Skip to main content

Sur le spectre de quelques opérateurs et les variétés de jacobi

Part of the Lecture Notes in Mathematics book series (LNM,volume 567)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. B. A. DUBROVIN, S. P. NOVIKOV-Periodic and conditionally periodic analogues of multisoliton solutions of the Korteweg-de Vries equation, Dokl. Akad. Nauk U.S.S.R., 6 (1974), 2131–2144.

    MathSciNet  Google Scholar 

  2. L. de BRANGES-Some Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, N. J., 1968.

    Google Scholar 

  3. L. FADDEEV and V. E. ZAKHAROV-Korteweg-de Vries equation: a completely integrable Hamiltonian system, Funkt. Anal. Priloz., 5 (1971), 18–27, Traduction dans Functional analysis and its application.

    MATH  Google Scholar 

  4. H. FLASCHKA-The Toda lattice, I, Phys. Rev. B 9, (1974), 1924–1925.

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. H. FLASCHKA-The Toda lattice, II, Progr. Theoretical Phys., 51 (1974), 703–716.

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. C. S. GARDNER, J. M. GREENE, M. D. KRUSKAL and R. M. MIURA-Method for solving the Korteweg-de Vries equation, Phys. Rev. letters, 19 (1967), 1095–1097.

    CrossRef  MATH  Google Scholar 

  7. C. S. GARDNER-Korteweg-de Vries equation and generalizations IV, The Kortewegde Vries equation as a Hamiltonian system, J. Math. Phys., 12 (1971), 1548–1551.

    CrossRef  MATH  Google Scholar 

  8. C. S. GARDNER, J. M. GREENE, M. D. KRUSKAL and R. M. MIURA-Korteweg-de Vries equation and generalizations, VI Methods for exact solutions, Comm. Pure Appl. Math., 27 (1974), 97–133.

    MATH  MathSciNet  Google Scholar 

  9. G. BORG-Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math. 78 (1945), 1–96.

    CrossRef  MathSciNet  Google Scholar 

  10. A. R. ITS, V. B. MATVEEV-The periodic Korteweg-de Vries equation, Funkt. Anal. i ego Pril., 9 (1975).

    Google Scholar 

  11. M. KAC, P. van MOERBEKE-Some probabilistic aspects of scattering theory, Compte-Rendus de la "Conf. on Functional Integr. and Appl.", 11, 4, Londres (1974), Oxford University Press.

    Google Scholar 

  12. M. KAC, P. van MOERBEKE-On some isospectral second order differential operators, Proc. Nat. Acad. Sci. USA, 71, 6 (1974), 2350–2351.

    CrossRef  MATH  Google Scholar 

  13. M. KAC, P. van MOERBEKE-On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices, Adv. in Math., 16, 2 (1975), 160–169.

    CrossRef  MATH  Google Scholar 

  14. M. KAC, P. van MOERBEKE-On some periodic Toda lattices, Proc. Nat. Acad. Sci., 72, 4 (1975), 1627–1629.

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. M. KAC, P. van MOERBEKE-The solution of the periodic Toda lattice, Proc. Nat. Acad. Sci., 72, 8 (1975), 2879–2880.

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. P. D. LAX-Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., 21 (1968), 467–490.

    MATH  MathSciNet  Google Scholar 

  17. P. D. LAX-Periodic solutions of the Korteweg-de Vries equation, Lectures in Appl. Math., 15 (1974), A.M.S. Providence R.I.

    Google Scholar 

  18. P. D. LAX-Periodic solutions of the Korteweg-de Vries equation, Comm. Pure Appl. Math., 28 (1975), 141–188.

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. H. P. McKEAN, P. van MOERBEKE-The spectrum of Hill’s equation (n < ∞), Inventiones Mathematicae, 30 (1975), 217–274.

    CrossRef  MATH  MathSciNet  Google Scholar 

  20. H. P. McKEAN, E. TRUBOWITZ-The spectrum of Hill’s equation …, Comm. Pure Applied Math., (1976), à paraître.

    Google Scholar 

  21. J. MOSER-Finitely many mass points on the line under the influence of an exponential potential, An integrable system, Battelle Rencontres (Seattle) Summer lectures, Springer-Verlag Lecture Notes in Physics, 1974.

    Google Scholar 

  22. J. MOSER-Three integrable Hamiltonian systems connected with isospectral deformations, Advances in Math., 15, 2 (1975), 197–220.

    CrossRef  Google Scholar 

  23. S. P. NOVIKOV-The periodic problem for the Korteweg-de Vries equation, Funkt. Anal. i ego Pril., 8 (1974), 54–66, Traduction en anglais dans Funct. Anal., (janv. 1975), 236–246.

    CrossRef  MATH  Google Scholar 

  24. P. van MOERBEKE-The spectrum of Jacobi matrices, Inventiones Math., 37(1976), 45–81.

    CrossRef  MATH  Google Scholar 

  25. V. I. ARNOLD et A. AVEZ-Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris, 1967.

    MATH  Google Scholar 

  26. M. ADLER-A new integrable system and a conjecture by Calogero, Bull. Amer. Math. Soc., (1976), à paraître.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 N. Bourbaki

About this paper

Cite this paper

McKean, H.P., van Moerbeke, P. (1977). Sur le spectre de quelques opérateurs et les variétés de jacobi. In: Séminaire Bourbaki vol. 1975/76 Exposés 471–488. Lecture Notes in Mathematics, vol 567. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0096061

Download citation

  • DOI: https://doi.org/10.1007/BFb0096061

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08064-0

  • Online ISBN: 978-3-540-37514-2

  • eBook Packages: Springer Book Archive