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Uniqueness theorems for a class of wave propagation problems. (English) Zbl 0191.39304


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[1] Avila, G. S. S., & C. H. Wilcox, The near-field behavior of the Green’s matrix in anisotropic wave motion. J. Math. Mech. 16, 867–884 (1967). · Zbl 0152.44306
[2] Grushin, V. V., On Sommerfeld-type conditions for a certain class of partial differential equations. Mat. Sb. (N.S.) 61, 147–174 (1963);
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[6] Littman, W., Decay at infinity of solutions to partial differential equations with constant coefficients. Trans. Amer. Math. Soc. 123, 449–459 (1966). · Zbl 0144.13403 · doi:10.1090/S0002-9947-1966-0197951-7
[7] Müller, C., Grundprobleme der Mathematischen Theorie Elektromagnetischer Schwingungen. Berlin-Göttingen-Heidelberg: Springer 1957. · Zbl 0087.21305
[8] Rellich, F., Über das Asymptotische Verhalten der Lösungen von {\(\Delta\)}u+ku=0 in unendlichen Gebieten. Jber. Deutschen Math. Verein 53, 57–64 (1943). · Zbl 0028.16401
[9] Schulenberger, J. R., The Green’s matrix for steady-state wave propagation in a class of inhomogeneous anisotropic media. Arch. Rational Mech. Anal. (to appear). · Zbl 0269.35033
[10] Schulenberger, J. R., Wave Propagation in Inhomogeneous Anisotropic Media. Thesis, University of Arizona, 1968.
[11] Schwartz, L., Théorie des Distributions, Vol. I, II. Paris: Hermann 1957.
[12] Shilov, G. E., Local properties of solutions of partial differential equations with constant coefficients [in Russian]. Usp. Mat. Nauk 21 (3), 115–194 (1966).
[13] Vainberg, B. R., Radiation, limiting absorption, and limiting amplitude principles in the general theory of partial differential equations. Usp. Mat. Nauk 21, 115–194 (1966).
[14] Werner, P., Zur mathematischen Theorie akustischer Wellenfelder. Arch. Rational Mech. Anal. 6, 231–260 (1960). · Zbl 0097.21103 · doi:10.1007/BF00276164
[15] Werner, P., Elektromagnetische Dipolfelder in nichthomogenen Medien. Arch. Rational Mech. Anal. 16, 1–33 (1964). · Zbl 0196.39503 · doi:10.1007/BF00248488
[16] Wilcox, C. H., A generalization of theorems of Rellich and Atkinson. Proc. Amer. Math. Soc. 7, 271–276 (1956). · Zbl 0074.08102 · doi:10.1090/S0002-9939-1956-0078912-4
[17] Wilcox, C. H., Wave operators and asymptotic solutions of wave propagation problems of classical physics. Arch. Rational Mech. Anal. 22, 37–78 (1966). · Zbl 0159.14302 · doi:10.1007/BF00281244
[18] Wilcox, C. H., Steady-state wave propagation in homogeneous anisotropic media. Arch. Rational Mech. Anal. 25, 201–242 (1967). · Zbl 0159.14401 · doi:10.1007/BF00251589
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