Abstract.
Given a locally compact group G acting on a locally compact space X and a probability measure σ on G, a real Borel function f on X is called σ-harmonic if it satisfies the convolution equation . We give conditions for the absence of nonconstant bounded harmonic functions. We show that, if G is a union of σ-admissible neighbourhoods of the identity, relative to X, then every bounded σ-harmonic function on X is constant. Consequently, for spread out σ, the bounded σ-harmonic functions are constant on each connected component of a [SIN]-group and, if G acts strictly transitively on a splittable metric space X, then the bounded σ-harmonic functions on X are constant which extends Furstenberg’s result for connected semisimple Lie groups.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
(Received 13 June 1998; in revised form 31 March 1999)
Rights and permissions
About this article
Cite this article
Chu, CH., Leung, CW. Harmonic Functions on Homogeneous Spaces. Mh Math 128, 227–235 (1999). https://doi.org/10.1007/s006050050060
Issue Date:
DOI: https://doi.org/10.1007/s006050050060