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additive functional; excessive functions; regular potential; semidynamical system; specific order
We consider a semidynamical system $(X,\Cal B,\Phi ,w)$. We introduce the cone $\Bbb A$ of continuous additive functionals defined on $X$ and the cone $\Cal P$ of regular potentials. We define an order relation ``$\leq $'' on $\Bbb A$ and a specific order ``$\prec $'' on $\Cal P$. We will investigate the properties of $\Bbb A$ and $\Cal P$ and we will establish the relationship between the two cones.
[1] Bezzarga M.: Coexcessive functions and duality for semi-dynamical systems. Rev. Roumaine Math. Pures Appl. 42 1-2 (1997), 15-30. MR 1650071
[2] Bezzarga M.: Théorie du potentiel pour les systèmes semi-dynamiques. Ph.D. Thesis, Faculty of Mathematics of the Bucharest University, Dec. 2000. Zbl 0861.31005
[3] Bezzarga M., Bucur Gh.: Théorie du potentiel pour les systèmes semi-dynamiques. Rev. Roumaine Math. Pures Appl. 39 (1994), 439-456. MR 1298884 | Zbl 0861.31005
[4] Bezzarga M., Bucur Gh.: Duality for Semi-Dynamical Systems. Potential Theory - ICPT94, Walter de Gruyter, Berlin-New York, 1996, pp.275-286. MR 1404713 | Zbl 0861.31006
[5] Bezzarga M., Moldoveanu E., Secelean N.: Dual resolvent for semidynamical systems. preprint (accessible at:
[6] Bhatia N.P., Hájek O.: Local Semi-Dynamical Systems. Lecture Notes in Math. 90, Springer, Berlin-New York, 1969. MR 0251328
[7] Blumenthal R.M., Getoor R.K.: Markov Processes and Potential Theory. Academic Press, New York and London, 1968. MR 0264757 | Zbl 0169.49204
[8] Boboc N., Bucur Gh., Cornea A.: Order and Convexity in Potential Theory. Lecture Notes in Math. 853, Springer, Berlin, 1981. MR 0613980 | Zbl 0534.31001
[9] Boboc N., Bucur Gh.: Potential theory on ordered sets II. Rev. Roumaine Math. Pures Appl. 43 (1998), 685-720. MR 1845086 | Zbl 0995.31008
[10] Dellacherie C., Meyer P.A.: Probabilités et potentiel. Chap. XV, Hermann, Paris, 1987. MR 0488194 | Zbl 0624.60084
[11] Getoor R.K.: Transience and Recurrence of Markov Process. Séminaire de Probabilité XIV 1978-1979, Lecture Notes in Math. 784, Springer, Berlin, 1980, pp.397-409. MR 0580144
[12] Hájek O.: Dynamical Systems in the Plane. Academic Press, London-New York, 1968. MR 0240418
[13] Saperstone S.H.: Semidynamical Systems in Infinite Dimensional Space. App. Math. Sciences 37, Springer, New York-Berlin, 1981. MR 0638477
[14] Sharpe M.: General Theory of Markov Process. Pure and Applied Mathematics, 133, Academic Press, Inc., Boston, MA, 1988. MR 0958914
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