Scattering theory for differential operators, I, operator theory

S. T. KURODA

doi:10.2969/jmsj/02510075

S. T. KURODA

著者情報

ジャーナルフリー

1973 年 25 巻 1 号 p. 75-104

DOI https://doi.org/10.2969/jmsj/02510075

詳細

Published: 1973 Received: 1971/12/21 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Agmon, Spectral properties of Schrödinger operators, Actes, Congrès intern. Math., 1970, Tome 2, 679-683.
2) M. S. Birman, Scattering problems for differential operators by the perturbation of spaces, Izv. Akad. Nauk USSR, 35 (1971), 440-455.
3) C. Goldstein, Perturbation of non-selfadjoint operators, I, Arch. Rational Mech. Anal., 37 (1970), 268-296.
4) J. S. Howland, Banach space techniques in the perturbation theory of self-adjoint operators with continuous spectra, J. Math. Anal. Appl., 20 (1967), 22-47.
5) T. Ikebe, Eigenfunction expansions associated with the Schroedinger operators, and their applications to scattering theory, Arch. Rational Mech. Anal., 5 (1960), 1-34.
6) T. Ikebe, On the eigenfunction expansion connected with the exterior problem for the Schrödinger equation, Japan. J. Math., 36 (1967), 33-55.
7) T. Kato, Growth properties of solutions of the reduced wave equation with a variable coefficient, Comm. Pure Appl. Math., 12 (1959), 403-425.
8) T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1966), 258-279.
9) T. Kato, Some results on potential scattering, Proc. Intern. Conf. Functional Anal. and Related Topics, Tokyo, 1969, Tokyo Univ. Press, 1970, 206-215.
10) T. Kato, Scattering theory and perturbation of continuous spectra, Actes Congrès intern. Math., 1970, Tome 1, 135-140.
11) T. Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields, Springer-Verlag, Berlin, Heidelberg, and New York, 1970, 99-131.
12) S. T. Kuroda, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. Analyse Math., 20 (1967), 57-117.
13) S. T. Kuroda, Some remarks on scattering for Schrödinger operators, J. Fac. Sci. Univ. Tokyo Sect. IA, 17 (1970), 315-329.
14) S. T. Kuroda, Spectral representations and the scattering theory for Schrödinger operators, Actes, Congrès intern. Math., 1970, Tome 2, 441-445.
15) S. T. Kuroda, Scattering theory for differential operators, II, self-adjoint elliptic operators, J. Math. Soc. Japan, 25(2) (1973).
16) P. Rejto, On partly gentle perturbations, I, J. Math. Anal. Appl., 17 (1967), 453-462.
17) N. Shenk and D. Thoe, Outgoing solutions of (-Δ+q-k²)u=f in an exterior domain, J. Math. Anal. Appl., 31 (1970), 81-116.

Right : [1] S. Agmon, Spectral properties of Schrödinger operators, Actes, Congrès intern. Math., 1970, Tome 2, 679-683.
[2] M. S. Birman, Scattering problems for differential operators by the perturbation of spaces, Izv. Akad. Nauk USSR, 35 (1971), 440-455.
[3] C. Goldstein, Perturbation of non-selfadjoint operators, I, Arch. Rational Mech. Anal., 37 (1970), 268-296.
[4] J. S. Howland, Banach space techniques in the perturbation theory of self-adjoint operators with continuous spectra, J. Math. Anal. Appl., 20 (1967), 22-47.
[5] T. Ikebe, Eigenfunction expansions associated with the Schroedinger operators, and their applications to scattering theory, Arch. Rational Mech. Anal., 5 (1960), 1-34.
[6] T. Ikebe, On the eigenfunction expansion connected with the exterior problem for the Schrödinger equation, Japan. J. Math., 36 (1967), 33-55.
[7] T. Kato, Growth properties of solutions of the reduced wave equation with a variable coefficient, Comm. Pure Appl. Math., 12 (1959), 403-425.
[8] T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1966), 258-279.
[9] T. Kato, Some results on potential scattering, Proc. Intern. Conf. Functional Anal. and Related Topics, Tokyo, 1969, Tokyo Univ. Press, 1970, 206-215.
[10] T. Kato, Scattering theory and perturbation of continuous spectra, Actes Congrès intern. Math., 1970, Tome 1, 135-140.
[11] T. Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields, Springer-Verlag, Berlin, Heidelberg, and New York, 1970, 99-131.
[12] S. T. Kuroda, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. Analyse Math., 20 (1967), 57-117.
[13] S. T. Kuroda, Some remarks on scattering for Schrödinger operators, J. Fac. Sci. Univ. Tokyo Sect. IA, 17 (1970), 315-329.
[14] S. T. Kuroda, Spectral representations and the scattering theory for Schrödinger operators, Actes, Congrès intern. Math., 1970, Tome 2, 441-445.
[15] S. T. Kuroda, Scattering theory for differential operators, II, self-adjoint elliptic operators, J. Math. Soc. Japan, 25 (2) (1973).
[16] P. Rejto, On partly gentle perturbations, I, J. Math. Anal. Appl., 17 (1967), 453-462.
[17] N. Shenk and D. Thoe, Outgoing solutions of (-Δ+q-k²)u=f in an exterior domain, J. Math. Anal. Appl., 31 (1970), 81-116.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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