and General, 10.1088/0305-4470/38/40/011, 38:40, (8641-8665), Online publication date: 7-Oct-2005. Carteret H, Ismail M and Richmond B (2003) Three routes to the exact asymptotics for the one-dimensional quantum walk, Journal of Physics A: Mathematical and General, 10.1088/0305-4470/36/33/305, 36:33, (8775-8795), Online publication date: 22-Aug-2003. This Issue08 May 1997Volume 453Issue 1960 Article InformationDOI:https://doi.org/10.1098/rspa.1997.0057Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/05/1997Published in print08/05/1997 License: Citations and impact
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