ArticleOriginal scientific text

Title

Asymptotic behaviour of semigroups of operators

Authors 1

Affiliations

  1. St., John's College, Oxford OX1 3JP, England

Bibliography

  1. H. Alexander, On a problem of Stolzenberg in polynomial convexity, Illinois J. Math. 22 (1978), 149-160.
  2. G. R. Allan, A. G. O'Farrell and T. J. Ransford, A Tauberian theorem arising in operator theory, Bull. London Math. Soc. 19 (1987), 537-545.
  3. G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79.
  4. W. Arendt, Resolvent positive operators, Proc. London Math. Soc. 54 (1987), 321-349.
  5. W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852.
  6. W. Arendt and C. J. K. Batty, A complex Tauberian theorem and mean ergodic semigroups, preprint.
  7. W. Arendt, F. Neubrander and U. Schlotterbeck, Interpolation of semigroups and integrated semigroups, Semesterbericht Funktionalanalysis Tübingen 15 (1988/89), 1-14.
  8. W. Arendt and J. Prüss, Vector-valued Tauberian theorems and asymptotic behavior of linear Volterra equations, SIAM J. Appl. Math. 23 (1992), 412-448.
  9. R. Arens, Inverse-producing extensions of normed algebras, Trans. Amer. Math. Soc. 88 (1958), 536-548.
  10. C. J. K. Batty, Tauberian theorems for the Laplace-Stieltjes transform, ibid. 322 (1990), 783-804.
  11. C. J. K. Batty and D. A. Greenfield, On the invertibility of isometric semigroup representations, preprint.
  12. C. J. K. Batty and Vũ Quôc Phóng, Stability of individual elements under one-parameter semigroups, Trans. Amer. Math. Soc. 322 (1990), 805-818.
  13. C. J. K. Batty and Vũ Quôc Phóng, Stability of strongly continuous representations of abelian semigroups, Math. Z. 209 (1992), 75-88.
  14. E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
  15. O. El Mennaoui, Comportement asymptotique des semi-groupes intégrés, J. Comput. Appl. Math., to appear.
  16. J. Esterle, E. Strouse and F. Zouakia, Theorems of Katznelson-Tzafriri type for contractions, J. Funct. Anal. 94 (1990), 273-287.
  17. J. Esterle, E. Strouse and F. Zouakia, Stabilité asymptotique de certains semigroupes d'opérateurs, J. Operator Theory, to appear.
  18. I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Mat. Sb. 9 (51) (1941), 49-50.
  19. D. A. Greenfield, D.Phil. thesis, Oxford, in preparation.
  20. E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc., Providence, 1957.
  21. S. Huang and F. Räbiger, Superstable C0-semigroups on Banach spaces, preprint.
  22. A. E. Ingham, On Wiener's method in Tauberian theorems, Proc. London Math. Soc. 38 (1935), 458-480.
  23. Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 313-328.
  24. J. Korevaar, On Newman's quick way to the prime number theorem, Math. Intelligencer 4 (1982), 108-115.
  25. U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985.
  26. Yu. I. Lyubich, On the spectrum of a representation of an abelian topological group, Dokl. Akad. Nauk SSSR 200 (1971), 777-780 (in Russian); English transl.: Soviet Math. Dokl. 12 (1971), 1482-1486.
  27. Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups, Birkhäuser, Basel, 1988.
  28. Yu. I. Lyubich and Vũ Quôc Phóng, Asymptotic stability of linear differential equations on Banach spaces, Studia Math. 88 (1988), 37-42.
  29. Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for almost periodicity of one-parameter semigroups, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 47 (1987), 36-41 (in Russian).
  30. Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for almost periodicity of representations of abelian semigroups, ibid. 51 (1987) (in Russian).
  31. R. Nagel and F. Räbiger, Superstable operators on Banach spaces, Israel J. Math. 81 (1993), 213-226.
  32. B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
  33. D. J. Newman, Simple analytic proof of the prime number theorem, Amer. Math. Monthly 87 (1980), 693-696.
  34. G. K. Pedersen, C*-Algebras and Their Automorphism Groups, Academic Press, London, 1979.
  35. Vũ Quôc Phóng, Theorems of Katznelson-Tzafriri type for semigroups of operators, J. Funct. Anal. 103 (1992), 74-84.
  36. G. M. Sklyar and V. Ya. Shirman, On the asymptotic stability of a linear differential equation in a Banach space, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 37 (1982), 127-132 (in Russian).
  37. G. Stolzenberg, Polynomially and rationally convex sets, Acta Math. 109 (1963), 259-289.
  38. E. L. Stout, The Theory of Uniform Algebras, Bogden & Quigley, Tarrytown-on-Hudson, 1971.
  39. J. Wermer, Banach Algebras and Several Complex Variables, Springer, New York, 1976.
  40. W. Żelazko, On a certain class of non-removable ideals in Banach algebras, Studia Math. 44 (1972), 87-92.
Pages:
35-52
Main language of publication
English
Published
1994
Exact and natural sciences