  Symmetric Jacobi matrices on one sided homogeneous trees are studied.
Essential selfadjointness of these matrices turns out to depend on the
structure of the tree. If a tree has one end and infinitely many origin points
the matrix is always essentially selfadjoint independently of the growth of its
coefficients. In case a tree has one origin and infinitely many ends, the
essential selfadjointness is equivalent to that of an ordinary Jacobi matrix
obtained by the restriction to the so called radial functions. For
nonselfadjoint matrices the defect spaces are described in terms of the Poisson
kernel associated with the boundary of the tree.
