Generalized Fourier Transform for Schrödinger Operators with Potentials of Order Zero

Journal of Functional Analysis

Volumn 167, Issue 2, 1999, Pages 345-369

  Agmon, Shmuel ^a   Cruz Sampedro, Jaime ^b   Herbst, Ira ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007543072     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3432     Document Type: Article

References (19)

1. Agmon S. A representation theorem for solutions of the Helmholtz equation and resolvent estimates for the Laplacian. Analysis et cetera. 1990;Academic Press, San Diego. p. 39-76.
2. Agmon S. Lectures on Elliptic Boundary Value Problems. 1965;Van Nostrand, Princeton.
3. 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Progress in Mathematics. 135:1996;Birkhäuser, Basel.
4. Barles G. On eikonal equations associated with Schrödinger operators with non spherical radiation conditions. Comm. Partial Differential Equations. 12:1987;263-283.
5. Combes J. M., Thomas L. Asymptotic behaviour of eigenfunctions for multi-particle Schrödinger operators. Comm. Math. Phys. 34:1973;251-270.
6. Constantin P. Scattering theory for Schrödinger operators in a class of domains with non compact boundaries. J. Funct. Anal. 44:1981;87-119.
7. J. Cruz-Sampedro, Ph.D. Thesis, University of Virginia, May 1991.
8. Herbst I. Spectral and scattering theory for Schrödinger operators with potentials independent of x Amer. J. Math. 113:1991;509-565.
9. Herbst I., Skibsted E. Free channel Fourier transform in the long-range N-body problem. J. Anal. Math. 65:1995;297-332.
10. Hörmander L. The Analysis of Partial Differential Operators. 1983;Springer-Verlag, Berlin/New York.
11. Ikebe T., Isozaki H. A stationary approach to the existence and completeness of long-range wave operators. Integral Equations Operator Theory. 5:1982;18-49.
12. Jäger W. Das asymptotische Verhalten von Lösungen eines Typs von Differential-Gleichungen. Math. Z. 112:1969;26-36.
13. Jäger W. Zur Theorie der Schwingungsgleichung mit variablen Koeffizienten in Außengebieten. Math. Z. 102:1967;62-88.
14. Lions P. Generalized Solutions of Hamilton-Jacobi Equations. 1982;Pitman, London.
15. Mourre E. Absence of singular continuous spectrum for certain self-adjoint operators. Comm. Math. Phys. 78:1981;391-408.
16. Perry P., Sigal I., Simon B. Spectral analysis of N-body Schrödinger operators. Ann. of Math. 114:1981;519-567.
17. Reed M., Simon B. Methods of Modern Mathematical Physics. 1982;Academic Press, San Diego.
18. Reed M., Simon B. Methods of Modern Mathematical Physics. 1982;Academic Press, San Diego.
19. Saitō Y. Schrödinger operators with a non spherical radiation condition. Pacific J. Math. 126, 1987;331-359.