Perturbations of Bi-continuous Semigroups with Applications to Transition Semigroups on C b(H)

Semigroup Forum

Volumn 68, Issue 1, 2004, Pages 87-107

  Farkas, Bálint ^a,b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b CENTRAL EUROPEAN UNIVERSITY   (Hungary)

Author keywords

Bi continuous semigroups; Equicontinuous semigroups; Not strongly continuous semigroups; Ornstein Uhlenbeck semigroup; Transition semigroup; Unbounded perturbation

Indexed keywords

BI-CONTINUOUS SEMIGROUPS; EQUICONTINUOUS SEMIGROUPS; NOT STRONGLY CONTINUOUS SEMIGROUPS; ORNSTEIN-UHLENBECK SEMIGROUP; TRANSITION SEMIGROUP; UNBOUNDED PERTURBATIONS;

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; RANDOM PROCESSES; THEOREM PROVING;

PERTURBATION TECHNIQUES;

EID: 1142268880     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-002-0024-2     Document Type: Article

References (34)

1. Albanese, A. A. and E. Mangino, Trotter-Koto theorems for bi-continuous semigroups, preprint (2002).
2. Cannarsa, P. and G. Da Prato, On a functional analytic approach to parabolic equations in infinite dimensions, J. Funct. Anal. 118 (1993), 2242.
3. Cerrai, S., A Hille-Yoshida theorem for weakly continuous semigroups, Semigroup Forum 49 (1994), 349-367.
4. Cerrai, S. and F. Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, J. Differential Equations 8 (1995), 465-486.
5. Da Prato, G., Bounded perturbations of Ornstein-Uhlenbeck semigroups, Progress in Nonlinear Differential Equations and Their Applications, vol. 50, Birkhäuser Verlag, Basel, 2002, 97-114.
6. Da Prato, G., Lipschitz perturbations of Ornstein-Uhlenbeck semigroups, preprint (2002).
7. Da Prato, G., "Markov Semigroups", Progress in Nonlinear Differential Equations and Their Applications, Lecture Notes in Mathematics, Springer-Verlag, New York, 2002, to appear.
8. Da Prato, G., A new regularity result for Ornstein-Uhlenbeck generators and applications, preprint (2002).
9. Da Prato, G. and A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal. 131(1) (1995), 94-114.
10. Da Prato, G. and J. Zabczyk, "Ergodicity for Infinite Dimensional Systems", London Mathematical Society Lecture Notes, vol. 229, Cambridge University Press, 1996.
11. Da Prato, G., and J. Zabczyk, "Stochastic Equations in Infinite Dimensions" , Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1992.
12. Dembart, B., Perturbation of semigroups on locally convex spaces, Bull. Amer. Math. Soc. 79 (1973), 986-991.
13. Dorroh, J. R. and J. W. Neuberger, Lie generators for semigroups of transformations on a polish space, Electron. J. Differential Equations 1 (1993), 1-7.
14. Dorroh, J. R. and J. W. Neuberger, A theory of strongly continuous semigroups in terms of Lie generators, J. Funct. Anal. 136 (1996), 114-126.
15. Dorroh, J. R. and J. W. Neuberger, "Linear extension of nonlinear semigroups", Progress in Nonlinear Differential Equations and their Applications, vol. 42, Birkhäuser Verlag, Berlin, 2000, 96-102.
16. Engel, K.-J. and R. Nagel, "One-parameter Semigroups for Linear Evolution Equations", Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000.
17. Farkas, B., Perturbations of bi-continuous semigroups, Tübinger Berichte zur Funktionalanalysis 11 (2001/2002), 97-113. (to appear in Studia Math.)
18. Goldys, B. and M. Kocan, Diffusion semigroups in spaces of continuous functions with mixed topology, J. Diff. Eq. 173 (2001), 17-39.
19. Kühnemund, F., A Hille-Yoshida theorem for bi-continuous semigroups, Semigroup Forum 67 (2003), 205-225.
20. Kühnemund, F., Approximation of bi-continuous semigroups, Tübinger Berichte zur Funktionalanalysis 10 (2000/2001), 100-117.
21. Kühnemund, F., "Bi-continuous semigroups on spaces with two topologies: Theory and applications", Ph.D. thesis, Eberhard Karls Universität Tübingen, 2001.
22. F. Kühnemund and J. M. A. M. van Neerven, A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions, to appear in J. Evol. Eq.
23. Kuo, H. H., "Gaussian Measures in Banach Spaces", Lecture Notes in Mathematics, vol. 463, Springer-Verlag, New York, 1998.
24. 2 spaces with respect to invariant measures, Trans. Amer. Math. Soc. 349 (1997), 155-169.
25. P -regularity for elliptic operators with unbounded coefficients, preprint (2002).
26. Priola, E., On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Math. 136 (1999), 271-295.
27. 2, Note di Mat. 21 (2002), 93-106.
28. Sentilles, F. D., Bounded continuous functions on a completely regular space, Trans. Amer. Math. Soc. 168 (1972), 311-336.
29. Shiryayev, A. N., "Probability", Graduate Texts in Mathematics, vol. 95, Springer-Verlag, 1984.
30. Tessitore, G. and J. Zabczyk, Trotter's formula for transition semigroups, Semigroup Forum 63 (2001), 114-126.
31. Vakhania, N. N., "Probability Distributions on Linear Spaces", North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York, 1981, Translated from the Russian by I. I. Kotlarski.
32. van Neerven, J. M. A. M., Nonsymmetric Ornstein-Uhlenbeck semigroups in Banach spaces, J. Funct. Anal. 155 (1998), 495-535.
33. Voigt, J., On the perturbation theory for strongly continuous semigroups, Math. Ann. 229 (1977), 163-171.
34. Walker, R. C., "The Stone-Čech Compactification", Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 83, Springer-Verlag, New York, 1974.