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Eigenfunction expansions and scattering theory for wave propagation problems of classical physics. (English) Zbl 0252.47047

MSC:
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P25 Scattering theory for PDEs
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[3] Ikebe, T., Remarks on the orthogonality of the eigenfunctions for the Sc · Zbl 0211.13801
[4] Ikebe, T., Scattering theory for uniformly propagative systems. Proc. International Conf. Functional Anal. and Related Topics, 1969, 225–230, Univ. of Tokyo Press, Tokyo 1970.
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[7] LaVita, J. A., J. R. Schulenberger, & C. H. Wilcox, The scattering theory of Lax and Phillips and wave propagation problems of classical physics. Applicable Anal. (to appear).
[8] Lax, P. D., & R. S. Phillips, Scattering Theory. New York: Academic Press 1967.
[9] Lax, P. D., & R. S. Phillips, Scattering theory. Rocky Mountain J. Math. 1, 173–223 (1971). · Zbl 0225.35081 · doi:10.1216/RMJ-1971-1-1-173
[10] Mochizuki, K., Spectral and scattering theory for symmetric hyperbolic systems in an exterior domain. Publ. RIMS, Kyoto Univ. 5, 219–258 (1969). · Zbl 0206.40102 · doi:10.2977/prims/1195194631
[11] Schulenberger, J. R., & C. H. Wilcox, Coerciveness inequalities for nonelliptic systems of partial differential equations. Ann. Mat. Pura Appl. 88, 229–306 (1971). · Zbl 0215.45302 · doi:10.1007/BF02415070
[12] Schulenberger, J. R., & C. H. Wilcox, A Rellich uniqueness theorem for steady-state wave propagation in inhomogeneous anisotropic media. Arch. Rational Mech. Anal. 41, 18–45 (1971). · Zbl 0218.35053 · doi:10.1007/BF00250176
[13] Schulenberger, J. R., & C. H. Wilcox, A coerciveness inequality for a class of nonelliptic operators of constant deficit. Ann. Mat. Pura Appl. (to appear). · Zbl 0237.35011
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[16] Schulenberger, J. R., & C. H. Wilcox, The limiting absorption principle and spectral theory for steady-state wave propagation in inhomogeneous anisotropic media. Arch. Rational Mech. Anal. 41, 46–65 (1971). · Zbl 0218.35054 · doi:10.1007/BF00250177
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[18] Shenk, N. A. II, Eigenfunction expansions and scattering theory for the wave equation in an exterior region. Arch. Rational Mech. Anal. 21, 120–150 (1966). · Zbl 0135.15602 · doi:10.1007/BF00266571
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[21] Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals. Oxford: University Press 1937. · Zbl 0017.40404
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[23] Wilcox, C. H., Measurable eigenvectors for Hermitian matrix valued polynominals. J. Math. Anal. Appl. (to appear). · Zbl 0223.35080
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[25] Yosida, K., Functional Analysis. Berlin-Göttingen-Heidelberg: Springer 1965. · Zbl 0126.11504
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