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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Completeness of the wave operators for scattering problems of classical physics


Authors: John R. Schulenberger and Calvin H. Wilcox
Journal: Bull. Amer. Math. Soc. 77 (1971), 777-782
MSC (1970): Primary 35P25, 47A40; Secondary 73D99, 76Q05, 78A45
MathSciNet review: 0295149
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  • 1. G. S. S. Ávila, Spectral resolution of differential operators associated with symmetric hyperbolic systems, Applicable Anal. 2 (1972/73), 283–299. MR 0390534 (52 #11359)
  • 2. A. L. Belopol'skiĭ and M. Š. Birman, The existence of wave operators in the theory of scattering with a pair of spaces, Izv. Akad. NaukSSSR32 (1968), 1162-1175 = Math. USSR Izv. 2 (1968), 1117-1130. MR 38 #7377.[Note]
  • 3. M. Š. Birman, A local test for the existence of wave operators, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 914–942 (Russian). MR 0248558 (40 #1810)
  • 4. R. Courant and D. Hilbert, Methods of mathematical physics. Vol. 2: Partial differential equations, Interscience, New York, 1962. MR 25 #4216.
  • 5. G. F. D. Duff, The Cauchy problem for elastic waves in an anistropic medium, Philos. Trans. Roy. Soc. London Ser. A 252 (1960), 249–273. MR 0111293 (22 #2157)
  • 6. Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473 (34 #3324)
  • 7. Tosio Kato, Scattering theory with two Hilbert spaces, J. Functional Analysis 1 (1967), 342–369. MR 0220097 (36 #3164)
  • 8. John R. Schulenberger and Calvin H. Wilcox, Coerciveness inequalities for nonelliptic systems of partial differential equations, Ann. Mat. Pura Appl. (4) 88 (1971), 229–305. MR 0313887 (47 #2439)
  • 9. John R. Schulenberger and Calvin H. Wilcox, Completeness of the wave operators for perturbations of uniformly propagative systems, J. Functional Analysis 7 (1971), 447–474. MR 0275221 (43 #978)
  • 10. J. R. Schulenberger and C. H. Wilcox, A coerciveness inequality for a class of nonelliptic operators of constant deficit, ONR Technical Summary Report #8, University of Denver, Denver, Colo., 1970.
  • 11. Calvin H. Wilcox, Wave operators and asymptotic solutions of wave propagation problems of classical physics, Arch. Rational Mech. Anal. 22 (1966), 37–78. MR 0199531 (33 #7675)
  • 12. Calvin H. Wilcox, Transient wave propagation in homogeneous anisotropic media, Arch. Rational Mech. Anal. 37 (1970), 323–343. MR 0261844 (41 #6455)
  • 13. Calvin H. Wilcox, Measurable eigenvectors for Hermitian matrix-valued polynomials, J. Math. Anal. Appl. 40 (1972), 12–19. MR 0318181 (47 #6728)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1971-12804-5
PII: S 0002-9904(1971)12804-5