Skip to main content
SpringerLink
Log in

The spectrum of a Schrödinger operator inL p ℝv isp-independent

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

LetH p =−1/2Δ+V denote a Schrödinger operator, acting inL p ℝv, 1≦p≦∞. We show that σ(H p )=σ(H 2) for allp∈[1, ∞], for rather general potentialsV.

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. Aizenman, M., Simon, B.: Brownian motion and Harnack inequality for Schrödinger operators. Commun. Pure Appl. Math.35, 209–273 (1982)

    Google Scholar 

  2. Auterhoff, J.: Interpolationseigenschaften des Spektrums linearer Operatoren aufL P -Räumen. Math. Z.184, 397–406 (1983)

    Google Scholar 

  3. Devinatz, A.: Schrödinger operators with singular potentials. J. Oper. Theory4, 25–35 (1980)

    Google Scholar 

  4. Dunford, N., Pettis, B. J.: Linear operations on summable functions. Trans. Am. Math. Soc.47, 323–392 (1940)

    Google Scholar 

  5. Hempel, R., Voigt, J.: On theL p-spectrum of Schrödinger operators. J. Math. Anal. Appl. (to appear)

  6. Jörgens, K.: Lineare Integraloperatoren. Stuttgart: B. G. Teubner, 1970

    Google Scholar 

  7. Kato, T.: Perturbation theory for linear operators. Second edition. Berlin Heidelberg, New York: Springer 1976

    Google Scholar 

  8. Reed, M., Simon, B.: Methods of modern mathematical physics I: Functional analysis. Revised and enlarged edition. New York: Academic Press 1980

    Google Scholar 

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

    Google Scholar 

  10. Sigal, I. M.: A generalized Weyl theorem andL P -spectra of Schrödinger operators. Preprint

  11. Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979

    Google Scholar 

  12. Simon, B.: Brownian motion,L P properties of Schrödinger operators and the localization of binding. J. Funct. Anal.35, 215–225 (1980)

    Google Scholar 

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

    Google Scholar 

  14. Voigt, J.: Absorption semigroups, their generators, and Schrödinger semigroups, J. Funct. Anal. (to appear)

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, D-8000, München 2, Federal Republic of Germany

    Rainer Hempel & Jürgen Voigt

Authors
  1. Rainer Hempel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jürgen Voigt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. Simon

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hempel, R., Voigt, J. The spectrum of a Schrödinger operator inL p ℝv isp-independent. Commun.Math. Phys. 104, 243–250 (1986). https://doi.org/10.1007/BF01211592

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01211592

Keywords

Search

Navigation