A class of Feller semigroups generated by pseudo differential operators.
A homogeneous Dirichlet problem for a nonlinear partial differential equation in an anisotropic Sobolec space.
On generalized Drichlet problems.
Commutator Estimates for Pseudodifferential Operators with Negative Definite Functions as Symbols.
Feller semigroups, Dirchlet forms, and pseudo differential operators.
Examples of non-local time dependent or parabolic Dirichlet spaces
In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To...
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.
We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.
Upper bounds and conservativeness for semigroups associated with a class of Dirichlet forms generated by pseudo differential operators.
On Gardings inequality.
On some translation invariant balayage spaces
It is well known that strong Feller semigroups generate balayage spaces provided the set of their excessive functions contains sufficiently many elements. In this note, we give explicit examples of strong Feller semigroups which do generate balayage spaces. Further we want to point out the role of the generator of the semigroup in the related potential theory.
Some Dirichlet spaces obtained by subordinate reflected diffusions.
In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
Feller semigroups obtained by variable order subordination.
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces
We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) -variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the...
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