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Asymptotic stability of Schrödinger semigroups onL 1(ℝN)

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Batty, C.J.K.: Asymptotic stability of Schrödinger semigroups: path integral methods Math. Ann. (to appear)

  3. Bénilan Ph.: Opérateurs accrétifs et semi-groupes dans les espacesL p. In: Fujita, H. (ed.) Funct. Anal. and Num. Anal. Japan-France Seminar. Tokyo and Kyoto 1976

  4. Brézis, H.: Analyse fonctionnelle. Paris: Masson 1963

    Google Scholar 

  5. Dautray, R., Lions, J.-L.: Analyse mathématique et calcul numérique, Paris: Masson 1987

    Google Scholar 

  6. Davies, E.B.: Heat Kernels and spectral theory. Cambridge: Cambridge University Press 1989

    MATH  Google Scholar 

  7. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Berlin Heidelber New York: Springer 1983

    MATH  Google Scholar 

  8. Hayman, W. K., Kennedy, P.B.: Subharmonic Functions. London: Academic Press 1976

    MATH  Google Scholar 

  9. Hempel, R., Voigt, J.: On theL p -spectrum of Schrödinger operators. J. Math. Anal. Appl.121, 138–159 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kato, T.:L p -Theory of Schrödinger operators with a singular potential. In: Nagel, R., Schlotterbeck, U., Wolff, H. (eds.): Aspects of Positivity in Functional Analysis. Amsterdam: North Holland 1986

    Google Scholar 

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

    MATH  Google Scholar 

  12. Nagel, R. (ed.) One-parameter Semigroups of Positive Operators. (Lect. Notes Math., vol. 1184) Berlin Heidelberg New York: Springer

  13. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. IV. London: Academic Press 1978

    Google Scholar 

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

    Article  MATH  Google Scholar 

  15. Voigt, J.: Absorption semigroups, their generators and Schrödinger semigroups. J. Oper. Theory20, 117–131 (1988)

    MATH  MathSciNet  Google Scholar 

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Author notes

  1. Charles J. K. Batty

    Present address: St. John's College, OX1 3JP, Oxford, UK

Authors and Affiliations

  1. Equipe de Mathématiques U.A. CNRS 741, Université de Franche-Comté, F-25030, Besançon Cedex, France

    Wolfgang Arendt, Charles J. K. Batty & Philippe Bénilan

Authors
  1. Wolfgang Arendt
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  2. Charles J. K. Batty
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  3. Philippe Bénilan
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Arendt, W., Batty, C.J.K. & Bénilan, P. Asymptotic stability of Schrödinger semigroups onL 1(ℝN). Math Z 209, 511–518 (1992). https://doi.org/10.1007/BF02570850

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  • DOI: https://doi.org/10.1007/BF02570850

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