Singularities of the scattering kernel for non convex obstacles

Vesselin M. Petkov; Luchezar N. Stoyanov

Journées équations aux dérivées partielles (1987)

  • page 1-10
  • ISSN: 0752-0360

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Petkov, Vesselin M., and Stoyanov, Luchezar N.. "Singularities of the scattering kernel for non convex obstacles." Journées équations aux dérivées partielles (1987): 1-10. <http://eudml.org/doc/93145>.

@article{Petkov1987,
author = {Petkov, Vesselin M., Stoyanov, Luchezar N.},
journal = {Journées équations aux dérivées partielles},
keywords = {singularities; scattering kernel; wave equation; obstacle; asymptotics; scattering invariants; scattering data},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {Singularities of the scattering kernel for non convex obstacles},
url = {http://eudml.org/doc/93145},
year = {1987},
}

TY - JOUR
AU - Petkov, Vesselin M.
AU - Stoyanov, Luchezar N.
TI - Singularities of the scattering kernel for non convex obstacles
JO - Journées équations aux dérivées partielles
PY - 1987
PB - Ecole polytechnique
SP - 1
EP - 10
LA - eng
KW - singularities; scattering kernel; wave equation; obstacle; asymptotics; scattering invariants; scattering data
UR - http://eudml.org/doc/93145
ER -

References

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  1. [1] Y. Colin de Verdière, Sur les longueurs des trajectoires périodiques d'un billard, pp. 122-139 dans Géométrie Symplectique et de Contact : Autour du théorème de Poincaré-Birkoff, Hermann, 1984. Zbl0599.58039MR86a:58078
  2. [2] C. Gérard, Asymptotique des poles de la matrice de scattering pour deux obstacles strictement convexes, Prépublication de l'Université Paris-Sud, 1986. Zbl0622.35054
  3. [3] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix, Publ. RIMS Kyoto Univ., 12, (1977), 69-88. Zbl0381.35064MR56 #6759
  4. [4] 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
  5. [5] M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles, preprint, 1985. Zbl0637.35068
  6. [6] S. Marvizi, R. Melrose, Spectral invariants of convex planar regions, J. Diff. Geometry, 17, (1982) 475-502. Zbl0492.53033MR85d:58084
  7. [7] S. Nakamura, H. Soga, Singularities of the scattering kernel for two balls, preprint, 1986. Zbl0638.35068
  8. [8] V. Petkov, High frequency asymptotics of the scattering amplitude for non-convex bodies, Comm. Part. Diff. Equations, 5, (1980), 193-329. Zbl0435.35065MR82c:35061
  9. [9] V. Petkov, L. Stojanov, Periodic geodesics of generic non-convex domains in ℝ2 and the Poisson relation, Bull. Amer. Math. Soc., 15, (1986), 88-90. Zbl0602.58050MR87i:58173
  10. [10] V. Petkov et L. Stojanov, Propriétés génériques de l'application de Poincaré et des géodesiques périodiques généralisées, Seminaire Equations aux Dérivées Partielles, Ecole Polytechnique, Exposé XI, 1985 - 1986. Zbl0611.58048
  11. [11] V. Petkov, L. Stojanov, Spectrum of the Poincaré map for periodic reflecting rays in generic domains, Math. Z., 194, (1987), 505-518. Zbl0673.58035MR88d:58129
  12. [12] V. Petkov, L. Stojanov, Periods of multiple reflecting geodesics and inverse spectral results, Amer. J. Math., (to appear). Zbl0652.35027
  13. [13] Ya. G. Sinai, Development of Krylov ideas. An addendum to the book : N.S. Krylov, Works on the foundations of statistical physics, Princeton Univ. Press, 1979, 239-281. 

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