Characteristic matrix of a periodically inhomogeneous layer

We propose an analytic representation of the characteristic matrix of a periodically inhomogeneous layer; the characteristic matrix of the homogenized medium is defined and it is shown that the structure of characteristic matrix of transversely isotropic media coincides with the structure of the characteristic matrix of a layered inhomogeneous isotropic medium.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 177–181, 1987.