On the poles of the scattering matrix for two convex obstacles

Mitsuru Ikawa

Journées équations aux dérivées partielles (1985)

  • Issue: 1, page 1-14
  • ISSN: 0752-0360

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Ikawa, Mitsuru. "On the poles of the scattering matrix for two convex obstacles." Journées équations aux dérivées partielles (1985): 1-14. <http://eudml.org/doc/93121>.

@article{Ikawa1985,
author = {Ikawa, Mitsuru},
journal = {Journées équations aux dérivées partielles},
keywords = {scattering matrix; wave equation; obstacles; order of the singularity; asymptotic expansion},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Ecole polytechnique},
title = {On the poles of the scattering matrix for two convex obstacles},
url = {http://eudml.org/doc/93121},
year = {1985},
}

TY - JOUR
AU - Ikawa, Mitsuru
TI - On the poles of the scattering matrix for two convex obstacles
JO - Journées équations aux dérivées partielles
PY - 1985
PB - Ecole polytechnique
IS - 1
SP - 1
EP - 14
LA - eng
KW - scattering matrix; wave equation; obstacles; order of the singularity; asymptotic expansion
UR - http://eudml.org/doc/93121
ER -

References

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  1. [1] C. Bardos, J.C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion, Comm. Partial Diff. Equ., (1982), 905-958. Zbl0496.35067MR84d:35120
  2. [2] M. Ikawa, Decay of solutions of the wave equation in the exterior of two convex obstacles, Osaka J. Math., 19 (1982), 459-509. Zbl0498.35008MR84e:35018
  3. [3] M. Ikawa, On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 23 (1983), 127-194. Zbl0561.35060MR84e:35118
  4. [4] M. Ikawa, On the poles of the scattering matrix for two strictly convex obstacles : Addendum, J. Math. Kyoto Univ., 23 (1983), 795-802. Zbl0559.35061
  5. [5] M. Ikawa, Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis, to appear in Osaka J. Math. Zbl0617.35102
  6. [6] M. Ikawa, Precise informations on the poles of the scattering matrix for two strictly convex obstacles, in preparation. Zbl0637.35068
  7. [7] P.D. Lax and R.S. Phillips, Scattering theory, Academic Press, New York, (1967). Zbl0186.16301
  8. [8] P.D. Lax and R.S. Phillips, A logarithmic bound on the location of the scattering matrix, Arch. Rat. Mech. and Anal., 40 (1971), 268-280. Zbl0216.13002MR45 #5594
  9. [9] G. Lebeau, to appear. 
  10. [10] R. Melrose, Polynomial bound on the distribution of poles in scattering by obstacles, Journées " Equations aux dérivées partielles ", Soc. Math. France, (1984). Zbl0621.35073
  11. [11] V.M. Petkov, Propriétés génériques des rayons réfléchissants et applications aux problèmes spectraux, Séminaire Bony-Sjöstrand-Meyer, 1984-1985, Exposé n° XII. Zbl0597.35092
  12. [12] V.M. Petkov and L. Stojanov, Periods of multiple reflecting geodesics and inverse spectral problems, preprint. Zbl0652.35027

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