Skip to main content
SpringerLink
Log in

Lower bounds for resonance widths in potential and obstacle scattering

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Explicit lower bounds are given for the size of the imaginary parts of resonances for Schrödinger operators with non-trapping or trapping potentials, and for the Dirichlet Laplacian in the exterior of a star-shaped obstacle, both acting in three dimensions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [B-L-R] Bardos, C., Lebeau, G., Rauch, J.: Scattering frequenceis and Gevrey 3 singularities. Invent. Math.90, 77–114 (1987)

    Article  Google Scholar 

  • [B-C-D] Briet, Ph., Combes, J.M., Duclos, P.: On the location of resonances for Schrödinger operators in the semiclassical limit I. Resonance free domains. J. Math. Anal. App.126, 90–99 (1987)

    Article  Google Scholar 

  • [D-H] Debièvre, S., Hislop, P.: Spectral resonances for the Laplace-Beltrami operator. Ann. Inst. H. Poincaré,48, 105–145 (1988)

    Google Scholar 

  • [H] Harrell, E. M.: General lower bounds for resonances in one dimension. Commun. Math. Phys.86, 221–225 (1982)

    Article  Google Scholar 

  • [LA-1] Lavine, R.: Commutators and scattering II; A class of one body problems, Ind. Univ. Math. J.21, 643–656 (1972)

    Article  Google Scholar 

  • [LA-2] Lavine, R.: Spectral density and sojourn times. In: Nuttall, J. (ed.) Atomic scattering theory. London, Ontario: Univ. Western Ontario 1978, pp. 45–61

    Google Scholar 

  • [LA-3] Lavine, R.: Constructive estimates in quantum scattering, unpublished

  • [LO] Loe, B.: Scattering by potentials of unbounded support, Ph.D. thesis, Brown University, to appear 1989

  • [M] Morawetz, C.: On the modes of decay for the wave equation in the exterior of a reflecting body. Proc. Roy. Irish Acad.C72, 113–120 (1972)

    Google Scholar 

  • [M-R-S] Morawetz, C., Ralston, J. and Strauss, W.: Decay of solutions of the wave equation outside nontrapping obstacles. Commun. Pure Appl. Math.30, 447–508 (1977)

    Google Scholar 

  • [R] Ralston, J.: The first variation of the scattering matrix: An addendum. J. Diff. Equations28, 155–162 (1978)

    Article  Google Scholar 

  • [R-S] Reed, M., Simon, B.: Methods of modern mathematical physics IV: analysis of operators. New York: Academic Press 1978

    Google Scholar 

  • [S] Sigal, I. M.: Sharp exponential bounds on resonance states and width of resonances. Adv. Appl. Math.9, 127–166 (1988)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Casilla 6177, Santiago, Chile

    Claudio Fernandez

  2. Department of Mathematics, University of Rochester, 14627, Rochester, NY, USA

    Richard Lavine

Authors
  1. Claudio Fernandez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard Lavine
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. Simon

Work partially supported by DiUC/FONDECYT (Chile)

Work partially supported by U.S. National Science Foundation grant DMS 8705610

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fernandez, C., Lavine, R. Lower bounds for resonance widths in potential and obstacle scattering. Commun.Math. Phys. 128, 263–284 (1990). https://doi.org/10.1007/BF02108782

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02108782

Keywords

Search

Navigation