Fundamental solutions and eigenfunction expansions for Schrödinger operators. II. Eigenfunction expansions

Mathematische Zeitschrift - Tập 199 - Trang 1-13 - 1988
Arne Jensen1, Hitoshi Kitada2
1Mathematics Institute, Aarhus University, Århus C, Denmark
2Department of Mathematics, University of Tokyo, Tokyo, Japan

Tài liệu tham khảo

Combescure, M.: Spectral and scattering theory for a class of strongly oscillating potentials. Commun. Math. Phys.73, 43–62 (1980) Combescure, M.: Propagation and local-decay properties for long-range scattering of quantum three-body systems. Ann. Inst. H. Poincaré Sect. A42, 39–72 (1985) Combescure, M., Ginibre, J.: Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials. Ann. Inst. H. Poincaré Sect. A24, 17–29 (1976) Dollard, J.D., Friedman, C.N.: Existence of Møller wave operators forV(r)=λsin(μ α r )/r β. Ann. Phys.111, 251–266 (1978) Enss, V.: Asymptotic completeness for quantum mechanical potential scattering I. Commun. Math. Phys.61, 285–291 (1978) Enss, V.: Quantum scattering theory for two- and three-body systems with potentials of short and long range. In: Schrödinger Operators (Proceedings C.I.M.E. 1984), pp. 39–176. Lecture Notes in Math.1159. Berlin-Heidelberg-New York: Springer 1985 Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. 2nd Ed. Berlin-Heidelberg-New York: Springer 1983 Hörmander, L.: The analysis of linear partial differential operators IV. Berlin-Heidelberg-New York: Springer 1985 Kitada, H.: Fourier integral operators with weighted symbols and micro-local resolvent estimates. J. Math. Soc. Japan39, 455–476 (1987) Kitada, H.: Fundamental solutions and eigenfunction expansions for Schrödinger operators I. Fundamental solutions. Math. Z.198, 181–190 (1988) Kuroda, S.T.: Scattering theory for differential operators I & II. J. Math. Soc. Japan25, 75–104 and 222–234 (1973) Reed, M., Simon, B.: Methods of modern mathematical physics III. Scattering theory. New York-San Francisco-London: Academic Press 1979 White, D.: Long-range potential scattering by Enss's method in two Hilbert spaces. Trans. Am. Math. Soc.295, 1–33 (1986) White, D.: Existence of Møller wave operators in quantum scattering theory. University of Toledo, preprint (1985)