Skip to main content
Log in

Zhislin's theorem revisited

  • Published:
Journal d’Analyse Mathématique 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. S. Agmon,Lectures on Exponential Decay of Solutions of Second-order Elliptic Equations: Bounds on Eigenfunctions of N-body Schrödinger Operators, Mathematical Notes 29, Princeton University Press and the University of Tokyo Press, 1982.

  2. H. Cycon, R. Froese, W. Kirsch and B. Simon,Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer-Verlag, Berlin, 1987.

    MATH  Google Scholar 

  3. G. J. Etgen and R. T. Lewis,The oscillation of elliptic systems, Math. Nachr.94 (1980), 43–50.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. D. Evans and R. T. Lewis,N-Body Schrödinger operators with finitely many bound states, Trans. Am. Math. Soc.322 (1990), 593–626.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. D. Evans, R. T. Lewis and Y. Saitò,Some geometric spectral properties of N-Body Schrödinger operators, Arch. Rational Mech. Anal.113 (1991), 377–400.

    Article  MATH  Google Scholar 

  6. W. D. Evans, R. T. Lewis and Y. Saitò,Geometric spectral properties of N-Body Schrödinger operators Part II, Phil. Trans. R. Soc. Lond. A338 (1992), 113–144.

    Article  MATH  Google Scholar 

  7. T. Kato,On the existence of solutions of the helium wave equation, Trans. Am. Math. Soc.70 (1951), 212–218.

    Article  MATH  Google Scholar 

  8. T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1976.

    MATH  Google Scholar 

  9. M. B. Ruskai,Limits on stability of positive molecular ions, Letters in Math. Phys.18 (1989), 121–132.

    Article  MATH  MathSciNet  Google Scholar 

  10. I. M. Sigal,Geometric methods in the quantum many-body problem. Nonexistence of very negative ions, Comm. Math. Phys.85 (1982), 309–324.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Uchiyama,Finiteness of the number of discrete eigenvalues of the Schrödinger operator for a three particle system, Publ. Res. Inst. Math. Sci. Kyoto Univ.A5 (1969), 51–63.

    MathSciNet  Google Scholar 

  12. S. A. Vulgal'ter and G. M. Zhislin,Finiteness of the discreet spectrum of many-particle Hamiltonians in symmetric spaces, Theor. Math. Phys. (1977), 602–614.

  13. S. A. Vulgal'ter and G. M. Zhislin,On the finiteness of discreet spectrum in the n-particle problem, Reports in Math. Phys. (1984), 39–90.

  14. S. A. Vulgal'ter and G. M. Zhislin,On the spectrum of Schrödinger operators of multiparticle systems with short-range potentials Trans. Moscow Math. Soc. (1987), 97–114.

  15. D. R. Yafaev,The point spectrum in the quantum-mechanical problem of many particles, Funct. Anal. Appl.6 (1972), 349–350.

    Article  Google Scholar 

  16. D. R. Yafaev,On the theory of the discrete spectrum of the three-particle Schrödinger operator, Math. USSR Sbornik23 (1974), 535–559.

    Article  MATH  Google Scholar 

  17. G. M. Zhislin,Discussion of the spectrum of Schrödinger operator for systems of many particles, Tr. Mosk. Mat. Obs.9 (1960), 81–128.

    Google Scholar 

  18. G. M. Zhislin,Spectrum of differential operators of quantum-mechanical manyparticle systems in space of functions of a given symmetry, Izv. Akad. Nauk SSSR33 (1969), 559–616.

    Google Scholar 

  19. G. M. Zhislin,On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions, Theor. Math. Phys.7 (1971), 571–578.

    Article  Google Scholar 

  20. G. M. Zhislin,Finiteness of the discrete spectrum in the quantum N-particle problem, Theor. Math. Phys.21 (1974), 971–990.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Professor Shmuel Agmon

This author expresses gratitude for support received from the Mathematics Component of NSF EPSCoR in Alabama

This author was partly supported by the U.S. National Science Foundation grant no. DMS-8719027.

This author was partly supported by the Mathematics Component of NSF EPSCoR in Alabama and also partly supported by the U.S. National Science Foundation grant no. DMS-8719027 He wishes to express gratitude for support received from Sonderforschungsbereich 123, West Germany. In particular, he wishes to thank Professor Willi Jäger of the University of Heidelberg for his kind hospitality during the author's stay at the University of Heidelberg in June and July, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Evans, W.D., Lewis, R.T. & Saitò, Y. Zhislin's theorem revisited. J. Anal. Math. 58, 191–212 (1992). https://doi.org/10.1007/BF02790364

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790364

Keywords

Navigation