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Eigenfunction expansions and scattering theory for the wave equation in an exterior region. (English) Zbl 0135.15602

##### Keywords:
partial differential equations
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##### References:
 [1] Lax, P.D., & R.S. Phillips, Scattering theory. Bull. Amer. Math. Soc. 70, 130–142 (1964). · Zbl 0117.09104 [2] Shizuta, Y., Eigenfunction expansion associated with the operator – {$$\Delta$$} in the exterior domain. Proc. Japan Acad. 39, 656–660 (1963). · Zbl 0143.14504 [3] Ikebe, T., Orthogonality of the eigenfunctions for the exterior problem connected with – {$$\Delta$$}. Arch. Rational Mech. Anal. 19, 71–73 (1965). · Zbl 0143.14601 [4] Werner, P., Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10, 29–66 (1962). · Zbl 0105.07405 [5] Ikebe, T., Eigenfunction expansions associated with the Schroedinger operator and their applications to scattering theory. Arch. Rational Mech. Anal. 5, 1–34 (1960). · Zbl 0145.36902 [6] Thoe, D., Scattering theory for the wave equation with a potential. Doctoral Thesis, Stanford University (1965), 147–155. [7] Hörmander, L., Linear Partial Differential Operators, p. 1–56. New York: Academic Press 1963. [8] Nirenberg, L., Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math. 8, 649–675 (1955). · Zbl 0067.07602 [9] Schechter, M., General boundary value problems for elliptic partial differential equations. Comm. Pure Appl. Math. 12, 457–486 (1959). · Zbl 0087.30204 [10] Gårding, L., Dirichlet’s problem for linear elliptic partial differential equations. Math. Scand. 1, 55–72 (1953). · Zbl 0053.39101 [11] Watson, G., The Theory of Bessel Functions, p. 73. Cambridge: University Press 1922. · JFM 48.0412.02 [12] Miranda, C., Equazioni alle Derivate Parziali di Tipo Ellittico, p. 1–35. Berlin-Göttingen-Heidelberg: Springer 1955. [13] Stone, M., Linear Transformations in Hilbert Space, p. 183. New York: American Mathematical Society 1932. · Zbl 0005.40003 [14] Titchmarsh, E., Introduction to the Theory of Fourier Integrals, p. 31. London: Oxford University Press 1937. · Zbl 0017.40404 [15] Bers, L., F. John, & M. Schechter, Partial Differential Equations, p. 221. New York: Interscience 1964. [16] John, F., Plane Waves and Spherical Means, p. 36. New York: Interscience 1955. · Zbl 0067.32101
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