Skip to main content
SpringerLink
Log in

Spectral theory of partial differential operators

  • Survey Papers
  • Conference paper
  • First Online:
Spectral Theory and Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 448))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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. Aronszajn, N.: On a problem of Weyl in the theory of singular Sturm Liouville equations. Amer.J.Math. 79, 597–610 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  2. Birman, M.Sh.: Scattering problems for differential operators with constant coefficients. Functional Anal.Appl. 3, 167–180 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  3. Böcker, U.: Invarianz des wesentlichen Spektrums bei Schrödinger-operatoren. Math.Ann. 207, 349–352 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  4. Eckardt, K.-J.: Scattering Theory for Dirac Operators. Math.Z. (to appear).

    Google Scholar 

  5. Glazman, I.M.: Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators. Israel Program for Scientific Translations, Jerusalem 1965.

    MATH  Google Scholar 

  6. Gustafson, K. and J. Weidmann: On the essential spectrum. J.Math. Anal.Appl. 25, 121–127 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  7. Ikebe, T. and T. Kato: Uniqueness of the self-adjoint extension of singular elliptic differential operators. Arch.Rational Mech. Anal. 9, 77–92 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  8. Ikebe, T. and T. Tayoshi: Wave and Scattering Operators for Second Order Elliptic Operators in IR3. Publ.Res.Inst.Math.Sci., Kyoto University, Ser.A, 4, No.2, 483–496 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  9. Jörgens, K.: Wesentliche Selbstadjungiertheit singulärer elliptischer Differentialoperatoren zweiter Ordnung in C ∞o (G). Math. Scand. 15, 5–17 (1964).

    MathSciNet  MATH  Google Scholar 

  10. __: Perturbations of the Dirac Operator. Conf.Ordinary and Partial Diff.Equ., Dundee/Scotland 1972, Lecture Notes in Math. 280, 87–102 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  11. Jörgens,K. and J.Weidmann: Spectral Properties of Hamiltonian operators. Lecture Notes in Math. 313, 1973.

    Google Scholar 

  12. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Book  MATH  Google Scholar 

  13. __: Some results on potential scattering. Proceedings of the International Conference on Functional Analysis and Related Topics, 206–215, Tokyo: University of Tokyo Press 1969.

    Google Scholar 

  14. __: Schrödinger operators with singular potentials. Israel J. Math. 13, 135–148 (1972).

    Article  MathSciNet  Google Scholar 

  15. Kuroda, S.T.: On the existence and unitary property of the scattering operators. Nuovo Cimento 12, 431–454 (1959).

    Article  MATH  Google Scholar 

  16. __: Scattering theory for differential operators. I operator theory, II self-adjoint elliptic operators. J.Math.Soc. Japan 25, 75–104 and 222–234 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  17. Schechter, M.: Spectra of partial differential operators. Amsterdam-London: North-Holland Publ.Comp. 1971.

    MATH  Google Scholar 

  18. __: On the essential spectrum of an arbitrary operator I. J.Math. Anal.Appl. 13, 205–215 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  19. __: Scattering theory for second order elliptic operators. Preprint 1974.

    Google Scholar 

  20. Simader, Ch.: Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen. Preprint 1974 (to appear in Math. Zeitschr.)

    Google Scholar 

  21. Simon, B.: Essential self-adjointness of Schrödinger operators with positive potentials. Math.Ann. 201, 211–220 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  22. __: Schrödinger operators with singular magnetic vector potentials. Math.Z. 131, 361–370 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  23. __: Essential self-adjointness of Schrödinger operators with singular potentials. Arch.Rational Mech.Anal. 52, 44–48 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  24. Veselić, K. and J. Weidmann: Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren. Math.Z. 134, 255–274 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  25. __: Asymptotic estimates of wave functions and the existence of wave operators. J.Functional Analysis (to appear).

    Google Scholar 

  26. __: Scattering theory for a general class of differential operators. Proc.Conf.Spectral Theory and Asymptotics of Differential Equations, Scheveningen, September 1973.

    Google Scholar 

  27. Weidmann, J.: Zur Spektraltheorie von Sturm-Liouville-Operatoren. Math.Z. 98, 268–302 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  28. __: Perturbations of self-adjoint operators in L2(G) with applications to differential operators. Conf.Ordinary and Partial Diff.Equ. Dundee/Scotland 1974 (to appear in Lecture Notes in Math.)

    Google Scholar 

  29. Yosida, K.: Functional Analysis. Berlin-Heidelberg-New York: Springer 1966.

    MATH  Google Scholar 

Download references

Authors
  1. Joachim Weidmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

William N. Everitt

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Weidmann, J. (1975). Spectral theory of partial differential operators. In: Everitt, W.N. (eds) Spectral Theory and Differential Equations. Lecture Notes in Mathematics, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067081

Download citation

  • DOI: https://doi.org/10.1007/BFb0067081

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07150-1

  • Online ISBN: 978-3-540-37444-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation