Sur la conjecture de Lax et Phillips pour un nombre fini d'obstacles strictement convexes

V. Petkov

Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996)

  • page 1-13

How to cite

top

Petkov, V.. "Sur la conjecture de Lax et Phillips pour un nombre fini d'obstacles strictement convexes." Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996): 1-13. <http://eudml.org/doc/112122>.

@article{Petkov1995-1996,
author = {Petkov, V.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {meromorphic function},
language = {fre},
pages = {1-13},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Sur la conjecture de Lax et Phillips pour un nombre fini d'obstacles strictement convexes},
url = {http://eudml.org/doc/112122},
year = {1995-1996},
}

TY - JOUR
AU - Petkov, V.
TI - Sur la conjecture de Lax et Phillips pour un nombre fini d'obstacles strictement convexes
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1995-1996
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 13
LA - fre
KW - meromorphic function
UR - http://eudml.org/doc/112122
ER -

References

top
  1. [BGR] C. Bardos, J.C. Guillot, J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné, Commun. Partial Diff. Equations7 (1982), 905-958. Zbl0496.35067MR668585
  2. [BL] M. Babillot and F. Ledrappier, Lalley's theorem on periodic orbits of hyperbolic flows, Preprint, Ecole Polytechnique, 1996. Zbl0915.58074
  3. [Be] V. Bernstein, Leçons sur les progrés récents de la théorie des séries de Dirichlet, Paris, Gauthier-Villards, 1933. Zbl0008.11503
  4. [Bu] N. Burq, Controle de l'équation des plaques en présence d'obstacles strictement convexes, Suppl. Bull. Soc. Math. France, Mémoire n° 55, 121 (1993), . Zbl0930.93007
  5. [F1] L. Farhy, Distribution near real axis of the scattering poles generated by a non-hyperbolic ray, Ann. Inst. H. Poincaré (Physique théorique), 60 (1994), 291-302. Zbl0808.35091MR1281648
  6. [F2] L. Farhy, Lower bounds on the number of scattering poles under lines parallel to the real axis, Commun. Partial Diff. Equations, 20 (1995), 729-740. Zbl0822.35105MR1326904
  7. [G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Bull. de S.M.F., Mémoire n° 31, 116 (1988). Zbl0654.35081MR998698
  8. [GM] V. Guillemin and R. Melrose, The Poisson summation formula for manifolds with boundary, Adv. in Math.32 (1979), 128-148. Zbl0415.35062MR539531
  9. [H] N.T. Haydn, Meromorphic extensions of the zeta function for Axiom A flows, Ergod. Th. & Dynam. Sys., 10 (1990), 347-360. Zbl0694.58035MR1062762
  10. [I1] M. Ikawa, Decay of solutions of the wave equation in the exterior of two convex obstacles, Osaka J. Math.19 (1982), 459-509. Zbl0498.35008MR676233
  11. [I2] M. Ikawa, Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis, Osaka J. Math.22 (1985), 657-689. Zbl0617.35102MR815439
  12. [I3] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies, Ann. Inst. Fourier38 (1988), 113-146. Zbl0636.35045MR949013
  13. [I4] M. Ikawa, On the existence of the poles of the scattering matrix for several convex obstacles, Proc. Japan Acad., Ser. A, 64 (1988), 69-102. Zbl0637.35068
  14. [I5] M. Ikawa, On the distribution of poles of the scattering matrix for several convex bodies, pp. 210-225 in Lecture Notes in Mathematics, vol. 1450, Springer, Berlin, 1990. Zbl0754.35103MR1084611
  15. [I6] M. Ikawa, Singular perturbation of symbolic flows and poles of the zeta function, Osaka J. Math.27 (1990), 281-300 and 29 (1992), 161-174. Zbl0708.58019MR1066627
  16. [I7] M. Ikawa, On Zeta function and scattering poles for several convex bodies, Exposé II, Journées Equtions aux Dérivées Partielles, Saint-Jean-de-Monts, Juin 1994. Zbl0872.58048MR1298673
  17. [LP] P. Lax and R. Phillips, Scattering Theory, New York, Academic Press1967. Zbl0186.16301MR217440
  18. [M1] R. Melrose, Polynomial bound on number of scattering poles, J. Funct. Anal., 53 (1983), 29-40. Zbl0535.35067MR724031
  19. [M2] R. Melrose, Polynomial bound on the distribution of poles in scattering by an obstacle, Journées Equations aux Dérivées Partielles, Saint-Jean-de-Monts, 1984. Zbl0621.35073
  20. [MS] R. Melrose and J. Sjöstrand, Singularities in boundary value problems, I, II. Comm. Pure Appl. Math.31 (1978), 593-617 and 35 (1982), 129-168. Zbl0546.35083
  21. [PP] W. Parry and M. Pollicott, Zeta functions and periodic orbits structure of hyperbolic dynamics, Astérique, 187-188, Soc. Math. de France, 1990. Zbl0726.58003MR1085356
  22. [PS1] V. Petkov and L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectal results, Amer. J. Math.109 (1987), 617-668. Zbl0652.35027MR900034
  23. [PS2] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, Chichester, John Wiley & Sons1992. Zbl0761.35077MR1172998
  24. [PV] V. Petkovand G. Vodev, Upper bound on the number of the scattering poles and the Lax-Phillips conjecture, Asymptotic Analysis7 (1993), 97-104. Zbl0801.35099MR1225440
  25. [Po] M. Pollicott, Meromorphic extensions of generalized zeta functions, Invent. Math.85 (1986), 147-164. Zbl0604.58042MR842051
  26. [SjZ1] J. Sjötrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc.4 (1991), 729-769. Zbl0752.35046MR1115789
  27. [SjZ2] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, Commun. Partial Diff. Equations18 (1993), 847-857. Zbl0784.35070MR1218521
  28. [Ste] Pl. Stefanov, Stability of the resonances under smooth perturbations of the boundary, Asymptotic Analysis, 9 (1994), 291-296. Zbl0814.35022MR1295296
  29. [St1] L. Stoyanov, Poisson relation for the scattering kernel and inverse scattering by obstacles, Séminaire EDP, Exposé V, Ecole Polytechnique, 1994-1995. Zbl0888.58070MR1362553
  30. [St2] L. Stoyanov, Exponential instability for a class of dispersing billiards, Preprint, Mathematics Department, University of Western Australia, 1995. Zbl0923.58028MR1677157
  31. [St3] L. Stoyanov, Generalized Hamiltonian flow and rigidity of the scattering length spectrum, Preprint, Mathematics Department, University of Western Australia, 1996. 
  32. [Va] B. Vainberg, Asymptotic Methods of Mathematical Physics, Gordon and Breach Sci. Publ.New York, 1988. Zbl0743.35001
  33. [Vo1] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys.146 (1992), 205-216. Zbl0766.35032MR1163673

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.