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Right Dual Process for Semidynamical Systems

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Abstract

We construct a dual semigroup of kernels associated to a semidynamical system. The above semigroup is in duality with the deterministic semigroup defined by Koopmann. We also prove the existence of right dual process associated to a semidynamical system.

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References

  1. Anderson, P.W., Halperin, B.I. and Varma, C.M.: Philos. Mag. 25(1) (1972).

  2. Beznea, L. and Boboc, N.: ‘Duality and biduality for excessive measures’, Rev. Roum. Math. Pures Appl. 39 (1994), 419–438.

    Google Scholar 

  3. Bezzarga, M. and Bucur, G.H.: ‘Théorie du potentiel pour les systèmes semi-dynamiques’, Rev. Roum. Math. Pures Appl. 39 (1994), 439–456.

    Google Scholar 

  4. Bezzarga, M. and Bucur, G.H.: ‘Duality for semi-dynamical systems’, in Potential Theory — ICPT 1994, Walter de Gruyter, Berlin, 1996, pp. 275–286.

    Google Scholar 

  5. Bezzarga, M.: ‘Co-excessive functions and duality for semi-dynamical systems’, Rev. Roum. Math. Pures Appl. 42(1–2) (1997).

  6. Bezzarga, M., Moldoveanu, E. and Secelean, N.: ‘Dual resolvent for semidynamical systems’, Preprint (accessible in: http://adela.karlin.mff.cuni.cz/katedry/kma/pt).

  7. Bhatia, N.P. and Hajek, O.: Local Semi-Dynamical Systems, Lecture Notes in Math. 90, Springer-Verlag, Berlin, 1969.

    Google Scholar 

  8. Boboc, N., Bucur, G.H. and Cornea, A.: Order and Convexity in Potential Theory, Lecture Notes in Math. 853, Springer-Verlag, Berlin, 1981.

    Google Scholar 

  9. Boboc, N. and Bucur, G.H.: ‘Potential theory on ordered sets I’, Rev. Roum. Math. Pures Appl. 43 (1998), 277–298.

    Google Scholar 

  10. Boboc, N. and Bucur, G.H.: ‘Potential theory on ordered sets II’, Rev. Roum. Math. Pures Appl. 43 (1998), 685–720.

    Google Scholar 

  11. Bourbaki, N.: General Topology, Hermann, Paris, 1966.

    Google Scholar 

  12. Cornea, A. and Licea, G.: Order and Potential Resolvent Families of Kernels, Lecture Notes in Math. 494, Springer-Verlag, Berlin, 1975.

    Google Scholar 

  13. Fridribhov, S. and Movnine, S.: Bases physiques de la technique électronique, Edition Mir, Moscou, Traduction Francaise, 1985.

  14. Dellachirie, C. and Meyer, P.A.: Probabilités et potentiel, Vols. XII-XVI, Hermann, Paris, 1987.

    Google Scholar 

  15. Getoor, R.K.: ‘Transience and recurrence of Markov processes’, in Séminaire de Probabilité XIV 1978–1979, Lecture Notes in Math. 784, Springer-Verlag, Berlin, 1980, pp. 397–409.

    Google Scholar 

  16. Getoor, R.K.: Excessive Measures, Birkhäuser, Boston, 1990.

    Google Scholar 

  17. Hajek, O.: Dynamical Systems in the Plane, Academic Press, London, 1968.

    Google Scholar 

  18. Hmissi, M.: ‘Semi-groupes déterministes’, in Lecture Notes in Math. 1393, Springer, Berlin, 1989, pp. 135–144.

    Google Scholar 

  19. Koopmann, B.O.: ‘Hamiltonian systems and transformation in Hilbert spaces’, Proc. Nat. Acad. Sci. USA 17(5) (1931), 315–318.

    Google Scholar 

  20. Meyer, P.A.: Processus de Markov, Lecture Notes in Math. 26, Springer, Berlin, 1967.

    Google Scholar 

  21. Meyer, P.A.: Processus de Markov: la frontière de Martin, Lecture Notes in Math. 77, Springer, Berlin, 1968.

    Google Scholar 

  22. Mokobodzki, G.: ‘Structure des cônes de potentiels’, Séminaire Bourbaki 372 (1968/69).

  23. Quéré, Y.: Physique des matériaux, École Polytechnique, Ellipses, Paris, 1988.

    Google Scholar 

  24. Saperstone, S.H.: Semidynamical Systems in Infinite Dimensional Space, Appl. Math. Sci. 37, Springer-Verlag, Berlin, 1981.

    Google Scholar 

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Bezzarga, M. Right Dual Process for Semidynamical Systems. Potential Analysis 21, 47–74 (2004). https://doi.org/10.1023/B:POTA.0000021336.18743.71

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  • DOI: https://doi.org/10.1023/B:POTA.0000021336.18743.71

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