Perturbations of the Wigner-Von Neumann potential leaving the embedded eigenvalue fixed

Annales Henri Poincare

Volumn 3, Issue 2, 2002, Pages 331-345

  Cruz Sampedro, J ^a   Herbst, I ^b   Martinez Avendano R ^c  

^a Área Académica de Química Instituto de Ciencias Básicas e Ingeniería Ciudad Del Conocimiento   (Mexico)

^b University of Virginia   (United States)

^c MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036435201     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-002-8619-4     Document Type: Article

References (30)

1. S. Agmon, On Perturbation of Embedded Eigenvalues, Partial Differential Equations and Mathematical Physics (Copenhagen, 1995; Lund, 1995), 1-14 Progr. Nonlinear Differential Equations Appl., 21, Birkhäuser Boston, Boston, MA, 1996.
2. S. Agmon, I. Herbst and E. Skibsted, Perturbations of Embedded Eigenvalues in the Generalized N-body Problem, Comm. Math. Phys. 122, 411-438 (1989).
3. M. Arai and J. Uchiyama, On the von Neumann and Wigner Potentials, J. Diff. Eq. 157 2, 348-372 (1999).
4. F. Atkinson, The Asymptotic Solutions of Second Order Differential Equations, Ann. Mat. Pura Appl. 37, 347-378 (1954).
5. E. Balslev and A. Venkov, Selberg's Eigenvalue Conjecture and the Siegel Zeros, Aarhus University preprint, 1998.
6. R. Carmona, Regularity Properties of Schrödinger and Dirichlet Semigroups, J. Funct. Anal. 33, 259-296 (1979).
7. J.S. Cassell, The Asymptotic Integration of some Oscillatory Differential Equations, Quart. J. Math. Oxford (2), 33, 281-296 (1982).
8. E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955.
9. Y. Colin de Verdiere, Pseudo-Laplaciens I, Ann. Inst. Fourier, Grenoble, 32, 3, 275-286 (1982).
10. Y. Colin de Verdiere, Pseudo-Laplaciens II, Ann. Inst. Fourier, Grenoble, 33, 2, 87-113 (1983).
11. J. Cruz and R. Martínez, Perturbations of the Wigner-von Neumann Potential, Memorias del XXVII Congreso Nacional, Soc. Mat. Mex., Aport. Matem. 16, 1995.
12. 1 Analyticity, J. London Math. Soc. (2) 52, 1, 177-184 (1995).
13. J. Dollard and C. Friedman, Product Integrals and the Schrödinger Equation, J. Math. Phys. 18, 1598-1607 (1977).
14. M. Eastham and H. Kalf, Schrödinger-type Operators with Continuous Spectra, Pitman Advanced Publishing Program, 1982.
15. W. Harris and D.A. Lutz, A Unified Theory of Asymptotic Integration, J. Math. Anal. Appl. 57, 3, 571-586 (1977).
16. ν) is p-Independent, Comm. Math. Phys. 104, 243-250 (1986).
17. p-Spectrum of Schrödinger Operators, J. Math. Anal. Appl. 121, 138-159 (1987).
18. N), Transactions of the American Mathematical Society, 236, 325-360 (1978).
19. D.B. Hinton, M. Klaus and K. Shaw, Embedded Half Bound States for Potentials of Wigner-von Neumann Type, Proc. London Math. Soc. (3) 62, 3, 607-646 (1991).
20. R. Phillips and P. Sarnak, Automorphic Spectrum and Fermi's Golden Rule, Journal D'analyse Mathématique, Vol. 59 (1992).
21. [21] J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Academic Press Inc., 1978.
22. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I-IV, Academic Press Inc., 1978.
23. P. Rejto and M. Taboada, A Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann-Wigner Potentials II. The Proof, J. Math. Anal. Appl. 208, 2, 311-336 (1997).
24. L. Royden, Real Analysis, Macmillan Publishing Co., 1968, Second Edition.
25. B. Simon, Resonances in n-body Quantum Systems with Dilation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory, Ann. of Math. 97, 247-274 (1973).
26. B. Simon, Schrödinger Semigroups, Bulletin (New Series) of the AMS, 7, 3, 447-526, (1982).
27. M. Taylor, Partial Differential Equations I, Applied Math Sciences 115, Springer, 1996.
28. J. Voigt, Absorption Semigroups, their Generators, and Schrödinger Semigroups, J. Funct. Anal. 67, 167-206 (1986).
29. J. Von Neumann and E.P. Wigner, Über Merkwürdige Diskrete Eigenwerte Z. Phys., 30, 465-467 (1929).
30. R. Weder, The Unified Approach to Spectral Analysis, Comm. Math. Phys. 60, 291-299 (1978).