Skip to main content

The Spectral Resolution for Linear Hamiltonian Systems with One Singular Point

  • Chapter
Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 133))

  • 487 Accesses

Abstract

We have reached an interesting point. The next goal is to find out exactly what the abstract spectral resolution, derived for arbitrary self-adjoint operators in a Hilbert space, looks like when applied to the self-adjoint linear Hamiltonian systems of Hinton and Shaw. Remarkably we can find detailed formulas for the spectral measure and the Hilbert space it generates, far more than is possible for the setting employed by Niessen.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. V. Atkinson, Discrete and Continuous Boundary Value Problems, Academic Press, New York, 1964.

    Google Scholar 

  2. F. Brauer, Spectral theory for linear systems of differential equations, Pacific J. Math. 10 (1960), 17–34.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.

    MATH  Google Scholar 

  4. D. B. Hinton and J. K. Shaw, Titchmarsh-Weyl theory for Hamiltonian Systems, Spectral Theory of Differential Operations, ed. I. W. Knowles and R. T. Lewis, North Holland.

    Google Scholar 

  5. J. K. Shaw —, On the spectrum of a singular Hamiltonian system, Quaes. Math. 5 (1982), 29–81.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. K. Shaw —, Well-posed boundary value problems for Hamiltonian systems of limit point or limit circle type, Lecture Notes on Mathematics, Vol. 964, Springer-Verlag, Berlin, 1982, 614–631.

    Google Scholar 

  7. J. K. Shaw —, Parameterization of the M (λ) function for a Hamiltonian system of limit circle type, Proc. Roy. Soc. Edinburgh 93 (1983), 349–360.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. M. Krall, Applied Analysis, D. Reidel, Dordrecht, Netherlands, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Basel AG

About this chapter

Cite this chapter

Krall, A.M. (2002). The Spectral Resolution for Linear Hamiltonian Systems with One Singular Point. In: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Operator Theory: Advances and Applications, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8155-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8155-5_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9459-3

  • Online ISBN: 978-3-0348-8155-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics