Regulated Smoothing for Schrödinger Evolution

International Mathematics Research Notices

Volumn , Issue 2, 1996, Pages

  Kapitanski, Lev ^a   Rodnianski, Igor ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842453919     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields, I, General interactions, Duke Math. J. 45 (1978), 847-883; II, Separation of center of mass in magnetic fields, Ann. Phys. 114 (1978), 431-451; III, Atoms in homogeneous magnetic fields, Comm. Math. Phys. 79 (1981), 529-572.
2. J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields, I, General interactions, Duke Math. J. 45 (1978), 847-883; II, Separation of center of mass in magnetic fields, Ann. Phys. 114 (1978), 431-451; III, Atoms in homogeneous magnetic fields, Comm. Math. Phys. 79 (1981), 529-572.
3. J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields, I, General interactions, Duke Math. J. 45 (1978), 847-883; II, Separation of center of mass in magnetic fields, Ann. Phys. 114 (1978), 431-451; III, Atoms in homogeneous magnetic fields, Comm. Math. Phys. 79 (1981), 529-572.
4. R. Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1-42.
5. W. Craig, T. Kappeler, and W. Strauss, Microlocal dispersive smoothing for the Schrödinger equation, preprint, 1994.
6. H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1987.
7. n and some applications, Trudy Moscow. Mat. Obshch. 36 (1978), 155-194 (in Russian); English translation in Trans. Moscow Math. Soc. 36 (1978).
8. n and some applications, Trudy Moscow. Mat. Obshch. 36 (1978), 155-194 (in Russian); English translation in Trans. Moscow Math. Soc. 36 (1978).
9. R. P. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, Hightstown, N.J., 1965.
10. D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Anal. Math. 35 (1979), 41-96.
11. _, Remarks on convergence of the Feynman path integrals, Duke Math. J. 47 (1980), 559-600.
12. W. Hunziker, On the space-time behavior of Schrödinger wavefunctions, J. Math. Phys. 7 (1966), 300-304.
13. T. Ikebe and T. Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Ratl. Mech. Anal. 9 (1962), 77-92.
14. A. Jensen, Commutator methods and smoothing property of the Schrödinger evolution group, Math. Z. 191 (1986), 53-59.
15. L. Kapitanski, Some generalizations of the Strichartz-Brenner inequality, Leningrad Math. J. 1(3) (1990), 693-726.
16. L. Kapitanski and Yu. G. Safarov, Dispersive smoothing for Schrödinger evolution, preprint, 1995.
17. H. Kitada, On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980) 193-226.
18. _, Fundamental solutions and eigenfunction expansions for Schrödinger operators; I, Fundamental solutions, Math. Z. 198 (1988), 181-190.
19. H. Kitada and H. Kumano-go, A family of Fourier integral operators and the fundamental solution for a Schrödinger equation, Osaka J. Math. 18 (1981), 291-360.
20. n and operators of Fredholm type, Proc. Japan Acad. Ser. A Math. Sci. 49 (1973), 397-402.
21. V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics, Math Physics. Appl. Math. 7, Reidel, Dordrecht, 1981.
22. T. A. Osborn and Y. Fujiwara, Time evolution kernels: uniform asymptotic expansions, J. Math. Phys. 24 (1983), 1093-1103.
23. T. Ozawa, Smoothing effects and dispersion of singularities for the Schrödinger evolution group, Arch. Rational Mech. Anal. 110 (1990), 165-186.
24. _, Invariant subspaces for the Schrödinger evolution group, Ann. Inst. H. Poincaré Phys. Théor. 54 (1991), 43-57.
25. n e applicazioni, Ann. Mat. Pura Appl. 93 (1972), 359-389.
26. P. Perry, Propagation of states in dilation analytic potentials and asymptotic completeness, Comm. Math. Phys. 81 (1981), 243-259.
27. C. Radin and B. Simon, Invariant domains for the time-dependent Schrödinger equation, J. Differential Equations 29 (1978), 289-296.
28. B. Simon, Functional Integration and Quantum Physics, Pure Appl. Math. 86, Academic Press, New York, 1979.
29. _, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 447-526.
30. F. Treves, Parametrices for a class of Schrödinger equations, Comm. Pure Appl. Math. 48 (1995), 13-78.
31. n, Amer. J. Math. 107 (1985), 1-21.
32. C. Wilcox, Uniform asymptotic estimates for wave packets in the quantum theory of scattering, J. Math. Phys. 6 (1965), 611-620.
33. K. Yajima, "On smoothing property of Schrödinger propagators" in Functional-Analytic Methods for Partial Differential Equations (Tokyo, 1989), Lecture Notes in Math. 1450, Springer-Verlag, Berlin, 1990, 20-35.
34. _, "Schrödinger evolution equations and associated smoothing effect" in Rigorous Results in Quantum Dynamics, ed. by J. Dittrich and P. Exner, World Scientific, River Edge, N.J., 1991, 167-185.
35. _, Schrödinger evolution equation with magnetic field, to appear in J. Anal. Math.
36. _, Smoothness and nonsmoothness of the fundamental solution for initial value problem for time-dependent Schrödinger equations, preprint, 1995.
37. S. Zelditch, Reconstruction of singularities for solutions of Schrödinger's equation, Comm. Math. Phys. 90 (1983), 1-26.