The paper focuses on the L p-Positivity Preservation property (L p-PP for short) on a
Riemannian manifold (M, g). It states that any L p function u with 1< p<+∞, which solves …

This thesis explores the $ L^ 2$-Theory for nonlocal operators of L\'evy type on bounded
domains, as well as their local counterparts. The research was completed at Bielefeld …

We study symmetric diffusion operators on metric measure spaces. Our main question is
whether essential self-adjointness or L p-uniqueness are preserved under the removal of a …

We discuss connections between the essential self-adjointness of a symmetric operator and
the constancy of functions which are in the kernel of the adjoint of the operator. We then …

We give two characterizations for the essential self-adjointness of the weighted Laplacian on
birth-death chains. The first involves the edge weights and vertex measure and is classically …

We prove the equivalence of two different types of capacities in abstract Wiener spaces. This
yields a criterion for the L p-uniqueness of the Ornstein-Uhlenbeck operator and its integer …

The central question discussed in this thesis is whether a given diffusion operators, ie, a
second order linear elliptic differential operator without zeroth order term, which is a priori …