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Propagation of Analytic Singularities for Short and Long Range Perturbations of the Free Schrödinger Equation

  • André Martinez
  • Shu Nakamura
  • Vania Sordoni
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 269)

Abstract

We study the propagation of the analytic wave front set for solutions to the Schrödinger equation associated with perturbations of the free Laplacian.

References

  1. 1.
    Craig, W., Kappeler, T., Strauss, W.: Microlocal dispersive smoothing for the Schrödinger equation. Commun. Pure Appl. Math. 48, 769–860 (1996)CrossRefGoogle Scholar
  2. 2.
    Hassell, A., Wunsch, J.: The Schrödinger propagator for scattering metrics. Ann. Math. 162 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ito, K.: Propagation of singularities for Schrödinger equations on the Euclidean space with a scattering metric. Commun. Partial Differ. Equ. 31(12), 1735–1777 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ito, K., Nakamura, S.: Singularities of solutions to Schrdinger equation on scattering manifold. Am. J. Math. 131(6), 1835–1865 (2009)CrossRefGoogle Scholar
  5. 5.
    Martinez, A.: An Introduction to Semiclassical and Microlocal Analysis. UTX Series. Springer, New York (2002)CrossRefGoogle Scholar
  6. 6.
    Martinez, A., Nakamura, S., Sordoni, V.: Analytic smoothing effect for the Schrödinger equation with long-range perturbation. Commun. Pure Appl. Math. 59, 1330–1351 (2006)CrossRefGoogle Scholar
  7. 7.
    Martinez, A., Nakamura, S., Sordoni, V.: Analytic wave front set for solutions to Schrödinger equations. Adv. Math. 222, 1277–1307 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Martinez, A., Nakamura, S., Sordoni, V.: Analytic wave front set for solutions to Schrödinger equations II - Long range perturbations. Commun. Partial Differ. Equ. 35(12), 2279–2309 (2010)CrossRefGoogle Scholar
  9. 9.
    Nakamura, S.: Propagation of the homogeneous wave front set for Schrödinger equations. Duke Math. J. 126, 349–367 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Nakamura, S.: Wave front set for solutions to Schrödinger equations. J. Funct. Anal. 256, 1299–1309 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Nakamura, S.: Semiclassical singularity propagation property for Schrödinger equations. J. Math. Soc. Jpn. 61(1), 177–211 (2009)CrossRefGoogle Scholar
  12. 12.
    Robbiano, L., Zuily, C.: Analytic theory for the quadratic scattering wave front set and application to the Schrödinger equation. Soc. Math. France Astérisque 283, 1–128 (2002)zbMATHGoogle Scholar
  13. 13.
    Sjöstrand, J.: Singularités analytiques microlocales. Soc. Math. France Astérisque 95, 1–166 (1982)zbMATHGoogle Scholar
  14. 14.
    Zelditch, S.: Reconstruction of singularities for solutions of Schrödinger equation. Commun. Math. Phys. 90, 1–26 (1983)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Graduate School of Mathematical ScienceUniversity of TokyoMeguro-kuJapan

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