In this short blog post, we study to what extent the Poisson integral of continuous functions on the Furstenberg boundary 
of a symmetric space of non-compact type can be extended continuously to the whole Karpelevich boundary or what parts thereof it can be extended. The interest in such integrals comes from the fact that the Poisson integrals of functions in 
exhaust all bounded harmonic functions on 
, a deep result of Furstenberg. The study of such extensions hence has its origins in classical harmonic analysis and solutions to Dirichlet problems on the Poincare disk.
Microblog for personal use