Skip to main content
Log in

Results inL p(ℝd) for the Schrödinger equation with a time-dependent potential

  • 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. Brenner, P., Thomée, V., Wahlbin, L.B.: Besov spaces and applications to difference methods for initial value problems. (Lect. Notes Math., vol. 434) Berlin Heidelberg New York: Springer 1974

    Google Scholar 

  2. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger operators. Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  3. Evans, D.E.: Time dependent perturbations and scattering of strongly continuous groups on Banach spaces. Math. Ann.221, 275–290 (1976)

    Google Scholar 

  4. Howland, J.: Stationary scattering theory for time-dependent Hamiltonians. Math. Ann.207, 315–335 (1974)

    Google Scholar 

  5. Jensen, A., Nakamura, S.: Mapping properties of functions of Schrödinger operators betweenL p-spaces and Besov spaces. Report. Djursholm: Institut Mittag-Leffler 1992

    Google Scholar 

  6. Jensen, A., Ozawa, T.: Existence and non-existence results for wave operators for perturbations of the Laplacian. Rev. Math. Phys.5, 601–629 (1993)

    Google Scholar 

  7. Journé, J.L., Soffer, A., Sogge, C.D.: Decay estimates for Schrödinger operators. Commun. Pure Appl. Math.44, 573–604 (1991)

    Google Scholar 

  8. Kapitanskiî.: Some generalizations of the Strichartz-Brenner inequality. Leningr. Math. J.1, 693–726 (1990)

    Google Scholar 

  9. Kitada, H., Yajima, K.: A scattering theory for time-dependent long-range potentials. Duke Math. J.49, 341–376 (1982)

    Google Scholar 

  10. Kitada, H., Yajima, K.: Remarsk on our paper “A scattering theory for time-dependent long-range potentials”. Duke Math. J.50, 1005–1015 (1983)

    Google Scholar 

  11. Lin, S.-C.: Wave operators and similarity for generators of semigroups in Banach spaces. Trans. Am. Math. Soc.139, 469–494 (1969)

    Google Scholar 

  12. Neidhardt, H.: On abstract linear evolution equations. I. Math. Nachr.103, 183–298 (1981)

    Google Scholar 

  13. Ruiz, A., Vega, L.: On local regularity of Schrödinger equations. Duke Math. J. (Int. Math. Res. Notices)69 (no. 1), 13–27 (1993)

    Google Scholar 

  14. Schonbek, T.: Decay of solutions of Schroedinger equations. Duke Math. J.46, 203–213 (1979)

    Google Scholar 

  15. Yafaev, D.R.: Scattering subspaces and asymptotic completeness for the time-dependent Schrödinger equation. Math. USSR, Sb.46, 267–283 (1983)

    Google Scholar 

  16. Yajima, K.: Existence of solutions for Schrödinger evolution equations. Commun. Math. Phys.110, 415–426 (1987)

    Google Scholar 

  17. Yajima, K.: On smoothing property of Schrödinger propagators. In: Fujita, H., Ikebe, T., Kuroda, S.T. (eds.) Functional-analytic methods for partial differential equations. (Lect. Notes Math., vol. 1450, pp. 20–35) Berlin Heidelberg New York: Springer 1990

    Google Scholar 

  18. Yajima, K.: Schrödinger evolution equations with magnetic fields. J. Anal. Math.56, 29–76 (1991)

    Google Scholar 

  19. Yajima, K.: TheL p-continuity of wave operators for Schrödinger operators. (Department of Mathematical Sciences, University of Tokyo, Preprint 1993)

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jensen, A. Results inL p(ℝd) for the Schrödinger equation with a time-dependent potential. Math. Ann. 299, 117–125 (1994). https://doi.org/10.1007/BF01459775

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459775

Mathematics Subject Classification (1991)

Navigation