Perturbation of Dirichlet forms by measures |
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Authors: | Peter Stollmann Jürgen Voigt |
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Institution: | (1) Fachbereich Mathematik, Universität Frankfurt, D-60054 Frankfurt, Germany;(2) Fachrichtung Mathematik, Technische Universität Dresden, D-01062 Dresden, Germany |
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Abstract: | Perturbations of a Dirichlet form
by measures are studied. The perturbed form
––++ is defined for – in a suitable Kato class and + absolutely continuous with respect to capacity. L
p-properties of the corresponding semigroups are derived by approximating – by functions. For treating +, a criterion for domination of positive semigroups is proved. If the unperturbed semigroup has L
p
-L
q
-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic on L
1 the same is shown to be true for the perturbed semigroup, for a large class of measures. |
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Keywords: | Primary 47D07 Secondary 31C25 |
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