Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian

Vesselin Petkov; Latchezar Stoyanov

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 62, Issue: 1, page 17-45
  • ISSN: 0246-0211

How to cite

top

Petkov, Vesselin, and Stoyanov, Latchezar. "Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian." Annales de l'I.H.P. Physique théorique 62.1 (1995): 17-45. <http://eudml.org/doc/76666>.

@article{Petkov1995,
author = {Petkov, Vesselin, Stoyanov, Latchezar},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {scattering rays; singularities of the scattering kernel; scattering matrix; obstacles},
language = {eng},
number = {1},
pages = {17-45},
publisher = {Gauthier-Villars},
title = {Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian},
url = {http://eudml.org/doc/76666},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Petkov, Vesselin
AU - Stoyanov, Latchezar
TI - Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 62
IS - 1
SP - 17
EP - 45
LA - eng
KW - scattering rays; singularities of the scattering kernel; scattering matrix; obstacles
UR - http://eudml.org/doc/76666
ER -

References

top
  1. [BGR] C. Bardos, J.C. Gumlot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné. Comm. PDE, Vol. 7, 1982, pp. 905-958. Zbl0496.35067MR668585
  2. [CPS] F. Cardoso, V. Petkov and L. Stoyanov, Singularities of the scattering kernel for generic obstacles. Ann. Inst. Henri Poincaré (Physique théorique), Vol. 53, 1990, pp. 445-466. Zbl0729.35099MR1096103
  3. [G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Bull. de S.M.F., Vol. 116, Mémoire n° 31, 1988. Zbl0654.35081MR998698
  4. [GGu] M. Golubitskii and V. Guillemin, Stabler Mappings and their Singularities, Berlin, Springer, 1973. Zbl0294.58004MR341518
  5. [Gu] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix. Publ. RIMS Kyoto Univ., Vol. 12, 1977, pp. 69-88. Zbl0381.35064MR448453
  6. [HI] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I. Berlin, Springer, 1985. MR404822
  7. [H2] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Berlin, Springer, 1985. Zbl0601.35001MR404822
  8. [11] M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles. J. Math. Kyoto Univ., Vol. 27, 1987, pp. 69-102. Zbl0637.35068MR878491
  9. [12] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies. Ann. Inst. Fourier, Vol. 38, 1988, pp. 113-146. Zbl0636.35045MR949013
  10. [13] M. Ikawa, On the existence of the poles of the scattering matrix for several convex bodies. Proc. Japan Acad., Ser. A, Vol. 64, 1988, pp. 91-93. Zbl0704.35113MR966394
  11. [14] M. Ikawa, On scattering by obstacles, Proceedings of ICM-90, Springer-Verlag, 1991, pp. 1145-1154. Zbl0757.35055MR1159299
  12. [LP] P. Lax and R. Phillips, Scattering Theory. New York, Academic Press, 1967. Zbl0186.16301MR217440
  13. [Ma] A. Majda, A representation formula for the scattering operator and the inverse problem for arbitrary bodies. Comm. Pure Appl. Math., Vol. 30, 1977, pp. 165- 194. Zbl0335.35076MR435625
  14. [MS] R. Melrose and J. Sjöstrand, Singularities in boundary value problems. I, II. Comm. Pure Appl. Math., Vol. 31, 1978, pp. 593-617 and Vol. 37, 1982, pp. 129-168. Zbl0368.35020MR492794
  15. [P1] V. Petkov, Scattering Theory for Hyperbolic Operators. Amsterdam, North–Holland, 1989. Zbl0687.35067MR1028780
  16. [P2] V. Petkov, Le comportement de la résolvante modifiée du Laplacien pour des obstacles captifs. Séminaire EDP, Exposé XVIII, École Polytechnique, 1991-1992. Zbl0850.35069MR1226497
  17. [PS1] V. Petkov and L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., Vol. 109, 1987, pp. 619-668. Zbl0652.35027MR900034
  18. [PS2] V. Petkov and L. Stoyanov, Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc., Vol. 312, 1989, pp. 203-235. Zbl0685.35083MR929661
  19. [PS3] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems. Chichester, John Wiley & Sons, 1992. Zbl0761.35077
  20. [SjZ1] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles. Comm. PDE, Vol. 18, 1993, pp. 847-857. Zbl0784.35070MR1218521
  21. [SjZ2] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II. J. Funct. Anal., Vol. 123, 1994, pp. 336-367. Zbl0823.35137MR1283032
  22. [St] L. Stoyanov, An inverse scattering resultfor several convex bodies. Preprint, Math. Dept., Univ. of Western Australia, 1993. 
  23. [V] B. Vainberg, Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ. Ltd., 1988. Zbl0518.35002MR1054376

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.