Abstract
We study positive continuous additive functionals of diffusion processes associated with Dirichlet forms. We also give necessary and sufficient conditions for a Feynman-Kac semigroup associated with a signed Borel measure to be a strongly continuous semigroup in the relevant L 2-space. We characterize their generators as second order partial differential operators with zero order term (potential) given by a signed measure (which can be so singular as to be nowhere Radon). We also discuss preservation of p-boundedness and L p -smoothing properties of semigroups under perturbations. We also study integral kernels of Feynman-Kac semigroups and provide upper bounds for them.
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Albeverio, S., Blanchard, P., Ma, Z. (1991). Feynman-Kac semigroups in terms of signed smooth measures. In: Hornung, U., Kotelenez, P., Papanicolaou, G. (eds) Random Partial Differential Equations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6413-8_1
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