Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 136 | 3 | 271-295
Tytuł artykułu

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
Słowa kluczowe
  • Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
  • [1] W. Arendt, Vector valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
  • [2] R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
  • [3] P. Cannarsa and G. Da Prato, Infinite dimensional elliptic equations with Hölder continuous coefficients, Adv. Differential Equations 1 (1996), 425-452.
  • [4] P. Cannarsa and G. Da Prato, Potential theory in Hilbert spaces, in: Proc. Sympos. Appl. Math. 54, Amer. Math. Soc., 1998, 27-51.
  • [5] S. Cerrai, A Hille-Yosida theorem for weakly continuous semigroups, Semigroup Forum 49 (1994), 349-367.
  • [6] S. Cerrai and F. Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, Differential Integral Equations 8 (1994), 465-486.
  • [7] G. Da Prato and A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal. 131 (1995), 94-114.
  • [8] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge Univ. Press, 1992.
  • [9] J. Diestel, Sequences and Series in Banach Spaces, Grad. Text. in Math. 92, Springer, New York, 1984.
  • [10] E. B. Dynkin, Markov Processes, Vol. I, Springer, Berlin, 1965.
  • [11] N. Ethier and T. G. Kurtz, Markov Processes, Characterization and Convergence, Wiley, 1986.
  • [12] M. Fuhrman and M. Röckner, Generalized Mehler semigroups: the non-Gaussian case, Potential Anal., to appear.
  • [13] L. Gross, Potential theory on Hilbert space, J. Funct. Anal. 1 (1967), 123-181.
  • [14] P. Guiotto, Non-differentiability of heat semigroups in infinite dimensional Hilbert spaces, Semigroup Forum 55 (1997), 232-236.
  • [15] M. Hieber and H. Kellerman, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180.
  • [16] B. Jefferies, Weakly integrable semigroups on locally convex spaces, ibid. 66 (1986), 347-364.
  • [17] B. Jefferies, The generation of weakly integrable semigroups, ibid. 73 (1987), 195-215.
  • [18] H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer, 1975.
  • [19] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, 1995.
  • [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
  • [21] E. Priola, Schauder estimates for a homogeneous Dirichlet problem in a half space of a Hilbert space, Nonlinear Anal., to appear.
  • [22] E. Priola, π-Semigroups and applications, preprint n. 9, Scuola Norm. Sup. Pisa, 1998.
  • [23] K. Yosida, Functional Analysis, 4th ed., Springer, Berlin, 1974.
  • [24] L. Zambotti, A new approach to existence and uniqueness for martingale problems in infinite dimensions, preprint n. 13, Scuola Norm. Sup. Pisa, 1998.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.