  In this paper, we consider the one-sided shift space on finitely many symbols
and extend the theory of what is known as rough analysis. We define difference
operators on an increasing sequence of subsets of the shift space that would
eventually render the Laplacian on the space of real-valued continuous
functions on the shift space. We then define the Green's function and the
Green's operator that come in handy to solve the analogue to the Dirichlet
boundary value problem on the shift space.
