Boundedness and continuity of the fundamental solution of the time dependent schrödinger equation with singular potentials

Tohoku Mathematical Journal

Volumn 50, Issue 4, 1998, Pages 577-595

  Yajima, Kenji ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032413495     PISSN: 00408735     EISSN: None     Source Type: Journal    
DOI: 10.2748/tmj/1178224900     Document Type: Article

References (21)

1. R. A. Adams, Sobolev spaces, Academic Press, New York-San Francisco-London, 1975.
2. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I, Schrõdinger equations, Geom. Funct. Anal. 3 (1993), 107-156.
3. W. Craig, T. Kappeler and W. Strauss, Microlocal dispersive smoothing for the Schrõdinger equation, Comm. Pure and Appl. Math. 48 (1995), 767-860.
4. H. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrõdinger operators, Springer-Verlag, Berlin, 1987.
5. D. Fujiwara, Remarks on convergence of the Feynman path integrals, Duke Math. J. 47 (1980), 41-96.
6. J. Ginibre, Y. Tsutsumi and G. Velo, On the Cauchy problem for the Zakharov system, preprint, Orsay (1996).
7. K. Ito, Generalized uniform complex measures in the Hilbertian metric space with their application to the Feynman integral, in Proc. Fifth Berkeley Symposium on Math. Statistics and Probability, Univ. California Press, 1966, pp. 145-161.
8. d) for the Schrõdinger equation with a time dependent potential, Math. Ann. 299 (1994), 117-125.
9. p-spaces and Besov spaces, Spectral and scattering theory and applications, Advanced Studies in Pure Math. 22, Kinokuniya, Tokyo, 1994, pp. 187-210.
10. J. L. Journé, A. Soffer and C. D. Sogge, Decay estimates for Schrõdinger operators, Comm. Pure Appl. Math. 44 (1991), 573-604.
11. L. Kapitanski and I. Rodnianski, Regulated smoothing for Schrõdinger evolution, Internat. Math. Research Letters 2 (1996), 41-54.
12. L. Kapitanski, I. Rodnianski and K. Yajima, On the fundamental solution of a perturbed harmonic oscillator, to appear in Topological methods in nonlinear analysis 1 (1997).
13. T. Schonbek, Decay of solutions of Schrõdinger equations, Duke Math. J. 46 (1979), 203-213.
14. B. Simon, Schrõdinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526.
15. K. Yajima, Existence of solutions for Schrõdinger evolution equations, Comm. Math. Phys. 110 (1987), 415-426.
16. K. Yajima, On smoothing property of Schrõdinger propagators, Lect. Notes in Math. 1450, Springer-Verlag, Berlin, 1990, pp. 20-35.
17. K. Yajima, Schrõdinger evolution equations with magnetic fields, J. d’Analyse Math. 56 (1991), 29-76.
18. k, p-continuity of wave operators for Schrõdinger operators, J. Math. Soc. Japan 47 (1995), 551-581.
19. k, p-continuity of wave operators for Schrõdinger operators III, J. Math. Sci. Univ. Tokyo 2 (1995), 311-346.
20. K. Yajima, Smoothness and non-smoothness of the fundamental solution of time dependent Schrõdinger equations, Comm. Math. Phys. 181 (1996), 605-629.
21. S. Zelditch, Reconstruction of singularities for solutions of Schrõdinger equations, Comm. Math. Phys. 90 (1983), 1-26.