Skip to main content
Log in

The spectrum of Jacobi matrices

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Akhiezer, N. I.: The classical moment problem. Edinburgh. Oliver and Boyd 1965

    Google Scholar 

  2. Flaschka, H.: The Toda lattice I. Phys. Rev., Sect. B9, 1924–1925 (1974)

    Google Scholar 

  3. Flaschka, H.: The Toda lattice II. Progr. Theor. Phys.51, 703–716 (1974)

    Google Scholar 

  4. Gantmacher, F. R., Krein, M. G.: Oszillationsmatrizen, Oszillation Kerne und kleine Schwingungen mechanischer Systeme. Berlin: Akad. Verlag 1960

    Google Scholar 

  5. Goldstein, H.: Classical mechanics. Reading: Addison Wesley 1959

    Google Scholar 

  6. Jacobi, C. G. L.: Gesammelte Werke. Bd. 7 supplement: Vorlesungen über Dynamik. Clebsch, A., Reimer, G. (Hrsg.). Berlin: Reimer 1884 (see 26, and 30. Vorlesung)

    Google Scholar 

  7. Kac, M., van Moerbeke, P.: On some periodic Toda lattice. Proc. Nat. Acad. Sci. USA72(4), 1627–1629 (1975)

    Google Scholar 

  8. Kac, M., van Moerbeke, P.: The solution of the periodic Toda lattice. Proc. Nat. Acad. Sci., USA72(8), 2879–2880 (1975)

    Google Scholar 

  9. Lax, P. D.: Integrals of non-linear equations of evolution and solitary waves. Comm. Pure. Appl. Math.21, 467–490 (1968)

    Google Scholar 

  10. McKean, H. P., van Moerbeke, P.: The spectrum of Hill's equation, Inventiones math.30, 217–274 (1975)

    Article  Google Scholar 

  11. Moser, J.: Finitely many mass points on the line under the influence of an exponential potential—An integrable system. Battelle Rencontres summer lectures. Lecture Notes in Math.

  12. Toda, M.: Wave propagation in anharmonic lattices. J. of Phys. Soc. of Japan23, 501–506(1967)

    Google Scholar 

  13. Whittaker, E. T.: A treatise on the analytical dynamics of particles and rigid bodies. New York: Dover 1904

    Google Scholar 

  14. Flaschka, H., McLaughlin, D. W.: Canonically conjugate variables for the Korteweg-de Vries equation and the Toda Lattice. Preprint

  15. Manakov, S. V.: Integration of discrete dynamical systems. Zhurnal Teor. Exp. Fiz.67, 543 (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Arne Beurling

This work was supported in part by NSF Grant MPS 74-00405 A 01 at Stanford University

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Moerbeke, P. The spectrum of Jacobi matrices. Invent Math 37, 45–81 (1976). https://doi.org/10.1007/BF01418827

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01418827

Keywords

Navigation