References
[AH] Avron, J.E., Herbst, I.W.: Spectral and Scattering Theory for Schrödinger Operators Related to the Stark Effect. Commun. Math. Phys.52, 239–254 (1977)
[E] Eckardt, K.J.: Scattering theory for Dirac operators. Math. Z.139, 105–131 (1974)
[He] Herbst, I.W.: Unitary Equivalence of Stark Hamiltonians. Math. Z.155, 55–70 (1977)
[Gr] Graf, G.M.: Asymptotic Completeness forN-Body Short-Range Systems: A New Proof. Commun. Math. Phys.132, 73–101 (1990)
[H] Hörmander, L.: The Analysis of Linear Partial Differential Operators IV. Berlin Heidelberg New York: Springer 1985
[IK] Isozaki, H., Kitada, H.: Modified wave operators with time-independent modifiers. J. Fac. Sci., Univ. Tokyo, Sect. IA32, 77–104 (1985)
[JK] Jensen, A., Kitada, H.: Fundamental Solutions and Eigenfunction Expansions for Schrödinger Operators, II. Eigenfunction Expansions. Math. Z.199, 1–13 (1988)
[JY] Jensen, A., Yajima, K.: On the long range scattering for Stark Hamiltonians. J. Reine Angew. Math.420, 179–193 (1991)
[Ki] Kitada, H.: Fundamental Solutions and Eigenfunction Expansions for Schrödinger operators, III. Complex Potentials. Sci. Pap. Coll. Arts, Sci. Univ. Tokyo39, 109–123 (1989)
[Ko] Kodaira, K.: On ordinary differential equations of any even order and the corresponding eigenfunction expansions. Am. J. Math.72, 502–544 (1950)
[PSW] Poerschke, T., Stolz, G., Weidmann, J.: Expansions in Generalized Eigenfunctions of Selfadjoint Operators. Math. Z.202, 397–408 (1989)
[RS] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, III. Scattering Theory. New York: Academic Press 1979
[S1] Simon, B.: Phase Space Analysis of Simple Scattering Systems: Extensions of some Work of Enss. Duke Math. J.46, 119–168 (1979)
[S2] Simon, B.: Schrödinger Semigroups. Bull. Am. Math. Soc.7, 447–526 (1982)
[S3] Simon, B.: Trace Ideals and their applications. London: Cambridge University Press 1979
[or] Sigal, I.M., Soffer, A.: TheN-particle Scattering Problem: Asymptotic Completeness for Short-Range Systems. Ann. Math.126, 35–108 (1987)
[St1] Stolz, G.: Expansions in Generalized Eigenfunctions of Schrödinger Operators with Singular Potentials. In: Operator Theory: Advances and Applications, vol. 48, pp. 353–372, Basel: Birkhäuser 1990
[St2] Stolz, G.: Entwicklung nach verallgemeinerten Eigenfunktionen von Schrödingeroperatoren. Thesis, University of Frankfurt (1989)
[VW] Veselić, K., Weidmann, J.: Potential Scattering in a Homogeneous Electrostatic Field. Math. Z.156, 93–104 (1977)
[W1] Weidmann, J.: Linear Operators in Hilbert Spaces. (Grad. Texts Math., vol. 68) Berlin Heidelberg New York: Springer 1980
[W2] Weidmann, J.: Spectral Theory of Ordinary Differential Operators. (Lect Notes Math., vol. 1258) Berlin Heidelberg New York: Springer 1987
[We] Weyl, H.: Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann.68, 220–269 (1910)
[Wh] White, D.: Long-range potential scattering by Enss's method in two Hilbert spaces. Trans. Am. Math. Soc.295, 1–33 (1986)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Poerschke, T., Stolz, G. On eigenfunction expansions and scattering theory. Math Z 212, 337–357 (1993). https://doi.org/10.1007/BF02571662
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571662