  The purpose of this paper is to find optimal estimates for the Green function
and the Poisson kernel for a half-line and intervals of the geometric stable
process with parameter $\alpha\in(0,2]$. This process has an infinitesimal
generator of the form
  $-\log(1+(-\Delta)^{\alpha/2})$. As an application we prove the scale
invariant Harnack inequality as well as the boundary Harnack principle.
