Skip to main content

On smoothing property of Schrödinger propagators

  • Conference paper
  • First Online:
Book cover Functional-Analytic Methods for Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1450))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asada, K. and D. Fujiwara, On some oscillatory integral transformations in L 2 (ℝn), Japan. J. Math. 4 (1978), 299–361.

    MathSciNet  MATH  Google Scholar 

  2. Carleson, L., Some analytical problems related to statistical mechanics, in “Euclidean Harmonic Analysis,” Lecture Notes in Math. 799, Springer-Verlag, Berlin and New York, 1979, pp. 5–45.

    Google Scholar 

  3. Constantin, P and J. C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413–439.

    Article  MathSciNet  MATH  Google Scholar 

  4. Dahlberg, B. E. J. and C. E. Kenig, A note on the almost everywhere behavior of solutions to the Schrödinger equation, in “Lecture Notes in Math. 908,” Springer-Verlag, Berlin and New York, 1982, pp. 205–208.

    Google Scholar 

  5. Fujiwara, D., Remarks on convergence of the Feynman path integrals, Duke Math. J. 47 (1980), 559–600.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ginibre, J. and G. Velo, The global Cauchy problem for non-linear Schrödinger equation revisited, Ann. Inst. H. Poincaré, Anal. Nonlinéare 2 (1985), 309–327.

    MathSciNet  MATH  Google Scholar 

  7. Kato, T., Wave operators and similarity for some non-selfadjoint operators, Math. Ann. 162 (1966), 258–279.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kato, T., On the Cauchy problem for the (generalized) Kortweg-de Vries equation, Studies in Appl. Math. Adv. in Math. Supplementary Studies 18, 93–128.

    Google Scholar 

  9. Kato, T. and K. Yajima, Some examples of smooth operators and associated smoothing effect, to appear, Rev. in Math. Phys.

    Google Scholar 

  10. Kenig, C. E. and A. Ruiz, A strong type (2,2) estimate for a maximal operator associated to the Schrödinger equation, Trans. Amer. Math. Soc. 280 (1983), 239–246.

    MathSciNet  MATH  Google Scholar 

  11. Kumano-go, H., Fundamental solution for a hyperbolic system with diagonal principal part, Comm. in P.D.E. 4 (1979), 959–1015.

    Article  MathSciNet  MATH  Google Scholar 

  12. Sjölin, P., Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699–715.

    Article  MathSciNet  MATH  Google Scholar 

  13. Strichartz, R. S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44, 705–714.

    Google Scholar 

  14. Taylor, M. E., “Pseudo-differential operators,” Princeton Univ. Press, Princeton, New Jersey, 1981.

    Google Scholar 

  15. Triebel, H., “Interpolation theory, function spaces, differential operators,” North Holland, Amsterdam, New York, Oxford, 1978.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Yajima, K., Schrödinger evolution equation with magnetic fields, to appear in J. d'Analyse Math.

    Google Scholar 

  18. Yamazaki, M., Unpublished notes (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hiroshi Fujita Teruo Ikebe Shige Toshi Kuroda

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Yajima, K. (1990). On smoothing property of Schrödinger propagators. In: Fujita, H., Ikebe, T., Kuroda, S.T. (eds) Functional-Analytic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084896

Download citation

  • DOI: https://doi.org/10.1007/BFb0084896

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53393-1

  • Online ISBN: 978-3-540-46818-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics