Skip to main content
Log in

Scattering frequencies and Gervey 3 singularities

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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)

    Google Scholar 

  • [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)

    Google Scholar 

  • [D.G.] Duistermaat, J.-J., Guillemin, V.: The spectrum of positive elliptic operators and periodic geodesics. Invent. Math.24, 39–80 (1975)

    Google Scholar 

  • [G.] Goodhue, W.: Scattering theory for hyperbolic systems with coefficients of Gevrey type. Trans. Am. Math. Soc.180, 337–346 (1973)

    Google Scholar 

  • [H.1] Hörmander, L.: Fourier integral operators. I. Acta Math.127, 79–183 (1971)

    Google Scholar 

  • [H.2] Hörmander, L.: The Analysis of linear partial differential operators 1. Lect. Notes Math., Vol. 256. Berlin-Heidelberg-New York: Springer 1983

    Google Scholar 

  • [L.] Lax, P.D.: Asymptotic solutions of initial value problems. Duke Math.J.24, 627–646 (1957)

    Google Scholar 

  • [LP.1] Lax, P.D., Phillips, R.S.: Scattering theory. New York: Academic Press 1967

    Google Scholar 

  • [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)

    Google Scholar 

  • [L.1] Lebeau, G.: Deuxième microlocalisation sur les sous-variétés isotropes. Ann. Inst. Fourier35, (2) 145–216 (1985)

    Google Scholar 

  • [L.2] Lebeau, G.: Régularité Gevrey trois pour la diffraction. Commun. Partial Differ. Equations9, (15) 1437–1494 (1984)

    Google Scholar 

  • [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)

    Google Scholar 

  • [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

    Google Scholar 

  • [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)

    Google Scholar 

  • [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

    Google Scholar 

  • [S.1] Sjöstrand, J.: Singularités analytiques microlocales. Astérisque95, 1–166 (1982)

    Google Scholar 

  • [S.2] Sjöstrand, J.: Propagation of analytic singularities for second order Dirichlet problems. Commun. Partial Differ. Equations5, (1) 41–94 (1980)

    Google Scholar 

  • [R.S.] Rauch, J., Sjöstrand, J.: Propagation of analytic singularities along diffracted rays. Indiana Univ. Math. J.30, (3) 389–401 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bardos, C., Lebeau, G. & Rauch, J. Scattering frequencies and Gervey 3 singularities. Invent Math 90, 77–114 (1987). https://doi.org/10.1007/BF01389032

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389032

Navigation