Some aspects of Analysis on symmetric spaces and homogeneous trees: from Radon transform to Bergman spaces

The thesis is focused on the Analysis on two classes of non Euclidean spaces: the symmetric spaces of the noncompact type and the homogeneous trees. I first solve in both the settings the problem of the Unitarization of the Radon transform. The last chapter is devoted to the study of the harmonic Bergman spaces on homogeneous trees.