Some aspects of poisson transform on homogeneous trees

Abstract

In this thesis we study certain properties of the eigenfunctions of the Laplacian and their application in harmonic analysis on homogeneous trees The topics we study in the thesis are the following First we characterize all eigenfunctions of the Laplacian on homogeneous trees which are the Poisson transform of L p functions defined on the boundary Using the duality argument we also prove the restriction theorem for the Helgason Fourier transforms on a homogeneous tree In 1980 J...