Wave and scattering operators for an evolving system d/dt-iA(t)

Atsushi INOUE

doi:10.2969/jmsj/02640608

Wave and scattering operators for an evolving system d/dt-iA(t)

Atsushi INOUE

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1974 Volume 26 Issue 4 Pages 608-624

DOI https://doi.org/10.2969/jmsj/02640608

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Published: 1974 Received: March 05, 1973 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Atsushi INOUE¹⁾
Right : Atsushi INOUE¹⁾²⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Mathematics Faculty of Science University of Tokyo

Right :
1) Department of Mathematics Faculty of Science University of Tokyo
2) Department of Mathematics Faculty of Science Hirosima University

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. D. Dollard, Adiabatic switching in the Schrödinger theory of scattering, J. Math. Phys., 7 (1966), 802-810.
2) M. Ikawa, Mixed problems for hyperbolic equations of second order, J. Math. Soc. Japan, 20 (1968), 580-608.
3) A. Inoue, Sur _??_u+u³=f dans un domaine non-cylindrique, à paraitre, J. Math. Anal. Appl., 46 (1974), 777-819.
3)' A. Inoue, Sur ??_u+u³=f dans un domaine non-cylindrique, C.R. Acad. Sci. Paris, 275 (1972), 659-662.
4) A. Inoue, Sur l'opérateur d'onde et de scattering pour ??_ dans un domaine non- cylindrique, à paraître.
5) A. Inoue, L'opérateur d'onde et de diffusion pour un système evolutif d/dt+iA(t), C.R. Acad. Sci. Paris, 275 (1972), 1323-1325.
6) T. Kato, Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan, 55 (1953), 208-234.
7) T. Kato, Perturbation theory for linear operators, Springer, Berlin-Heidelberg- New York, 1966.
8) P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, New York- London, 1967.
9) S. Mizohata, Le problème de Cauchy pour les équations paraboliques, J. Math. Soc. Japan, 8 (1956), 269-299.
10) S. Mizohata, Theory of partial differential equations, Iwanami, Tokyo, 1965 (in Japanese).
11) I. E. Segal, Dispersion for non-linear relativistic equations, II, Ann. Sci. École Norm. Sup., 1 (1968), 459-497.
12) W. A. Strauss, Decay and asymptotics for ??_u=F(u), J. Functional Analysis. 2 (1968), 409-457.
13) K. Yosida, Fundtional Analysis, Springer, Berlin-Heidelberg-New York, 1965.

Right : [1] J. D. Dollard, Adiabatic switching in the Schrödinger theory of scattering, J. Math. Phys., 7 (1966), 802-810.
[2] M. Ikawa, Mixed problems for hyperbolic equations of second order, J. Math. Soc. Japan, 20 (1968), 580-608.
[3] A. Inoue, Sur _??_u+u³=f dans un domaine non-cylindrique, à paraître, J. Math. Anal. Appl., 46 (1974), 777-819.
[3]' A. Inoue, Sur _??_u+u³=f dans un domaine non-cylindrique, C. R. Acad. Sci. Paris, 275 (1972), 659-662.
[4] A. Inoue, Sur l'opérateur d'onde et de scattering pour _??_ dans un domaine noncylindrique, à paraître.
[5] A. Inoue, L'opérateur d'onde et de diffusion pour un système evolutif d/dt+iA(t), C. R. Acad. Sci. Paris, 275 (1972), 1323-1325.
[6] T. Kato, Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan, 55 (1953), 208-234.
[7] T. Kato, Perturbation theory for linear operators, Springer, Berlin-Heidelberg-New York, 1966.
[8] P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, New York-London, 1967.
[9] S. Mizohata, Le problème de Cauchy pour les équations paraboliques, J. Math. Soc. Japan, 8 (1956), 269-299.
[10] S. Mizohata, Theory of partial differential equations, Iwanami, Tokyo, 1965 (in Japanese).
[11] I. E. Segal, Dispersion for non-linear relativistic equations, II, Ann. Sci. École Norm. Sup., 1 (1968), 459-497.
[12] W. A. Strauss, Decay and asymptotics for _??_u=F(u), J. Functional Analysis, 2 (1968), 409-457.
[13] K. Yosida, Fundtional Analysis, Springer, Berlin-Heidelberg-New York, 1965.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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