On exit laws for subordinated semigroups by means of 𝒞 1 -subordinators

Mohamed Hmissi; Ezzedine Mliki

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 4, page 605-617
  • ISSN: 0010-2628

Abstract

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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 𝒞 1 -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.

How to cite

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Hmissi, Mohamed, and Mliki, Ezzedine. "On exit laws for subordinated semigroups by means of $\mathcal {C}^{1}$-subordinators." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 605-617. <http://eudml.org/doc/246407>.

@article{Hmissi2010,
abstract = {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.},
author = {Hmissi, Mohamed, Mliki, Ezzedine},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sub-Markovian semigroup; potential; Bochner subordination; exit law; $\mathcal \{C\}^\{1\}$-subordinator; one-sided stable subordinator; sub-Markovian semigroup; Bochner subordination; exit law; -subordinator; one-sided stable subordinator},
language = {eng},
number = {4},
pages = {605-617},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On exit laws for subordinated semigroups by means of $\mathcal \{C\}^\{1\}$-subordinators},
url = {http://eudml.org/doc/246407},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Hmissi, Mohamed
AU - Mliki, Ezzedine
TI - On exit laws for subordinated semigroups by means of $\mathcal {C}^{1}$-subordinators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 4
SP - 605
EP - 617
AB - 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.
LA - eng
KW - sub-Markovian semigroup; potential; Bochner subordination; exit law; $\mathcal {C}^{1}$-subordinator; one-sided stable subordinator; sub-Markovian semigroup; Bochner subordination; exit law; -subordinator; one-sided stable subordinator
UR - http://eudml.org/doc/246407
ER -

References

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  1. Bachar I., On exit laws for semigroups in weak duality, Comment. Math. Univ. Carolin. 42 (2001), no. 4, 711–719. Zbl1090.31501MR1883379
  2. Berg C., Forst G., Potential Theory on Locally Compact Abelian Groups, Springer, Berlin-Heidelberg-New York, 1975. Zbl0308.31001MR0481057
  3. Bliedtner J., Hansen W., Potential Theory. An Analytic and Probabilistic Approach to Balayage, Universitext, Springer, Berlin-Heidelberg-New York, 1986. Zbl0706.31001MR0850715
  4. Carasso J., Kato T., 10.1090/S0002-9947-1991-1018572-4, Trans. Amer. Math. Soc. 327 (1991), 867–878. Zbl0743.47017MR1018572DOI10.1090/S0002-9947-1991-1018572-4
  5. Dellacherie C., Meyer P.A., Probabilités et potentiel, Chapter XII-XVI, Hermann, Paris, 1987. Zbl0624.60084MR0488194
  6. Dynkin E.B., 10.1016/0022-1236(82)90112-4, J. Funct. Anal. 47 (1982), 381–418. MR0665023DOI10.1016/0022-1236(82)90112-4
  7. Fitzsimmons P.J., Getoor R.K., 10.1007/BF01457159, Math. Ann. 281 (1988), 495–512. Zbl0627.60067MR0954155DOI10.1007/BF01457159
  8. Fitzsimmons P.J., 10.1016/0022-1236(89)90038-4, J. Funct. Anal. 85 (1989), 287–306. MR1012207DOI10.1016/0022-1236(89)90038-4
  9. Glover M., Rao H., Sikic H., Song R., Γ -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. MR1321619
  10. Hmissi F., On energy formulas for symmetric semigroups, Ann. Math. Sil. 19 (2005), 7–18. Zbl1102.31010MR2225433
  11. Hmissi M., 10.1007/BF02567086, Manuscripta Math. 75 (1992), 293–302. Zbl0759.60080MR1167135DOI10.1007/BF02567086
  12. Hmissi M., 10.1007/BF03025742, Math. Z. 213 (1993), 647–656. Zbl0790.31006MR1231882DOI10.1007/BF03025742
  13. Hmissi M., On the functional equation of exit laws for lattice semigroups, Rocznik Nauk.-Dydakt. Prace Mat. No. 15 (1998), 63–71. Zbl1160.39326MR1826075
  14. Hmissi M., Mejri H., On representation by exit laws for some Bochner subordinated semigroups, Ann. Math. Sil. 22 (2008), 7–26. Zbl1190.47042MR2569077
  15. Hmissi M., Mejri H., Mliki E., On the fractional powers of semidynamical systems, Grazer Math. Ber. 351 (2007), 66–78. Zbl1152.45005MR2381104
  16. Hmissi M., Mejri H., Mliki E., On the abstract exit equation, Grazer Math. Ber. 354 (2009), 84–98. MR2649011
  17. Jacob N., Pseudo Differential Operators and Markov Processes, Vol. 2: Generators and their semigroups, Imperial College Press, London, 2003. 
  18. Sato K., Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, 68, Cambridge University Press, Cambridge, 1999. Zbl0973.60001MR1739520
  19. Yosida K., Functional Analysis, Springer, Heidelberg-New York, 1965. Zbl0830.46001

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