Semigroup Forum

, Volume 46, Issue 1, pp 347–351

Entire vectors and time reversible Cauchy problems

  • Laurent Autret
Research Article


Our major aim in this paper is to show the algebraic and topological equivalence between the set of all entire vectors ε(A) for a linear operatorA and the solution space of the corresponding abstract Cauchy problem, when—A is the generator of a strongly continuous holomorphic semigroup.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Autret, L.,Vecteurs entiers et réversibilité des problèmes paraboliques, Thèse de l'Université de Poitiers, 1992.Google Scholar
  2. [2]
    Bers, L., John, F., and M. Schechter, “Partial Differential Equations”, John Wiley and Sons, New York, 1964.MATHGoogle Scholar
  3. [3]
    Davies, E.B., “One-parameter semigroups”, Academic Press, London, 1980.MATHGoogle Scholar
  4. [4]
    deLaubenfels, R.,Entire solutions of the abstract Cauchy problem, Semigroup Forum42 (1991), 83–105.MATHMathSciNetGoogle Scholar
  5. [5]
    deLaubenfels, R., “Functional calculus, existence families and the abstract Cauchy problem”, preprint.Google Scholar
  6. [6]
    deLaubenfels, R.,Holomorphic C-existence families, Tokyo Math. J., to appear.Google Scholar
  7. [7]
    Goldstein, J.A., “Semigroups of Operators and Applications”, Oxford University Press, New York, 1985.MATHGoogle Scholar
  8. [8]
    Goodman, R.,Complex Fourier analysis on a nilpotent Lie group, Trans. Amer. Math. Soc.160 (1971), 373–391.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Komura, T.,Semigroups of operators in locally convex spaces, J. Funct. Anal.2 (1968), 258–296.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Krein, S.G., Laptev, G.I., and G.A. Cvetkova,On Hadamard correctness of the Cauchy problem for the equation of evolution, Soviet Math. Dokl.11 (1970), 763–766.Google Scholar
  11. [11]
    Nelson, E.,Analytic vectors, Ann. of Math.70 (1959), 572–615.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Pazy, A., “Semigroups of Linear Operators and Applications to Partial Differential Equations”, Springer-Verlag, New York, 1983.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1993

Authors and Affiliations

  • Laurent Autret
    • 1
  1. 1.Département de MathématiquesUniversité de PoitiersPoitiersFrance

Personalised recommendations