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Mapping properties of wave and scattering operators for two-body Schrödinger operators

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Abstract

The modified wave and scattering operators are shown to be bounded between weighted L 2-spaces for two-body Schrödinger operators with long range potentials.

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References

  1. Amrein, W. O., Cibils, B., and Sinha, K. B., Configuration space properties of the S-matrix and time delay in potential scattering. Ann. Inst. H. Poincaré, Phys. Théor. 47, 367–382 (1987).

    Google Scholar 

  2. Cycon, H. L., Froese, R. G., Kirsch, W., and Simon, B., Schrödinger Operators, Springer-Verlag, Heidelberg, 1987.

    Google Scholar 

  3. Herbst, I. and Skibsted, E., Time-dependent approach to radiation conditions, Duke Math. J. 64, 119–147 (1991).

    Google Scholar 

  4. Isozaki, H., Differentiability of generalized Fourier transforms associated with Schrödinger operators, J. Math. Kyoto Univ. 25, 789–806 (1985).

    Google Scholar 

  5. Isozaki, H., Decay rates of scattering states for Schrödinger operators, J. Math. Kyoto Univ. 26, 595–603 (1986).

    Google Scholar 

  6. Isozaki, H. and Kitada, H., Modified wave operators with time-independent modifiers, J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 32, 77–104 (1985).

    Google Scholar 

  7. Isozaki, H. and Kitada, H., Scattering matrices for two-body Schrödinger operators, Sci. Papers College Arts Sci. Univ. Tokyo 35, 81–107 (1985).

    Google Scholar 

  8. Isozaki, H. and Kitada, H., A remark on the micro-local resolvent estimates for two body Schrödinger operators, Publ. RIMS, Kyoto Univ. 21, 889–910 (1985).

    Google Scholar 

  9. Jensen, A. and Kato, T., Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46, 583–611 (1979).

    Google Scholar 

  10. Jensen, A., Propagation estimates for Schrödinger type operators, Trans. Amer. Math. Soc. 291, 129–144 (1985).

    Google Scholar 

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

    Google Scholar 

  12. Lions, J. L. and Magenes, E., Problèmes aux limites non homogenes et applications, Dunod, Paris, 1968.

    Google Scholar 

  13. Nakamura, S., Time-delay and Lavine's formula, Comm. Math. Phys. 109, 397–415 (1987).

    Google Scholar 

  14. Perry, P. A., Propagation of states in dilation analytic potentials and asymptotic completeness, Comm. Math. Phys. 81, 243–259 (1981).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220, Aalborg Ø, Denmark

    Arne Jensen

  2. Department of Pure and Applied Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, 153, Tokyo, Japan

    Shu Nakamura

Authors
  1. Arne Jensen
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  2. Shu Nakamura
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Jensen, A., Nakamura, S. Mapping properties of wave and scattering operators for two-body Schrödinger operators. Lett Math Phys 24, 295–305 (1992). https://doi.org/10.1007/BF00420489

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