| Title:
|
On exit laws for subordinated semigroups by means of $\cal{C}^{1}$-subordinators (English) |
| Author:
|
Hmissi, Mohamed |
| Author:
|
Mliki, Ezzedine |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
605-617 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on $L^2(m)$. We mainly investigate subordinated semigroups in the Bochner sense by means of $\mathcal{C}^{1}$-subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup. (English) |
| Keyword:
|
sub-Markovian semigroup |
| Keyword:
|
potential |
| Keyword:
|
Bochner subordination |
| Keyword:
|
exit law |
| Keyword:
|
$\mathcal{C}^{1}$-subordinator |
| Keyword:
|
one-sided stable subordinator |
| MSC:
|
31C15 |
| MSC:
|
39B42 |
| MSC:
|
47D03 |
| MSC:
|
60J99 |
| idZBL:
|
Zbl 1222.47069 |
| idMR:
|
MR2858264 |
| . |
| Date available:
|
2010-11-30T16:22:36Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140841 |
| . |
| Reference:
|
[1] Bachar I.: On exit laws for semigroups in weak duality.Comment. Math. Univ. Carolin. 42 (2001), no. 4, 711–719. Zbl 1090.31501, MR 1883379 |
| Reference:
|
[2] Berg C., Forst G.: Potential Theory on Locally Compact Abelian Groups.Springer, Berlin-Heidelberg-New York, 1975. Zbl 0308.31001, MR 0481057 |
| Reference:
|
[3] Bliedtner J., Hansen W.: Potential Theory. An Analytic and Probabilistic Approach to Balayage.Universitext, Springer, Berlin-Heidelberg-New York, 1986. Zbl 0706.31001, MR 0850715 |
| Reference:
|
[4] Carasso J., Kato T.: On subordinated holomorphic semigroups.Trans. Amer. Math. Soc. 327 (1991), 867–878. Zbl 0743.47017, MR 1018572, 10.1090/S0002-9947-1991-1018572-4 |
| Reference:
|
[5] Dellacherie C., Meyer P.A.: Probabilités et potentiel.Chapter XII-XVI, Hermann, Paris, 1987. Zbl 0624.60084, MR 0488194 |
| Reference:
|
[6] Dynkin E.B.: Green's and Dirichlet spaces associated with fine Markov process.J. Funct. Anal. 47 (1982), 381–418. MR 0665023, 10.1016/0022-1236(82)90112-4 |
| Reference:
|
[7] Fitzsimmons P.J., Getoor R.K.: On the potential theory of symmetric Markov processes.Math. Ann. 281 (1988), 495–512. Zbl 0627.60067, MR 0954155, 10.1007/BF01457159 |
| Reference:
|
[8] Fitzsimmons P.J.: Markov processes and nonsymmetric Markov processes without regularity.J. Funct. Anal. 85 (1989), 287–306. MR 1012207, 10.1016/0022-1236(89)90038-4 |
| Reference:
|
[9] Glover M., Rao H., Sikic H., Song R.: $\Gamma$-potentials, classical and modern potential theory and applications.Nato ASI Series, Series C Vol. 430, Kluwer Academic Publ., Dordrecht-Boston-London, 1994, pp. 217–232. MR 1321619 |
| Reference:
|
[10] Hmissi F.: On energy formulas for symmetric semigroups.Ann. Math. Sil. 19 (2005), 7–18. Zbl 1102.31010, MR 2225433 |
| Reference:
|
[11] Hmissi M.: Lois de sortie et semi-groupes basiques.Manuscripta Math. 75 (1992), 293–302. Zbl 0759.60080, MR 1167135, 10.1007/BF02567086 |
| Reference:
|
[12] Hmissi M.: Sur la représentation par les lois de sortie.Math. Z. 213 (1993), 647–656. Zbl 0790.31006, MR 1231882, 10.1007/BF03025742 |
| Reference:
|
[13] Hmissi M.: On the functional equation of exit laws for lattice semigroups.Rocznik Nauk.-Dydakt. Prace Mat. No. 15 (1998), 63–71. Zbl 1160.39326, MR 1826075 |
| Reference:
|
[14] Hmissi M., Mejri H.: On representation by exit laws for some Bochner subordinated semigroups.Ann. Math. Sil. 22 (2008), 7–26. Zbl 1190.47042, MR 2569077 |
| Reference:
|
[15] Hmissi M., Mejri H., Mliki E.: On the fractional powers of semidynamical systems.Grazer Math. Ber. 351 (2007), 66–78. Zbl 1152.45005, MR 2381104 |
| Reference:
|
[16] Hmissi M., Mejri H., Mliki E.: On the abstract exit equation.Grazer Math. Ber. 354 (2009), 84–98. MR 2649011 |
| Reference:
|
[17] Jacob N.: Pseudo Differential Operators and Markov Processes, Vol. 2: Generators and their semigroups.Imperial College Press, London, 2003. |
| Reference:
|
[18] Sato K.: Lévy Processes and Infinitely Divisible Distributions.Cambridge Studies in Advanced Mathematics, 68, Cambridge University Press, Cambridge, 1999. Zbl 0973.60001, MR 1739520 |
| Reference:
|
[19] Yosida K.: Functional Analysis.Springer, Heidelberg-New York, 1965. Zbl 0830.46001 |
| . |
