Justification of the stationary phase approximation in time-domain asymptotics

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 453, Issue 1960, 1997, Pages 1019-1031

  Mcclure, J P ^a   Wong, R ^b  

^a UNIVERSITY OF MANITOBA   (Canada)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242288382     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1997.0057     Document Type: Article

References (12)

1. Chapman, C. J. 1992 Time-domain asymptotics and the method of stationary phase. Proc. R. Soc. Lond. A 437, 25-40.
2. Chester, C., Friedman, B. & Ursell, F. 1957 An extension of the method of steepest descents. Proc. Camb. Phil. Soc. 53, 599-611.
3. van der Corput, J. G. 1948 On the method of critical points. I. Proc. Nederl. Acad. Wetensch. 51, 650-658.
4. Erdélyi, A. 1956 Asymptotic expansions. New York: Dover.
5. Hörmander, L. 1983 The analysis of linear partial differential operators. Berlin: Springer.
6. Kelvin, Lord 1887 On the waves produced by a single impulse in water of any depth, or in a dispersive medium. Phil. Mag. 23, 252-255.
7. Körner, T. W. 1988 Fourier analysis. Cambridge University Press.
8. Olver, F. W. J. 1974 Error bounds for stationary phase approximations. SIAM J. Math. Analysis 5, 19-29.
9. Prentice, P. R. 1994 Time-domain asymptotics. I. General theory for double integrals. Proc. R. Soc. Lond. A 466, 341-360.
10. Rudin, W. 1964 Principles of mathematical analysis, 2nd edn. New York: McGraw-Hill.
11. Watson, G. N. 1918 The limits of applicability of the principle of stationary phase. Proc. Camb. Phil. Soc. 19, 49-55.
12. Wong, R. 1989 Asymptotic approximations of integrals. Boston, MA: Academic.