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Some problems on Markov semigroups. (English) Zbl 0854.47027
Demuth, Michael (ed.) et al., Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras. Berlin: Akademie Verlag. Math. Top. 11, 163-217 (1996).
Summary: We present the perturbation theory for generators of Markov semigroups acting on $$L^p$$. The domain of the generator of Markov semigroups is characterized by means of the domain of the quadratic form. For the particular case of Markov perturbations the well known KLMN-theorem is extended to the $$L^p$$-spaces. We also investigate the analyticity and integral properties of the perturbed semigroups and obtain some useful inequalities for generators and semigroups. Several classes of perturbations of Markov generators are considered. Some applications to second order elliptic operators are given. We discuss also the uniqueness problem for the case of generators of Markov semigroups perturbed by potentials.
For the entire collection see [Zbl 0847.00012].

##### MSC:
 47D07 Markov semigroups and applications to diffusion processes