|
$L^p \to L^{p'}$ estimates for time-dependent Schrödinger operators
Authors:
J. L. Journé, A. Soffer and C. D. Sogge
Journal:
Bull. Amer. Math. Soc. 23 (1990), 519-524
MSC (1985):
Primary 35J10
MathSciNet review:
1035837
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
P.
Constantin and J.-C.
Saut, Local smoothing properties of
dispersive equations, J. Amer. Math. Soc.
1 (1988), no. 2,
413–439. MR
928265 (89d:35150), http://dx.doi.org/10.1090/S0894-0347-1988-0928265-0
- 2.
Arne
Jensen, Spectral properties of Schrödinger operators and
time-decay of the wave functions results in
𝐿²(𝑅^{𝑚}), 𝑚≥5, Duke Math. J.
47 (1980), no. 1, 57–80. MR 563367
(81e:35092)
- 3.
Arne
Jensen, Spectral properties of Schrödinger operators and
time-decay of the wave functions. Results in
𝐿²(𝑅⁴), J. Math. Anal. Appl.
101 (1984), no. 2, 397–422. MR 748579
(85j:35138), http://dx.doi.org/10.1016/0022-247X(84)90110-0
- 4.
Arne
Jensen and Tosio
Kato, Spectral properties of Schrödinger operators and
time-decay of the wave functions, Duke Math. J. 46
(1979), no. 3, 583–611. MR 544248
(81b:35079)
- 5.
Carlos
E. Kenig and Christopher
D. Sogge, A note on unique continuation for
Schrödinger’s operator, Proc. Amer.
Math. Soc. 103 (1988), no. 2, 543–546. MR 943081
(89i:35043), http://dx.doi.org/10.1090/S0002-9939-1988-0943081-3
- 6.
A. Melin, Intertwining methods in multi-dimensional scattering theory I, University of Lund and Lund Institute of Technology preprint series, 1987:13.
- 7.
Jeffrey
Rauch, Local decay of scattering solutions to
Schrödinger’s equation, Comm. Math. Phys.
61 (1978), no. 2, 149–168. MR 0495958
(58 #14590)
- 8.
Michael
Reed and Barry
Simon, Methods of modern mathematical physics. I, 2nd ed.,
Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980.
Functional analysis. MR 751959
(85e:46002)
- 9.
Per
Sjölin, Regularity of solutions to the Schrödinger
equation, Duke Math. J. 55 (1987), no. 3,
699–715. MR
904948 (88j:35026), http://dx.doi.org/10.1215/S0012-7094-87-05535-9
- 10.
A.
Soffer and M.
I. Weinstein, Multichannel nonlinear scattering theory for
nonintegrable equations, Integrable systems and applications
(Île d’Oléron, 1988), Lecture Notes in Phys.,
vol. 342, Springer, Berlin, 1989, pp. 312–327. MR 1034551
(90m:35189), http://dx.doi.org/10.1007/BFb0035679
- 11.
Walter
A. Strauss, Nonlinear scattering theory at low energy, J.
Funct. Anal. 41 (1981), no. 1, 110–133. MR 614228
(83b:47074a), http://dx.doi.org/10.1016/0022-1236(81)90063-X
- 12.
Robert
S. Strichartz, Restrictions of Fourier transforms to quadratic
surfaces and decay of solutions of wave equations, Duke Math. J.
44 (1977), no. 3, 705–714. MR 0512086
(58 #23577)
- 13.
Luis
Vega, Schrödinger equations: pointwise
convergence to the initial data, Proc. Amer.
Math. Soc. 102 (1988), no. 4, 874–878. MR 934859
(89d:35046), http://dx.doi.org/10.1090/S0002-9939-1988-0934859-0
- 1.
- P. Constantin and J. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 431-439. MR 928265
- 2.
- A. Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions results in L2(R), m ≥ 5, Duke Math. J. 47 (1980), 57-80. MR 563367
- 3.
- A. Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions results in L2(R4), J. Math. Anal. Appl. 101 (1984), 397-422. MR 748579
- 4.
- A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), 583-611. MR 544248
- 5.
- C. E. Kenig and C. D. Sogge, A note on unique continuation for Schrödinger's operator, Proc. Amer. Math. Soc. 103 (1988), 543-546. MR 943081
- 6.
- A. Melin, Intertwining methods in multi-dimensional scattering theory I, University of Lund and Lund Institute of Technology preprint series, 1987:13.
- 7.
- J. Rauch, Local decay of scattering solutions to Schrödinger's equation, Comm. Math. Phys. 61 (1978), 149-168. MR 495958
- 8.
- M. Reed and B. Simon, Methods of modern mathematical Physics, vol. III, Academic Press, New York, 1979. MR 751959
- 9.
- P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715. MR 904948
- 10.
- A. Soffer and M. I. Weinstein, Multichannel nonlinear scattering theory for nonintegral equations, Comm. Math. Phys. (to appear). MR 1034551
- 11.
- W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133; Sequel, 43(1981), 281-293. MR 614228
- 12.
- R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714. MR 512086
- 13.
- L. Vega, Schrödinger equations: Pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878. MR 934859
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1985):
35J10
Retrieve articles in all journals
with MSC (1985):
35J10
Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1990-15967-1
PII:
S 0273-0979(1990)15967-1
|
