Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow

Mathematische Annalen

Volumn 318, Issue 2, 2000, Pages 355-389

  Doi, Shin Ichi ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039250942     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080000128     Document Type: Article

References (25)

1. W. Craig, Les moments microlocaux et la régularité des solutions de l'équations de Schrödinger, in "Séminaire Equations aux Dérivées Partielles 1995-1996," Ecole Polytechnique, 1996, Exposé XX.
2. W. Craig, T. Kappeler and W. Strauss, Microlocal dispersive smoothing for the Schrödinger equation, Commun. Pure Applied Math. 48 (1995), 769-860.
3. J. Dereziński and C. Gérard, Asymptotic completeness of classical and quantum N-particle systems, Springer-Verlag, Berlin Heidelberg New York, 1997.
4. S. Doi, Remarks on the Cauchy problem for Schrödinger-type equations, Commun. Partial Differential Equations 21 (1996), 163-178.
5. S. Doi, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math J. 82 (1996), 679-706.
6. S. Doi, Smoothing effect for Schrödinger evolution equation via commutator algebra, in "Séminaire Equations aux Dérivées Partielles 1996-1997," Ecole Polytechnique, 1997, Exposé XX.
7. S. Doi, Commutator algebra and abstract smoothing effect, J. Funct. Anal. 168 (1999), 428-469.
8. D. Fujiwara, Remarks on the convergence of the Feynman path integrals, Duke Math. J. 47 (1980), 559-600.
9. C. Gérard, H. Isozaki, and E. Skibsted, Commutator algebra and resolvent estimates, Advanced Studies in Pure Mathematics 23 (1994), 69-82.
10. B. Helffer and J. Sjöstrand, Équation de Schrödinger avec champ magnétique et équation de Harper, Lecture Notes in Physics 345, Springer-Verlag, 1989, 118-197.
11. L. Hörmander, The analysis of linear partial differential operators III, Springer-Verlag, Berlin Heidelberg New York, 1985.
12. K. Kajitani, Smoothing effect in Gevrey classes for Schrödinger equations I, Preprint.
13. K.Kajitani and S. Wakabayashi, Analytically smoothing effect for Schrödinger type equations with variable coefficients, Preprint.
14. L. Kapitanski and I. Rodianski, Regulated smoothing for Schrödinger evolution, International Mathematics Research Notices 2 (1996), 41-54.
15. L. Kapitanski, I. Rodianski, and K. Yajima, On the fundamental solution of a perturbed harmonic oscillator, Topological Methods in Nonlinear Analysis 9 (1997), 77-106.
16. L. Kapitanski and Y. Safarov, Dispersive smoothing for Schrödinger equations, Mathematical Research Letters 3 (1996), 77-91.
17. C. Kenig, G. Ponce, and L. Vega, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations, Invent. Math. 134 (1998), 489-545.
18. R. Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces, in "Spectral and scattering theory" (M. Ikawa, ed.), Marcel Dekker, 1994, 85-130.
19. L. Robbiano and C. Zuily, Microlocal analytic smoothing effect for Schrödinger equation, Preprint, Université de Paris-Sud.
20. L. Robbiano and C. Zuily, Effet régularisant microlocal analytique pour l'équation de Schrödinger: le cas des données oscillantes, Preprint, Université de Paris-Sud.
21. J. Wunsch, Propagation of singularities and growth for Schrödinger operators, Duke Math. J. 98 (1999), 137-186.
22. J. Wunsch, The trace of the generalized harmonic oscillator, Ann. Inst. Fourier, Grenoble 49 (1999), 351-373.
23. K. Yajima, On smoothing property of Schrödinger propagators, Lecture Notes in Math. 1450, Springer-Verlag, 1990, 20-35.
24. K. Yajima, Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations, Commun. Math. Phys. 181 (1996), 605-629.
25. S. Zelditch, Reconstruction of singularities for solutions of Schrödinger's equation, Commun. Math. Phys. 90 (1983), 1-26.