Skip to main content
SpringerLink
Log in

Polynomial boundedness of eigensolutions and the spectrum of schrödinger operators

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

References

  1. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger operators. Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  2. Eastham, M.S.P., Kalf, H.: Schrödinger-type operators with continuous spectra. Boston: Pitman 1982

    Google Scholar 

  3. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, second ed. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  4. Halvorsen, S.G.: Counterexamples in the spectral theory of singular Sturm-Liouville operators. In: Sleeman, B.D., Michael, I.M. (eds.) Ordinary and partial differential equations. (Lect. Notes Math., vol. 415, pp. 373–382) Berlin Heidelberg New York: Springer 1974

    Google Scholar 

  5. Hinz, A.M.: Asymptotic behavior of solutions of −Δv+qv=γv and the distance of γ to the essential spectrum. Math. Z.194, 173–182 (1987)

    Article  Google Scholar 

  6. Hinz, A.M.: Regularity of solutions for singular Schrödinger equations. Rev. Math. Phys.4, 95–161 (1992)

    Article  Google Scholar 

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

    Google Scholar 

  8. Kato, T.: Schrödinger operators with singular potentials. Isr. J. Math.13, 135–148 (1972)

    Google Scholar 

  9. Leinfelder, H., Simader, C.G.: Schrödinger operators with singular magnetic vector potentials. Math. Z.176, 1–19 (1981)

    Article  Google Scholar 

  10. Poerschke, T., Stolz, G., Weidmann, J.: Expansions in generalized eigenfunctions of selfadjoint operators. Math. Z.202, 397–408 (1989)

    Article  Google Scholar 

  11. Reed, M., Simon, B.: Methods of modern mathematical physics, II: Fourier analysis, self-adjointness. New York, Academic Press 1975

    Google Scholar 

  12. Shnol' I.Eh.: Ob ogranichennykh resheniyakh uravneniya vtorogo poryadka v chastnykh proizvodnykh. Dokl. Akad. Nauk SSSR89, 411–413 (1953)

    Google Scholar 

  13. Shnol', I.Eh.: O povedenii sobstvennykh funktsij. Dokl. Akad. Nauk SSSR94, 389–392 (1954)

    Google Scholar 

  14. Simon, B.: Schrödinger operators with singular magnetic vector potentials. Math. Z.131, 361–370 (1973)

    Article  Google Scholar 

  15. Simon, B.: Spectrum and continuum eigenfunctions of Schrödinger operators. J. Funct. Anal.42, 347–355 (1981)

    Article  Google Scholar 

  16. Simon, B.: Schrödinger semigroups. Bull. Am. Math. Soc. New Ser.7, 447–526 (1982)

    Google Scholar 

  17. Simon, B.: Trace ideals and their applications Cambridge: Cambridge University Press 1979

    Google Scholar 

  18. Stolz, G.: Entwicklung nach verallgemeinerten Eigenfunktionen von Schrödingeroperatoren. Thesis. Frankfurt am Main (1989)

  19. Stolz, G.: Expansions in generalized eigenfunctions of Schrödinger operators with singular potentials. In: de Branges, L., Gohberg, I., Rovnyak, J. (eds.) Topics in Operator Theory, Ernst D. Hellinger Memorial Volume pp. 353–372 Basel: Birkhäuser 1990

    Google Scholar 

  20. Weidmann, J.: Linear operators in Hilbert spaces. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

Download references

Author information

Author notes

  1. Günter Stolz

    Present address: Fachbereich Mathematik, Universität Frankfurt, Robert-Mayer-Strass 6-10, W-6000, Frankfurt am Main, Federal Republic of Germany

Authors and Affiliations

  1. Mathematisches Institut, Universität München, Theresienstrasse 39, W-8000, München 2, Federal Republic of Germany

    Andreas M. Hinz

  2. Department of Mathematics, University of California, 405 Hilgard Ave., 90024, Los Angeles, CA, USA

    Günter Stolz

Authors
  1. Andreas M. Hinz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Günter Stolz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hinz, A.M., Stolz, G. Polynomial boundedness of eigensolutions and the spectrum of schrödinger operators. Math. Ann. 294, 195–211 (1992). https://doi.org/10.1007/BF01934321

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01934321

Mathematics Subject Classification (1991)

Search

Navigation