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Trace distributions associated to the Schrödinger operator

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References

  1. S. Agmon and Y. Kannai,On the asymptotic behaviour of spectral functions and resolvent kernels of elliptic operators, Isr. J. Math.5 (1967), 1–30.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Agmon,Lower bounds for solutions of the Schrödinger equations, J. Analyse Math.23 (1970), 1–25.

    Article  MATH  MathSciNet  Google Scholar 

  3. M.S. Birman and M.G. Krein,On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR144 (1962), 475–478. Also in Soviet Math. Dokl.3 (1962), 740–744.

    MathSciNet  Google Scholar 

  4. Y. Colin de Verdier,Une formule de trace pour l’opérateur de Schrödinger dans R 3, Ann. Sci. Éc. Norm Sup.14 (1981), 27–39.

    Google Scholar 

  5. L. Guillopé,Asymptotique de la phase de diffusion pour l’opérateur de Schrödinger dans R n, Séminaire sur les équations dérivées partielles 1984–1985, no. V, École Polytechnique, 1985.

  6. L. Hörmander,The Analysis of Linear Partial Differential Operators I–IV, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983.

    Google Scholar 

  7. L. Hörmander,On the asymptotic distribution of the eigenvalues of pseudodifferential operators in R n, Ark. Mat.17 (1979), 297–313.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Hörmander,The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359–443.

    Article  MATH  Google Scholar 

  9. A. Melin,On functions of the Schrödinger operator and a trace formula, inIntegral Equations and Inverse Problems, Pitman Research Notes in Mathematics Series 235 (1991), 154–174.

  10. P. Perry, I.M. Sigal and B. Simon,Spectral analysis of N-body Schrödinger operators, Ann. of Math.114 (1981), 519–567.

    Article  MathSciNet  Google Scholar 

  11. D. Robert,Asymptotique de la phase de diffusion a haute énergie pour des perturbations du Laplacien, Séminaire sur les équations dérivées partielles 1988–1989, no. XVII, École Polytechnique, 1989.

  12. D. Robert,Asymptotique a grande énergie de la phase de diffusion pour un potential, École Polytechnique, 1989, preprint.

  13. I.M. Sigal,On long range scattering, Duke Math. J.60 (1990), 473–496.

    Article  MATH  MathSciNet  Google Scholar 

  14. B. Simon,Trace ideals and their applications, London Math. Soc. Lecture Notes Series 35, Cambridge University Press, 1979.

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Dedicated to Professor Shmuel Agmon

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Melin, A. Trace distributions associated to the Schrödinger operator. J. Anal. Math. 59, 133–160 (1992). https://doi.org/10.1007/BF02790222

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