Skip to main content
Log in

Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in ℝn

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bardos, C., Guilot, J., Ralston, J.: La relation de Poisson pour l'equation des ondes dans un ouvert non borne application la theorie de la diffusion. Commun. Partial Differ. Equations7, 905–958 (1982)

    Google Scholar 

  2. Intissar, A.: A polynomial bound on the number of scattering poles for a potential in even dimensional space ℝn. Commun. Partial Differ. Equations11, 367–396 (1986)

    Google Scholar 

  3. Intissar, A.: On the value distribution of the scattering poles associated to the Schrödinger operator\(H = ( - i\vec V + \vec b(x))^2 + a(x)\) in ℝn,n≧3. Preprint

  4. Lax, P.D., Phillips, R.S.: Scattering theory. New York: Academic Press 1967

    Google Scholar 

  5. Melrose, R.B.: Polynomial bounds on the number of scattering poles. J. Funct. Anal.53, 287–303 (1983).

    Google Scholar 

  6. Melrose, R.B.: Polynomial bounds on the distribution of poles in scattering by an obstacle. Journées Equations aux dérivées partielle. Saint-Jean-de-montes (1984)

  7. Melrose, R.B.: Weyl asymptotics for the phase in obstacle scattering. Commun. Partial Differ. Equations13, 1431–1439 (1988)

    Google Scholar 

  8. Petkov, V.M.: Phase de diffusion pour des perturbations captives. Journées Equations aux dérivées partielles, Saint-Jean-de-Montes. (1990)

  9. Titchmarsh, E.C.: The theory of functions. Oxford: Oxford University Press 1968

    Google Scholar 

  10. Vainberg, B.: Asymptotic methods in equations of mathematical physics. New York: Gordon and Breach 1988

    Google Scholar 

  11. Vodev, G.: Polynomial bounds on the number of scattering poles for symmetric systems. Ann. Inst. Henri Poincaré Phys. théor.54, 199–208 (1991)

    Google Scholar 

  12. Vodev, G.: Polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in ℝn,n≧3 odd. Osaka J. Math.28 (1991) (to appear)

  13. Zworski, M.: Distribution, of poles for scattering on the real line J. Funct. Anal.73, 277–296 (1987)

    Google Scholar 

  14. Zworski, M.: Sharp polynomial bounds on the number of scattering poles of radial potentials. J. Funct. Anal.82, 370–403 (1989)

    Google Scholar 

  15. Zworski, M.: Sharp polynomial bounds on the number of scattering poles. Duke Math. J.59, 311–323 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by Bulgarian Ministry of Science and Education under grant No. 52

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vodev, G. Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in ℝn . Math. Ann. 291, 39–49 (1991). https://doi.org/10.1007/BF01445189

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01445189

Keywords

Navigation