  The exact Green's functions of a finite-size Luttinger Liquid (LL) connected
to impedances are computed at zero and finite temperature. Bosonization for a
LL with Impedance boundary conditions (IBC) is proven to hold. The LL with open
boundary conditions (for both Neumann and Dirichlet cases) is explicitly
recovered as a special limit when one has infinite impedances. Additionally
when the impedances are equal to the characteristic impedance of the Luttinger
liquid then the finite Luttinger liquid is shown to be effectively equivalent
to an infinite Luttinger liquid.
