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Bernsteins theorem for completely excessive measures

  • Hedi Ben Saad (a1) and Klaus Janßen (a2)
Extract

Bernstein’s theorem states that the following properties are equivalent for a function ψ:]0, ∞ [→ R (which then is called completely monotone):

moreover, the measure σ in iii) is uniquely determined.

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References
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[1] Ben Saad, H., Janßen, K., A characterization of parabolic potential theory, Math. Ann., 272 (1985), 281289.
[2] Berg, C., Christensen, J. P. R., Ressel, P., Harmonic analysis on semigroups, New York-Berlin-Heidelberg-Tokyo, Springer, 1984.
[3] Berg, C., Forst, G., Potential theory on locally compact abelian groups, Berlin-Heidelberg-New York, Springer, 1975.
[4] Beznea, L., Ultrapotentials and positive eigenfunctions for an absolutely continuous resolvent of kernels, Nagoya Math. J., 112 (1988), 125142.
[5] Boboc, N., Bucur, G., Cornea, A., Order and convexity in potential theory, Lecture notes in math., 853, Berlin-Heidelberg-New York, Springer, 1981.
[6] Dellacherie, C., Meyer, P. A., Probabilités et potentiel, Chap. I à IV. Paris, Hermann, 1975.
[7] Dellacherie, C., Meyer, P. A., Probabilités et potentiel, Chap. XII à XVI. Paris, Hermann, 1987.
[8] Getoor, R. K., On the construction of kernels, Séminaire de Prob. de Strasbourg IX, 443463, Lecture notes in math., 465. Berlin-Heidelberg-New York, Springer, 1975.
[9] Itô, M., Positive eigen elements for an infinitesimal generator of a diffusion semigroup and their integral representations, Potential theory Copenhagen 1979, 163184. Lecture notes in math., 787, Berlin-Heidelberg-New York, Springer, 1980.
[10] Itô, M., Suzuki, N., Completely superharmonic measures for the infinitesimal generator A of a diffusion semigroup and positive eigen elements of A, Nagoya Math. J., 83 (1981), 53106.
[11] Janßen, K., Representation of excessive measures, Seminar on stochastic processes 1986, 85105. Progress in probability and statistics, vol. 13. Boston-Basel-Stuttgart, Birkhäuser, 1987.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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