Duality and integral representation for excessive measures (Q1204279)

The author generalizes results that treat the integral representation of excessive measures with respect to a given substochastic resolvent. She proves that there exists a unique integral representation over extremal excessive measures if either the underlying state space is a Radon space or the excessive measure is supported on a standard Borel subset or the resolvent is proper and absolutely continuous with respect to a \(\sigma\)- finite measure. For the proof the excessive measure is decomposed into a dissipative and a conservative measure and each case is handled separately, the first one using a duality result that characterizes the linear functionals induced by the energy functional and all bounded excessive measures.