Skip to main content
Log in

Asymptotic stability of Schrödinger semigroups: path integral methods

  • 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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, R.A.: Sobolev spaces. New York: Academic Press 1975

    Google Scholar 

  2. Agmon, S.: Lectures on elliptic boundary value problems. Princeton: van Nostrand 1965

    Google Scholar 

  3. Aizenman, M., Simon, B.: Brownian motion and Harnack's inequality for Schrödinger operators. Commun. Pure Appl. Math.35, 209–271 (1982)

    Google Scholar 

  4. Arendt, W., Batty, C.J.K.: Tauberian theorems and stability of one-parameter semigroups. Trans. Am. Math. Soc.306, 837–852 (1988)

    Google Scholar 

  5. Arendt, W., Batty, C.J.K.: Exponential stability of Schrödinger semigroups. (Preprint)

  6. Arendt, W., Batty, C.J.K.: Absorption semigroups and Dirichlet boundary conditions. (Preprint)

  7. Arendt, W., Batty, C.J.K. Bénilan, Ph.: Asymptotic stability of Schrödinger semigroups onL 1(R N). Math. Z. (to appear)

  8. Cycon, H.L., Froese, R.G., Kirsch, W., Simor, B.: Schrödinger operators with applications to quantum mechanics and global geometry. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  9. Demuth, M., van Casteren, J.A.: On spectral theory of self-adjoint Feller generators. Rev. Math. Phys.1, 325–414 (1989)

    Google Scholar 

  10. Hempel, R., Voigt, J.: The spectrum of a Schrödinger operator inL p (R ν) isp-independent. Commun. Math. Phys.104, 243–250 (1986)

    Google Scholar 

  11. Kato, T.:L p-theory of Schrödinger operators. In: Nagel, R., Schlotterbeck, U., Wolff, M. (eds.) Aspects of positivity in functional analysis, pp. 63–78. Amsterdam: North-Holland 1986

    Google Scholar 

  12. Knight, F.B.: Essentials of Brownian motion and diffusion. Providence: Am. Math. Soc. 1981

    Google Scholar 

  13. Lyubich, Yu.I., Vũ Quôc Phóng: Asymptotic stability of linear differential equations on Banach spaces. Studia Math.88, 37–42 (1988)

    Google Scholar 

  14. McKean, H.P., −Δ plus a bad potential. J. Math. Phys.18, 1277–1279 (1977)

    Google Scholar 

  15. Nagel, R. (ed.): One-parameter semigroups of positive operators. (Lect. Notes Math., vol. 1184) Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  16. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  17. Port, S.C., Stone, C.J.: Brownian motion and classical potential theory. New York: Academic Press 1978

    Google Scholar 

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

    Google Scholar 

  19. Simon, B.: Brownian motion,L p properties of Schrödinger operators, and the localization of binding. J. Funct. Anal.35, 215–229 (1980)

    Google Scholar 

  20. Simon, B.: Large time behavior of theL p norm of Schrödinger semigroups. J. Funct. Anal.40, 66–83 (1981)

    Google Scholar 

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

    Google Scholar 

  22. Voigt, J.: Absorption semigroups, their generators, and Schrödinger semigroups. J. Funct. Anal.67, 167–205 (1986)

    Google Scholar 

  23. Voigt, J.: Absorption semigroups. J. Oper. Theory20, 117–131 (1988)

    Google Scholar 

  24. Williams, D.: Diffusions, Markov processes, and martingales, I. Chichester: Wiley 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Batty, C.J.K. Asymptotic stability of Schrödinger semigroups: path integral methods. Math. Ann. 292, 457–492 (1992). https://doi.org/10.1007/BF01444631

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444631

Mathematics Subject Classification (1991)

Navigation