Skip to main content
SpringerLink
Log in

The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

The symmetry of singular Hamiltonian differential operators is proved under the standard "definiteness condition", which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dunford, N., Schwartz, J. T.: Linear operators (II), Wiley-interscience, New York, 1963

  2. Krall, A. M.: M(λ) theory for singular Hamiltonian systems with one singular point. SIAM J. Math. Anal., 20, 664–700 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Krall, A. M.: M(λ) theory for singular Hamiltonian systems with two singular points. SIAM J. Math. Anal., 20, 701–715 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hinton, D. B., Shaw, J. K.: On the spectrum of a singular Hamiltonian system (I). Ques. Math., 5, 29–81 (1982)

    MATH  MathSciNet  Google Scholar 

  5. Hinton, D. B., Shaw, J. K.: On the spectrum of a singular Hamiltonian system (II). Ques. Math., 10, 1–48 (1986)

    MATH  MathSciNet  Google Scholar 

  6. Lesch, M., Malamud, M.: On the deficiency indices and self-adjointness of symmetric Hamiltonian systems. J. Di.. Equ., 189, 556–615 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Atkinson, F. V.: Discrete and continuous Boundary problems, Academic Press, New York, 1964

  8. Hinton, D. B., Schneider, A.: On the Tichmarsh–Weyl coefficients for singular S-Hamiltonian systems (I). Math. Nachr., 163, 323–342 (1993)

    MATH  MathSciNet  Google Scholar 

  9. Hinton, D. B., Schneider, A.: On the Titchmarsh–Weyl Coefficients for Singular S-Heritian Systems (II). Math. Nachr., 185, 67–84 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mcleod, J. B.: The number of integrable-square solutions of ordinary differential equations. Quart J. Math. Oxford (2), 17, 285–290 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  11. Walker, P. W.: A vector-matrix formulation for formally symmetric ordinary di.erential equations with application to solutions of integrable square. J. London Math. Soc., 9, 151–159 (1974)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China

    Jian Gang Qi

Authors
  1. Jian Gang Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Gang Qi.

Additional information

This work is supported by Ningbo Doctoral Science Foundation (No. 2004A620018)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qi, J.G. The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices. Acta Math Sinica 22, 41–50 (2006). https://doi.org/10.1007/s10114-005-0535-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0535-3

Keywords

MR (2000) Subject Classification

Search

Navigation