Diffusion Semigroups in Spaces of Continuous Functions with Mixed Topology

Journal of Differential Equations

Volumn 173, Issue 1, 2001, Pages 17-39

  Goldys, B ^a   Kocan, M ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Kolmogorov equation; Mixed topology; Stochastic semilinear equation; Transition semigroup

Indexed keywords

EID: 0006289519     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3918     Document Type: Article

References (21)

1. Alexiewicz A. On sequences of operations, II. Studia Math. 11:1950;200-236.
2. Cerrai S. A Hille-Yosida theorem for weakly continuous semigroups. Semigroup Forum. 49:1994;349-367.
3. Cerrai S. Weakly continuous semigroups in the space of functions with polynomial growth. Dynam. Systems Appl. 4:1995;351-371.
4. Cerrai S., Gozzi F. Strong solutions of Cauchy problems associated to weakly continuous semigroups. Differential Integral Equations. 8:1995;465-486.
5. G. Da Prato, Parabolic equations in Hilbert spaces, preprint, Scuola Normale Superiore, Pisa, 1996.
6. Da Prato G., Elworthy K. D., Zabczyk J. Strong Feller property for stochastic semilinear equations. Stochastic Anal. Appl. 13:1995;35-45.
7. Da Prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge Univ. Press, Cambridge.
8. Davies E. B. One Parameter Semigroups. 1980;Academic Press, New York.
9. Engelking R. General Topology. 1989;Heldermann Verlag, Berlin.
10. Ethier S. N., Kurtz T. G. Markov Processes. 1986;Wiley, New York.
11. Fichtenholz G. Sur les fonctionelles linéaires, continues au sens généralisé Mat. Sb. 4:1938;193-214.
12. Fremlin D., Garling D., Haydon R. Bounded measures on topological spaces. Proc. London Math. Soc. 25:1972;115-136.
13. Goldys B., Maslowski B. Ergodic control of semilinear stochastic equations and Hamilton-Jacobi equations. J. Math. Anal. Appl. 234:1999;592-631.
14. Jefferies B. Weakly integrable semigroups on locally convex spaces. J. Funct. Analysis. 66:1986;347-364.
15. Jefferies B. The generation of weakly integrable semigroups. J. Funct. Anal. 73:1987;195-215.
16. Kõmura T. Semigroups of operators in locally convex spaces. J. Funct. Anal. 2:1968;258-296.
17. E. Priola, π-Semigroups and applications, preprint, No. 9, Scuola Normale Superiore di Pisa, 1998.
18. G. Tessitore, and, J. Zabczyk, Comments on transition semigroups and stochastic invariance, preprint, No. 15, Scuola Normale Superiore di Pisa, 1998.
19. Wheeler R. F. A survey of Baire measures and strict topologies. Exposition Math. 2:1983;97-190.
20. Wiweger A. Linear spaces with mixed topology. Studia Math. 20:1961;47-68.
21. Yosida K. Functional Analysis. 1980;Springer-Verlag, Heidelberg.