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Completeness of the wave operators for scattering problems of classical physics. (English) Zbl 0224.35072


MSC:

35P25 Scattering theory for PDEs
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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. · Zbl 0238.35062 · doi:10.1080/00036817208839045
[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).
[4] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. 2: Partial differential equations, Interscience, New York, 1962. MR 25 #4216. · Zbl 0099.29504
[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. · Zbl 0103.42502 · doi:10.1098/rsta.1960.0006
[6] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0148.12601
[7] Tosio Kato, Scattering theory with two Hilbert spaces, J. Functional Analysis 1 (1967), 342 – 369. · Zbl 0171.12303
[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. · Zbl 0215.45302 · doi:10.1007/BF02415070
[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. · Zbl 0223.47007
[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. · Zbl 0237.35011
[11] Calvin H. Wilcox, Wave operators and asymptotic solutions of wave propagation problems of classical physics, Arch. Rational Mech. Anal. 22 (1966), 37 – 78. · Zbl 0159.14302 · doi:10.1007/BF00281244
[12] Calvin H. Wilcox, Transient wave propagation in homogeneous anisotropic media, Arch. Rational Mech. Anal. 37 (1970), 323 – 343. · Zbl 0201.43201 · doi:10.1007/BF00249668
[13] Calvin H. Wilcox, Measurable eigenvectors for Hermitian matrix-valued polynomials, J. Math. Anal. Appl. 40 (1972), 12 – 19. · Zbl 0223.35080 · doi:10.1016/0022-247X(72)90024-8
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