Skip to main content Accessibility help
×
Home

Density of Resonances for Strictly Convex Analytic Obstacles

  • Johannes Sjöstrand (a1)

Abstract

We estimate the density of resonances close to a critical curve, for strictly convex obstacles with analytic boundary. Contrary to the C -case, already treated with Zworski, the estimates are in terms of dynamical quantities. A new feature in the proof is a certain averaging procedure.

Résumé

Nous estimons la densité des résonances près d'une courbe critique, pour des obstacles strictement convexes à bord analytique. Contrairement au cas C , déjà traité avec Zworski, les estimations font appel aux quantités dynamiques. Une procédure de moyennisation est un aspect nouveau dans la demonstration.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Density of Resonances for Strictly Convex Analytic Obstacles
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Density of Resonances for Strictly Convex Analytic Obstacles
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Density of Resonances for Strictly Convex Analytic Obstacles
      Available formats
      ×

Copyright

References

Hide All
[BG] Babich, V.M. and Grigoreva, N.S., , Funktsional Anal, i Prilozhen. (1) 8 (1974), 7174.
[BaLR] Bardos, C., Lebeau, G. and Rauch, J., singularities, Invent. Math. 90 (1987), 77114.
[Be] Besse, A.,Manifolds all of whose geodesies are closed, Springer Verlag, 1978.
[BoS] Boutet de Monvel, L. and Sjostrand, J., Sur la singularity des noyaux de Bergman et de Szego, Asterisque 34-35 (1976), 12S-164.
[FZ] Filippov, V.B. and Zayev, A.B., Rigorous justification of the asymptotic solutions of sliding wave type, J. Soviet Math. (2) 30 (1985), 23952406.
[HaL] Hargé, T. and Lebeau, G., Diffraction par un convexe, Invent. Math. (1) 118 (1994), 161196.
[HS] Helffer, B. and J.Sjöstrand, Résonances en limite semiclassique, Bull. Soc. Math. France (3) 114, Memoire 24/25, (1986).
[L] Lebeau, G., pour la diffraction, Comment. Partial Differential Equations (15) 9 (1984), 14371494.
[P] Popov, G., Asymptotics of Green s functions in the shadow, C. R. Acad. Bulgare Sci. (10) 38 (1985), 1287. 1290.
[S1] Sjöstrand, J., Propagation of analytic singularities for second order Dirichlet problems, Comment. Partial Differential Equationa (1) 5 (1980), 4194.
[S2] Sjöstrand, J., Singularités analytiques microlocales, Astérisque 95 (1982).
[SZ1] Sjostrand, J. and Zworski, M., Estimates on the number of scattering poles near the real axis for strictly convex obstacles, Ann. Inst. Fourier (3) 43(1993), 169-190.
[SZ2] Sjostrand, J., The complex scaling method for scattering by strictly convex obstacles, Institut Mittag-Leffler 10, Ark. Mat., 19921993. preprint, to appear.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Density of Resonances for Strictly Convex Analytic Obstacles

  • Johannes Sjöstrand (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed