Skip to main content
Log in

An abstract stationary approach to perturbation of continuous spectra and scattering theory

  • 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.

Institutional subscriptions

References

  1. Asano, K., Notes on Hilbert transforms of vector valued functions in the complex plane and their boundary values, to appear.

  2. Birman, M. Š., Existence conditions for wave operators,Izv. Akad. Nauk SSSR Ser. Mat.27 (1963), 883–906 (Russian)

    MATH  MathSciNet  Google Scholar 

  3. Birman, M. Š., A local criterion for the existence of wave operators,Dokl. Akad. Nauk SSSR 159 (1964), 485–488=Soviet Math. Dokl. 5 (1964), 1505-1509.

    MathSciNet  Google Scholar 

  4. Birman, M. Š. and S. B. Entina, A stationary approach in the abstract theory of scattering,Dokl. Akad. Nauk SSSR 155 (1964), 506–508=Soviet Math. Dokl. 5 (1965), 432–435.

    MathSciNet  Google Scholar 

  5. de Branges, L., Perturbations of self-adjoint transformations,Amer. J. Math. 84 (1962), 543–560.

    Article  MATH  MathSciNet  Google Scholar 

  6. Dunford, N. and B. J. Pettis, Linear operators on summable functions,Trans. Amer. Math. Soc. 47 (1940), 323–392.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dunford, N. and J. T. Schwartz, Linear Operators, Part I, Part II, Interscience, New York, 1958 and 1963.

    Google Scholar 

  8. Faddeev, L. D., About Friedrichs' model in the theory of perturbations of continuous spectra,Trudy Mat. Inst. Steklov 73 (1964), 292–313 (Russian).

    MATH  MathSciNet  Google Scholar 

  9. Friedrichs, K. O., Perturbation of spectra in Hilbert space,Lect. Appl. Math. vol III, Amer. Math. Soc., Providence, 1965.

    MATH  Google Scholar 

  10. Ikebe, T., Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory.Arch. Rat. Mech. Anal.,5 (1960), 1–34.

    Article  MATH  MathSciNet  Google Scholar 

  11. Kato, T., On finite-dimensional perturbations of self-adjoint operators,J. Math. Soc. Japan 9 (1957), 239–249.

    Article  MATH  MathSciNet  Google Scholar 

  12. Kato, T., Wave operators and unitary equivalence,Pacific J. Math. 15 (1965), 171–180.

    MATH  MathSciNet  Google Scholar 

  13. Kato, T., Wave operators and similarity for some non-selfadjoint operators,Math. Ann. 162 (1966) 258–279.

    Article  MATH  MathSciNet  Google Scholar 

  14. Kuroda, S. T., Finite-dimensional perturbation and a representation of scattering operator,Pacific J. Math. 13 (1963), 1305–1318.

    MATH  MathSciNet  Google Scholar 

  15. Kuroda, S. T., On a stationary approach to scattering problem,Bull. Amer. Math. Soc. 70 (1964), 556–560.

    MATH  MathSciNet  Google Scholar 

  16. Kuroda, S. T., Stationary methods in the theory of scattering. Perturbation theory and its applications in quantum mechanics, 185–214, Wiley, New York, 1966.

    Google Scholar 

  17. Muskhelishvili, N. J., Singular integral equations, Noordhoff, Groningen, 1953.

    MATH  Google Scholar 

  18. Rejto, P. A., On gentle perturbations, I, II,Comm. Pure Appl. Math. 16 (1963), 279–303;17 (1964), 257–292.

    Article  MathSciNet  Google Scholar 

  19. Rosenberg, M., The square integrability of matrix-valued functions with respect to a non-negative hermitian measure,Duke Math. J. 31 (1964), 291–298.

    Article  MATH  MathSciNet  Google Scholar 

  20. Schatten, R., Norm ideals of completely continous operators, Erg. Math. Neue Folge 27, Springer, Berlin, 1960.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was partly supported by Matsunaga Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuroda, S.T. An abstract stationary approach to perturbation of continuous spectra and scattering theory. J. Anal. Math. 20, 57–117 (1967). https://doi.org/10.1007/BF02786670

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786670

Keywords

Navigation