Symmetric harmonic groups and translation invariant Dirichlet spaces

Central Gaussian Convolution Semigroups on Compact Groups: A Survey

“…Properties (AC) and (CK) are very natural properties to consider. The importance of properties such as (CK * ) and (CK#) first appeared in the early work of Forst [31], Berg [21,23,24] and Bendikov [1,2]. These properties play an essential role in what follows.…”

“…Three early references relevant to the subject of this paper are [31,34,44]. Heyer's book [36] is a thorough introduction to the fundamental objects that we will discuss in this survey, i.e., Brownian motions and Gaussian convolutions semigroups on compact connected groups.…”

On Brownian and Poissonian convolution semigroups on the infinite dimensional torus

“…On account of the paper [3] by Forst it is interesting to know under which conditions ~'~ p~ is finite and continuous on T* "-,{0}.…”

Potential theory on the infinite dimensional torus

“…In [9] Forst considered the problem of constructing a harmonic group from a special Dirichlet space in the case of the base space being a locally compact abelian group G. The Dirichlet space is given in terms of a symmetric convolution semigroup on G, which in turn is the transition semigroup of a Hunt process on G. Then Forst proves that if the convolution semigroup satisfies certain axioms (cf. Theorem 1.12 below), then the harmonic functions defined in terms of the Hunt process satisfy the axioms of a harmonic group.…”