×

zbMATH — the first resource for mathematics

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
PDF BibTeX Cite
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
[4] Ikebe, T.: Spectral representation for Schrödinger operators with long-range potentials, II. Publ. RIMS Kyoto Univ.11 (1976), 551–558. · Zbl 0345.35032
[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
[9] Schwartz, J. T.: Non-linear Functional Analysis. New York-London-Paris, Gordon and Breach Science 1969. · Zbl 0203.14501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.