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1995 | 115 | 1 | 53-71
Tytuł artykułu

Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^2(μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^2(μ)$. A closability criterion for such forms is presented. Examples are also given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
115
Numer
1
Strony
53-71
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-03-02
poprawiono
1994-09-13
Twórcy
  • Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32 20133 Milano, Italy
Bibliografia
  • [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, 1976.
  • [2] S. Cerrai, A Hille-Yosida theorem for weakly continuous semigroups, preprint, Scuola Normale Superiore di Pisa, 1993.
  • [3] S. Cerrai and F. Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, preprint, Scuola Normale Superiore di Pisa, 1993.
  • [4] G. Da Prato and P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. 54 (1975), 305-387.
  • [5] G. Da Prato and J. Zabczyk, Regular densities of invariant measures in Hilbert spaces, preprint, Scuola Normale Superiore di Pisa, 1993.
  • [6] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University Press, 1992.
  • [7] M. Fuhrman, Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces, preprint, Dipartimento di Matematica, Politecnico di Milano, n. 105/p, ottobre 1993.
  • [8] Z. M. Ma and M. Röckner, Dirichlet Forms, Springer, 1992.
  • [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
  • [10] B. Schmuland, Non-symmetric Ornstein-Uhlenbeck processes in Banach space via Dirichlet forms, Canad. J. Math. 45 (1993), 1324-1338.
  • [11] A. Yagi, Coïncidence entre des espaces d'interpolation et des domaines de puissances fractionnaires d'opérateurs, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 173-176.
  • [12] J. Zabczyk, Symmetric solutions of semilinear stochastic equations, in: Stochastic Partial Differential Equations and Applications, G. Da Prato and L. Tubaro (eds.), Lecture Notes in Math. 1390, Springer, 1989, 237-256.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv115i1p53bwm
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