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Perturbation of Dirichlet forms by measures. (English) Zbl 0861.31004

This paper studies the perturbation of Dirichlet forms \({\mathfrak h}\) by measures \(\mu\). In this paper, the authors defined the perturbed form \({\mathfrak h}-\mu_-+ \mu_+\) for \(\mu_-\) in a suitable Kato class and \(\mu_+\) absolutely continuous with respect to the capacity.
The main results of the paper are: (1) if the unperturbed semigroup has \(L_p\)-\(L_q\)-smoothing properties then the perturbed semigroup also has the properties; and (2) if the unperturbed semigroup is holomorphic in \(L_1\) then, for a larger class of measures \(\mu\), the perturbed semigroup also has the same property.

MSC:

31C25 Dirichlet forms
47D07 Markov semigroups and applications to diffusion processes
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