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Ultrapotentials and positive eigenfunctions for an absolutely continuous resolvent of kernels

  • Lucian Beznea (a1)
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Let (X, ) be a measurable space and be a submarkovian resolvent of kernels (with the initial kernel V proper) on X which is absolutely continuous and has a dual resolvent (with the same properties) with respect to a σ-finite measure.

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References
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[1] Boboc, N., Bucur, Gh. and Cornea, A., Order and convexity in potential theory: H-cones, Lecture Notes in Math., 853, Springer, Berlin-Heidelberg-New York, 1981.
[2] Boboc, N. and Musţafã, P., Fonctions complètement surharmoniques associées aux operateurs différentiels de second ordre du type elliptique, Ann. Fac. Sci. de Kinshasa, Zaire; Section Math-Phys., 1 (1975), 249281.
[3] Boboc, N. and Nkomba-Tshola, M. M., Eléments complètement excessifs par rapport à une résolvante, Ann. Fac. Sci. de Kinshasa, Zair; Section Math.-Phys., 2 (1976), 130.
[4] Choquet, G., Deux exemples classiques de représentation intégral, Enseignement Math., 15 (1969), 6375.
[5] Constantinescu, C. and Cornea, A., Potential theory on harmonie spaces, Springer, Berlin-Heidelberg-New York, 1972.
[6] Itô, M., Positive eigen elements for an infinitesimal generator of a diffusion semigroup and their integral representations, In: Potential Theory Copenhagen 1979, Lecture Notes in Math., 787, Springer, 1980.
[7] Itô, M. and Suzuki, N., Completely superharmonic measures for the infinitesimal generator A of a diffusion semi-group and positive eigen elements of A , Nagoya Math. J., 83 (1981), 53106.
[8] Meyer, P.-A., Probability and Potentials, Blaisdell Publishing Comp. 1966.
[9] Meyer, P.-A., Processus de Markov: la frontière de Martin, Lecture Notes in Math., 77, Springer, Berlin-Heidelberg-New York, 1968.
[10] Schaefer, H. H., Banach lattices and positive operators, Springer, Berlin-Heidelberg-New York, 1974.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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