  We construct a linear response theory of applying shear deformations from
boundary walls in the film geometry in Kubo's theoretical scheme. Our method is
applicable to any solids and fluids. For glasses, we assume quasi-equilibrium
around a fixed inherent state. Then, we obtain linear-response expressions for
any variables including the stress and the particle displacements, even though
the glass interior is elastically inhomogeneous. In particular, the shear
modulus can be expressed in terms of the correlations between the interior
stress and the forces from the walls. It can also be expressed in terms of the
inter-particle correlations, as has been shown in the previous literature. Our
stress relaxation function includes the effect of the boundary walls and can be
used for inhomogeneous flow response. We show the presence of long-ranged,
long-lived correlations among the fluctuations of the forces from the walls and
the displacements of all the particles in the cell. We confirm these
theoretical results numerically in a two-dimensional model glass. As an
application, we describe propagation of transverse sounds after boundary wall
motions using these time-correlation functions We also find resonant sound
amplification when the frequency of an oscillatory shear approaches that of the
first transverse sound mode.
