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A stationary approach to the existence and completeness of long-range wave operators. (English) Zbl 0496.35069


MSC:

35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
47A40 Scattering theory of linear operators
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs

Citations:

Zbl 0319.35059
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Full Text: DOI

References:

[1] Hörmander, L.: The existence of wave operators in scattering theory. Math. Z.146 (1976), 68–91. · Zbl 0319.35059
[2] Ikebe, T. and Saito, Y.: Limiting absorption method and absolute continuity for the Schrödinger operator. J. Math. Kyoto Univ.12 (1972), 513–542. · Zbl 0257.35022
[3] Ikebe, T. and Isozaki, H.: Completeness of modified wave operators for long-range potentials. Publ. RIMS Kyoto Univ.15 (1979), 679–718. · Zbl 0432.35061 · doi:10.2977/prims/1195187871
[4] Ikebe, T.: Spectral representation for Schrödinger operators with long-range potentials, II. Publ. RIMS Kyoto Univ.11 (1976), 551–558. · Zbl 0345.35032 · doi:10.2977/prims/1195191477
[5] Isozaki, H.: Eikonal equations and spectral representations for long-range Schrödinger Hamiltonians. J. Math. Kyoto Univ.20 (1980), 243–261. · Zbl 0527.35022
[6] Kako,T.: Existence and equivalence of two types of long-range modified wave operators. J. Fac. Sci. Univ. Tokyo Sec. IA25 (1978), 133–147. · Zbl 0377.47009
[7] Kato, T.: Perturbation Theory for Linear Operators. 2nd Ed. Berlin-Heiderberg-New York, Springer Verlag 1976. · Zbl 0342.47009
[8] Kitada, H.: Scattering thoery for Schrödinger operators with long-range potentilas, II. J. Math. Soc. Japan30 (1978), 603–632. · Zbl 0388.35055 · doi:10.2969/jmsj/03040603
[9] Schwartz, J. T.: Non-linear Functional Analysis. New York-London-Paris, Gordon and Breach Science 1969. · Zbl 0203.14501
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