Fundamental solutions and eigenfunction expansions for Schrödinger operators I. Fundamental solutions

Mathematische Zeitschrift - Tập 198 - Trang 181-190 - 1988
Hitoshi Kitada1
1Department of Mathematics, University of Tokyo, Tokyo, Japan

Tài liệu tham khảo

Agmon, S.: Spectral properties of Schrödinger operators and scattering theory. Ann. Sc. Norm Super. Pisa, Cl. Sci., IV Ser.2, 151–218 (1975)

Agmon, S.: Some new results in spectral and scattering theory of differential operators onR n. Séminaire Goulaouic-Schwartz, Ecole Polytechnique, Palaiseau, 1978/79

Agmon, S.: Spectral theory of Schrödinger operators on Euclidean and on non-Euclidean spaces. Commun. Pure Appl. Math.39, S3-S16 (1986)

Calderón, A.P.: Vaillancourt, R., A class of bounded pseudodifferential operators. Proc. Natl. Acad. Sci. USA69, 1185–1187 (1972)

Fujiwara, D.: A construction of the fundamental solution for the Schrödinger equation, J. D'Analyse Math.35, 41–96 (1979)

Fujiwara, D.: Remarks on convergence of the Feynman path integrals. Duke Math. J.47, 559–600 (1980)

Ikebe, T.: Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory. Arch. Rational Mech. Anal.5, 1–34 (1960)

Ikebe, T.: Spectral representation for Schrödinger operators with long-range potentials. J. Funct. Anal.20, 158–177 (1975)

Jäger, W.: Ein gewöhnlicher Differential operator zweiter Ordnung für Funktionen mit Werten in einem Hilbertraum. Math. Z.113, 68–98 (1970)

Jensen, A.: Commutator methods and a smoothing property of the Schrödinger evolution group. Math. Z.191, 53–59 (1986)

Jensen, A., Kitada, H.: Fundamental solutions and eigenfunction expansions for Schrödinger operators, II. Eigenfunction expansions. Preprint (1987)

Kato, T., Kuroda, S.T.: Theory of simple scattering and eigenfunction expansions. In: Functional analysis and related fields, pp. 99–131. Berlin-Heidelberg-New York: Springer 1970

Kato, T., Kuroda, S.T.: The abstract theory of scattering. Rocky Mt. J. Math.1, 127–171 (1971)

Kitada, H., Kumano-go, H.: A family of Fourier integral operators and the fundamental solution for a Schrödinger equation. Osaka J. Math.18, 291–360 (1981)

Kumano-go, H.: Pseudo differential operators. Cambridge-Massachusets-London, England: The MIT Press 1983

Kuroda, S.T.: Perturbation of eigenfunction expansions. Proc. Natl. Acad. Sci. USA57, 1213–1217 (1967)

Kuroda, S.T.: “Spectral theory II” in Monographs for Elementary Math. edited by K. Kodaira. Tokyo: Iwanami-Shoten 1979 (in Japanese)

Saitō, Y.: Spectral representations for Schrödinger operators with long-range potentials. Lecture Notes in Math.727, Berlin-Heidelberg-New York: Springer 1979

Sigal, I.M., Soffer, A.:N-particle scattering problem: Asymptotic completeness for short-range systems. Ann. Math.126, 35–108 (1987)

Simon, B.: Schrödinger semigroups. Bull. Am. Math. Soc.7, 447–526 (1982)

Zelditch, S.: Reconstruction of singularities for solutions of Schrödinger's equation. Commun. Math. Phys.90, 1–26 (1983)

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Mathematische Zeitschrift

Tập 198

181-190

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