Potential theory on infinite products and locally compact groups
The paper is concerned with potential theory on a connected and locally connected locally compact group \(E\) of a countable basis topology. The aim is to study Bauer and Brelot translation invariant harmonic sheaves. The main result of the paper states that any such \(E\) carries an invariant Brelot harmonic sheaf and that every invariant elliptic Bauer harmonic sheaf is in fact a Brelot sheaf if and only if \(E\) is a finite dimensional Lie group. The proof is based upon a study of product diffusions on an infinite product of compact Riemannian manifolds.
infinite product of compact Riemannian manifolds
scientific article; zbMATH DE number 1396417
scientific article