Continuity and Representation of Gaussian Mehler Semigroups

Potential Analysis

Volumn 13, Issue 3, 2000, Pages 199-211

  Van Neerven, J M A M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Covariance operator; Gaussian Mehler semigroup; Pointwise continuous; Reflexivity; Schauder basis; Transition semigroup; Weakly continuous

Indexed keywords

EID: 0034355732     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008799213878     Document Type: Article

References (13)

1. Anderson, T. W.: 'The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities', Proc. Amer. Math. Soc. 6 (1955), 170-176.
2. Bogachev, V. I., Röckner, M. and Schmuland, B.: 'Generalized Mehler semigroups and applications', Prob. Th. Relat. Fields 105 (1996), 193-225.
3. Cerrai, S.: 'A Hille-Yosida theorem for weakly continuous semigroups', Semigroup Forum 49 (1994), 349-367.
4. Cerrai, S. and Gozzi, F.: 'Strong solutions of Cauchy problems associated to weakly continuous semigroups', Differential Integral Eq. 8 (1995), 465-486.
5. Da Prato, G. and Lunardi, A.: 'On the Ornstein-Uhlenbeck operator in spaces of continuous functions', J. Funct. Anal. 131 (1995), 94-114.
6. Da Prato, G. and Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1992.
7. Ledoux, M. and Talagrand, M.: Probability in Banach Spaces, Ergebnisse d. Math. u. ihre Grenzgebiete, vol. 23, Springer-Verlag, 1991.
8. van Neerven, J. M. A. M.: The Adjoint of a Semigroup on Linear Operators, Lecture Notes in Math. 1529, Springer-Verlag, 1992.
9. van Neerven, J. M. A. M.: 'Non-symmetric Ornstein-Uhlenbeck semigroups in Banach spaces', J. Funct. Anal. 155 (1998), 495-535.
10. van Neerven, J. M. A. M. and Zabczyk, J.: 'Norm discontinuity of Ornstein-Uhlenbeck semigroups', to appear in Semigroup Forum.
11. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
12. Vakhania, N. N., Tarieladze, V. I. and Chobanyan, S. A.: Probability Distributions on Banach Spaces, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1987.
13. Zippin, M.: 'A remark on bases and reflexivity in Banach spaces', Israel J. Math. 6 (1968), 74-79.