In this very short post, we look at the properties of a certain bump function of the collection of all geodesic rays emanating from a fixed point 
towards irregular points on the geodesic boundary 
of a non-compact symmetric space
Notes on polar coordinates for symmetric spaces
In this short blog post, we are going to introduce a “coordinate system” on Riemannian symmetric spaces called polar coordinates, that arise as an immediate consequence of Cartan’s decomposition theorem. The quotation marks are due to the fact that we have some choice in how to express a point in these coordinates.
Continue reading “Notes on polar coordinates for symmetric spaces”Karpelevich’s compactification and extensions of Poisson integrals
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.