  Quasiperiodic media is a class of almost periodic media which is generated
from periodic media through a "cut and project" procedure. Bloch waves are
typically defined through a direct integral decomposition of periodic
operators. A suitable direct integral decomposition is not available for almost
periodic operators. To remedy this, we lift an almost periodic operator to a
degenerate periodic operator in higher dimensions. Approximate Bloch waves are
obtained for a regularized version of the degenerate equation. Homogenized
coefficients for quasiperiodic media are determined in terms of the first Bloch
eigenvalue of the regularized lifted equation. A notion of quasiperiodic Bloch
transform is defined and employed to obtain homogenization limit for an
equation with highly oscillating quasiperiodic coefficients.
