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On the long-range stationary wave operator. (English) Zbl 0435.47011


MSC:

47A40 Scattering theory of linear operators
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References:

[1] Alsholm, P. and Kalo, T., Scattering with long-range potentials, Proc. Sympo. Pure Math., 23, 393-399, American Mathematical Society, Providence, R. I., (1973). · Zbl 0263.47008
[2] Alsholm, P., Wave operators for long-range scattering, Thesis, U. C. Berkeley, (1972). · Zbl 0359.47006 · doi:10.1016/0022-247X(77)90081-6
[3] Ikebe, T., Eigenfunction expansions associated with the Schrodinger operators and their applications to scattering theory, Arch. Rational Mech. Anal., 5 (1960), 1-34. · Zbl 0145.36902 · doi:10.1007/BF00252896
[4] Ikebe, T., Spectral representations for Schrodinger operators with long-range po- tentials, J. Functional Anal., 20 (1975), 158-177. · Zbl 0315.35067 · doi:10.1016/0022-1236(75)90048-8
[5] Ikebe, T., Spectral representations for Schrodinger operators with long-range poten- tials,-Perturbation by short-range potentials-, Publ. RIMS, Kyoto Univ., 11(1976), 551-558. · Zbl 0345.35032 · doi:10.2977/prims/1195191477
[6] Ikebe, T., Wave operators and spectral representations, (a lecture given at the Symposium at Katata on Partial Differential Equations, October 1972).
[7] Ikebe, T. and SaitS, Y., Limiting absorption method and absolute continuity for the Schrodinger operator, J. Math. Kyoto Univ., 1 (1972), 513-542. · Zbl 0257.35022
[8] Kato, T. and Kuroda, S. T., Theory of simple scattering and eigenfunction expan- sions, Functional analysis and related fields, Springer, 1970, 99-131. · Zbl 0224.47004
[9] Kato, T. and Kuroda, S. T., Abstract theory of scattering, Rocky Mt. J. Math., 1 (1971), 127-171. · Zbl 0241.47005 · doi:10.1216/RMJ-1971-1-1-127
[10] Pinchuk, G., Abstract time-independent wave operator theory for long-range poten- tials, (to appear).
[11] Saito, Y., On the asymptotic behavior of the solutions of the Schrodinger equation (-A+Q(y-K*W=F, (to appear. · Zbl 0356.35019
[12] Saito, Y., Eigenfunction expansions for the Schrodinger operators with long-range potentials Q(;y)=O(|;y|-e) £>0, (to appear.
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