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Bulletin of the American Mathematical Society

Rays, waves and asymptotics

Joseph B. Keller
Source: Bull. Amer. Math. Soc. Volume 84, Number 5 (1978), 727-750.
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Primary Subjects: 35–02, 35A35, 35B40, 78–02, 78A05, 78A25, 78A45
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bams/1183541137
Mathematical Reviews number (MathSciNet): MR499726
Zentralblatt MATH identifier: 0393.35002

References

1. M. Born and E. Wolf, Principles of optics, Pergamon Press, Oxford, 1975.
2. P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, New York, 1953.
Zentralblatt MATH: 0051.40603
Mathematical Reviews (MathSciNet): MR59774
3. D. S. Jones, The theory of electromagnetism, Pergamon Press, Oxford, 1964.
Zentralblatt MATH: 0121.21604
Mathematical Reviews (MathSciNet): MR161555
4. R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Partial Differential Equations, Interscience, New York, 1962.
Zentralblatt MATH: 0099.29504
5. J. B. Keller, The geometrical theory of diffraction, Proc. Sympos. Microwave Optics, Eaton Electronics Research Lab., McGill Univ., Montreal, Canada, June, 1953, 4 pp.
Zentralblatt MATH: 0092.20604
6. J. B. Keller, The geometric optics theory of diffraction, The McGill Symposium on Microwave Optics, Vol. 2, B. S. Karasik and F. J. Zucker, eds., Air Force Cambridge Research Center, Bedford, Mass., 1959, pp. 207-210.
7. J. B. Keller, A geometrical theory of diffraction, in Calculus of Variations and Its Applications, L. M. Graves, ed., Proc. Sympos. Appl. Math., Vol. 8, Amer. Math. Soc., Providence, R. I., 1958, pp. 27-52. MR 20 #640.
Zentralblatt MATH: 0092.20604
Mathematical Reviews (MathSciNet): MR94120
8. J. B. Keller, Diffraction by a convex cylinder, Inst. Radio Eng.-Trans. Antennas and Propagation, AP-4 (1956), 312-321. MR 20 #641.
Mathematical Reviews (MathSciNet): MR94121
9. J. B. Keller, Diffraction by an aperture, J. Appl. Phys. 28 (1957), 426-444. MR 20 #5833; 21 #571.
Zentralblatt MATH: 0077.41202
Mathematical Reviews (MathSciNet): MR101763
Digital Object Identifier: doi:10.1063/1.1722767
10. B. D. Seckler and J. B. Keller, The geometrical theory of diffraction in inhomogeneous media, J. Acous. Soc. Amer. 31 (1959), 192-205. MR 20 #5035, #6926.
Zentralblatt MATH: 0092.20604
Mathematical Reviews (MathSciNet): MR100493
Digital Object Identifier: doi:10.1121/1.1907692
11. B. R. Levy and J. B. Keller, Diffraction by a smooth object, Comm. Pure Appl. Math. 12 (1959), 159-209. MR 21 #1130.
Mathematical Reviews (MathSciNet): MR102337
Digital Object Identifier: doi:10.1002/cpa.3160120108
12. J. B. Keller, Back scattering from a finite cone, Inst. Radio Eng.-Trans. Antennas and Propagation, AP-8 (1960), 175-182.
13. J. B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Amer. 52 (1962), 116-130. MR 24 #B1115.
Zentralblatt MATH: 0092.20604
Mathematical Reviews (MathSciNet): MR135064
Digital Object Identifier: doi:10.1364/JOSA.52.000116
14. J. B. Keller, Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems, Ann.Physics 4 (1958), 180-188. MR 20 #5650.
Zentralblatt MATH: 0085.43103
Mathematical Reviews (MathSciNet): MR99207
Digital Object Identifier: doi:10.1016/0003-4916(58)90032-0
15. J. B. Keller and S. I. Rubinow, Asymptotic solution of eigenvalue problems, Ann. Physics 9 (1960), 24-75.
Zentralblatt MATH: 0087.43002
16. M. C. Shen, R. E. Meyer and J. B. Keller, Spectra of water waves in channels and around islands, Phys. Fluids 11 (1968), 2289-2304.
Zentralblatt MATH: 0207.27502
17. J. B. Keller and F. C. Karal, Surface wave excitation and propagation, J. Appl. Phys. 31 (1960), 1039-1046. MR 25 #2753.
Mathematical Reviews (MathSciNet): MR139319
Digital Object Identifier: doi:10.1063/1.1735742
18. H. Y. Yee, L. B. Felsen and J. B. Keller, Ray theory of reflection from the open end of a waveguide, SIAM J. Appl. Math. 16 (1968), 268-300. MR 39 #641.
Zentralblatt MATH: 0155.43501
Mathematical Reviews (MathSciNet): MR239284
Digital Object Identifier: doi:10.1137/0116023
19. W. Streifer and J. B. Keller, Complex rays with an application to Gaussian beams, J. Opt. Soc. Amer. 61 (1971), 40-43.
20. J. B. Keller, R. M. Lewis and B. D. Seckler, Asymptotic solution of some diffraction problems, Comm. Pure Appl. Math 9 (1956), 207-265. MR 17, 41; 18, 43.
Zentralblatt MATH: 0073.44105
Mathematical Reviews (MathSciNet): MR79182
Digital Object Identifier: doi:10.1002/cpa.3160090205
21. F. G. Friedlander, Sound pulses, Cambridge Univ. Press, New York, 1958. MR 20 #3703.
Zentralblatt MATH: 0079.41001
Mathematical Reviews (MathSciNet): MR97233
22. F. C. Karal and J. B. Keller, Elastic wave propagation in homogeneous and inhomogeneous media, J. Acoust. Soc. Amer. 31 (1959), 694-705. MR 21 #2416.
Mathematical Reviews (MathSciNet): MR103648
Digital Object Identifier: doi:10.1121/1.1907775
23. S. I. Rubinow and J. B. Keller, Asymptotic solution of the Dirac equation, Phys. Rev. (2) 131 (1963), 2789-2796. MR 28 #2792.
Mathematical Reviews (MathSciNet): MR159575
Digital Object Identifier: doi:10.1103/PhysRev.131.2789
24. R. N. Buchal and J. B. Keller, Boundary layer problems in diffraction theory, Comm. Pure Appl. Math. 13 (1960), 85-114. MR 22 # 1797.
Zentralblatt MATH: 0094.41803
Mathematical Reviews (MathSciNet): MR119789
Digital Object Identifier: doi:10.1002/cpa.3160130109
25. Ju. A. Kravcov, a) A modification of the geometrical optics method, Izv. Vysš. Učebn. Zaved. Radiofizika 7 (1964), 664-673. (Russian) b) Asymptotic solutions of Maxwell's equations near a caustic, Izv. Vysš. Učebn. Zaved. Radiofizika 7 (1964), 1049-1056. (Russian)
26. D. Ludwig, Wave propagation near a smooth caustic, Bull. Amer. Math. Soc. 71 (1965), 776-779. MR 32 #753.
Zentralblatt MATH: 0142.37503
Mathematical Reviews (MathSciNet): MR183271
Digital Object Identifier: doi:10.1090/S0002-9904-1965-11390-8
Project Euclid: euclid.bams/1183527308
27. D. Ludwig, Uniform asymptotic expansions at a caustic, Comm. Pure Appl. Math. 19 (1966), 15-250. MR 33 #4446.
Zentralblatt MATH: 0163.13703
Mathematical Reviews (MathSciNet): MR196254
Digital Object Identifier: doi:10.1002/cpa.3160190207
28. D. S. Ahluwalia, J. Boersma and R. M. Lewis, Uniform asymptotic theory of diffraction by a plane screen, SIAM J. Appl. Math. 16 (1968), 783-807. MR 39 #2392.
Mathematical Reviews (MathSciNet): MR241047
Digital Object Identifier: doi:10.1137/0116065
29. J. J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm, Pure Appl. Math. 27 (1974), 207-281.
Zentralblatt MATH: 0285.35010
Mathematical Reviews (MathSciNet): MR405513
Digital Object Identifier: doi:10.1002/cpa.3160270205
30. C. S. Morawetz, Decay for solutions of the exterior problem for the wave equation, Comm. Pure Appl. Math 28 (1975), 229-264.
Zentralblatt MATH: 0304.35064
Mathematical Reviews (MathSciNet): MR372432
Digital Object Identifier: doi:10.1002/cpa.3160280204
31. C. O. Bloom and N. D. Kazarinoff, Short wave radiation problems in inhomogeneous media: asymptotic solutions, Springer-Verlag, New York, 1976.
Zentralblatt MATH: 0325.35003
Mathematical Reviews (MathSciNet): MR470439

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