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Spectre de l’équation de schrödinger, application a la stabilité de la matière [d’après J. Lebowitz, E. Lieb, B. Simon et W. Thirring]

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Bibliographie

  1. Th. AUBIN-Problèmes isopérimétriques et espaces de Sobolev, C.R. Acad. Sci. Paris, 280(1975), p. 279–281.

    Google Scholar 

  2. Th. AUBIN-Espaces de Sobolev sur les variétés riemanniennes, Bull. Sci. Math., 100(1976), p. 149–173.

    MathSciNet  MATH  Google Scholar 

  3. Th. AUBIN-Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journ. Math. Pures et Appl., 55(1976), p. 269–296.

    MathSciNet  MATH  Google Scholar 

  4. J.F. BARNES, H.J. BRASCAMP et E.H. LIEB-Lower bound for the ground state energy at the Schrödinger equation using the sharp form of Young’s inequality, dans [15], pages 83 à 90.

    Google Scholar 

  5. M.S. BIRMAN-Mat. Sbornik, 55(1961), p. 125–174 [Traduction anglaise: The spectrum of singular boundary value problems, Amer. Math. Soc. Translations, Series 2, 53(1966), p. 23–80.]

    MathSciNet  Google Scholar 

  6. G.A. BLISS-An integral inequality, Journ. London Math. Soc., 5(1930), p. 40–46.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. R. COURANT et D. HILBERT-Methods of mathematical Physics, volume 1, Interscience, 1953.

    Google Scholar 

  8. F.J. DYSON et A. LENARD-Stability of matter I: Journ. Math. Phys., 8(1967), p. 423–434, et II: ibid., 9(1968), p. 698–711.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. G.H. HARDY, J.E. LITTLEWOOD et G. POLYA-Inequalities, Cambridge University Press, deuxième édition, 1952.

    Google Scholar 

  10. V. GLASER, A. MARTIN, H. GROSSE et W.E. THIRRING-A family of optimal conditions for the absence of bound states in a potential, dans [15], pages 169 à 194.

    Google Scholar 

  11. T. KATO-Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., 70(1951), p. 195–211.

    MathSciNet  MATH  Google Scholar 

  12. E.H. LIEB-The stability of matter, Reviews of Modern Physics, 48(1976), p. 555–569.

    CrossRef  MathSciNet  Google Scholar 

  13. E.H. LIEB et J.L. LEBOWITZ-The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei, Adv. Math., 9(1972), p. 316–398.

    CrossRef  MathSciNet  Google Scholar 

  14. E.H. LIEB et W.E. THIRRING-Inequalities for the moments of eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, dans [15], pages 169 à 194.

    Google Scholar 

  15. E.H. LIEB, B. SIMON et A.S. WIGHTMAN (éditeurs)-Studies in Mathematical Physics (Essays in honor of Valentine Bargmann), Princeton University Press, 1976.

    Google Scholar 

  16. J. MILNOR-Morse theory, Annals of Math. Studies, vol. 51, Princeton University Press, 1963.

    Google Scholar 

  17. G.D. MOSTOW-Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. I.H.E.S., 34(1968), p. 53–104.

    MathSciNet  MATH  Google Scholar 

  18. G. ROSEN-Minimum value for c in the Sobolev inequality ‖Φ3‖ ≤ c ‖∇Φ‖3, S.I.A.M. Journ. Appl. Math., 21(1971), p. 30–32.

    CrossRef  MATH  Google Scholar 

  19. J. SCHWINGER-On the bound states of a given potential, Proc. Nat. Acad. Sci. U.S.A., 47(1961), p. 122–129.

    CrossRef  MathSciNet  Google Scholar 

  20. B. SIMON-On the number of bound states of two-body Schrödinger operators-a review, dans [15], paper 305 à 326.

    Google Scholar 

  21. B. SIMON-Quantum mechanics for hamiltonians defined by quadratic forms, Princeton University Press, 1971.

    Google Scholar 

  22. S. SOBOLEV-Sur un théorème d’Analyse Fonctionnelle, Mat. Sbornik, 46(1938), p. 471–496.

    Google Scholar 

  23. S. SOBOLEV-Sur les équations aux dérivées partielles hyperboliques non-linéaires, Edizioni Cremonese, Roma, 1961.

    Google Scholar 

  24. E. STEIN-Singular integrals and differentiability properties of functions, Princeton University Press, 1970.

    Google Scholar 

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© 1978 N. Bourbaki

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Cartier, P. (1978). Spectre de l’équation de schrödinger, application a la stabilité de la matière [d’après J. Lebowitz, E. Lieb, B. Simon et W. Thirring]. In: Séminaire Bourbaki vol. 1976/77 Exposés 489–506. Lecture Notes in Mathematics, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070756

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  • DOI: https://doi.org/10.1007/BFb0070756

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