References
[B.G.R.] Bardos, C., Guillot, J.-C., Ralston, J.: La relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion. Commun. Partial Differ. Equations7, (8) 905–958 (1982)
[B.L.R.] Bardos, C., Lebeau, G., Rauch, J.: Méthodes semi classiques en mécaniques quantique. 1984. Publications de l'Université de Nantes
[BdM.] Boutet de Monvel, L.: Séminaire. Opérateurs Pseudodifférentiels Analytiques, Grenoble, 1975
[C.] Chazarain, J.: Formule de Poisson pour les variétés riemaniennes. Invent. Math.24, 65–82 (1974)
[D.G.] Duistermaat, J.-J., Guillemin, V.: The spectrum of positive elliptic operators and periodic geodesics. Invent. Math.24, 39–80 (1975)
[G.] Goodhue, W.: Scattering theory for hyperbolic systems with coefficients of Gevrey type. Trans. Am. Math. Soc.180, 337–346 (1973)
[H.1] Hörmander, L.: Fourier integral operators. I. Acta Math.127, 79–183 (1971)
[H.2] Hörmander, L.: The Analysis of linear partial differential operators 1. Lect. Notes Math., Vol. 256. Berlin-Heidelberg-New York: Springer 1983
[L.] Lax, P.D.: Asymptotic solutions of initial value problems. Duke Math.J.24, 627–646 (1957)
[LP.1] Lax, P.D., Phillips, R.S.: Scattering theory. New York: Academic Press 1967
[LP.2] Lax, P.D., Phillips, S.R.: A logarithmic bound on the location of the poles of the scattering mat. Arch. Rat. Mech. Anal.40, 268–280 (1971)
[L.1] Lebeau, G.: Deuxième microlocalisation sur les sous-variétés isotropes. Ann. Inst. Fourier35, (2) 145–216 (1985)
[L.2] Lebeau, G.: Régularité Gevrey trois pour la diffraction. Commun. Partial Differ. Equations9, (15) 1437–1494 (1984)
[L.3] Lebeau, G.: Propagation Gervey pour le problème mixte. Advanced in microlocal analysis, 1986 NATO ASI published by Reidel (Garnir editor)
[M.1] Melrose, R.: Singularities and energy decay in acoustical scattering. Duke Math. J.46, (1) 43–59 (1979)
[M.2] Melrose, R.: Polynomial bound on the number of scattering poles. J. Funct. Anal.53,287–303 (1983); also Proc. of St.Jean de Monts 1984 seminar
[M.S.] Melrose, R., Sjostrand, J.: Singularities of boundary value problems I and II. Commun. Pure Appl. Math.31, 595–617 (1978);35, 129–168 (1982)
[P] Popov, G.: Estimates near the shadow and poles of the S. matrix. (Preprint)
[S.K.K.] Sato, M., Kawai, T., Kashiwara, M.: Microfunctions and pseudo differential equations. Lect. Notes Math., Vol. 287. Berlin-Heidelberg-New York: Springer 1973
[S.1] Sjöstrand, J.: Singularités analytiques microlocales. Astérisque95, 1–166 (1982)
[S.2] Sjöstrand, J.: Propagation of analytic singularities for second order Dirichlet problems. Commun. Partial Differ. Equations5, (1) 41–94 (1980)
[R.S.] Rauch, J., Sjöstrand, J.: Propagation of analytic singularities along diffracted rays. Indiana Univ. Math. J.30, (3) 389–401 (1981)
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Bardos, C., Lebeau, G. & Rauch, J. Scattering frequencies and Gervey 3 singularities. Invent Math 90, 77–114 (1987). https://doi.org/10.1007/BF01389032
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DOI: https://doi.org/10.1007/BF01389032