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60j45 (primary)

Bulletin of the London Mathematical Society (1)

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ON THE TIGHTNESS OF CAPACITIES ASSOCIATED WITH SUB-MARKOVIAN RESOLVENTS
LUCIAN BEZNEA, NICU BOBOC
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 6 / December 2005

Published online by Cambridge University Press:

12 December 2005, pp. 899-907

Print publication:

December 2005
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This paper investigates the tightness property of the capacity induced by the reduction operator with respect to the resolvent of a right Markov process. Tightness is verified in two particular situations: under the ‘weak duality hypothesis’, and if a substitute for ‘the axiom of polarity for the dual theory’ holds. In the second context, the quasi-continuity property for the excessive functions is derived. These are extensions and improvements of results of Lyons and Röckner, Ma and Röckner, Le Jan, and Fitzsimmons, mainly obtained in the context of Dirichlet forms.