High-frequency homogenization of nonstationary periodic equations

In L-2(R), we consider an elliptic differential operator A(e), e >0, of the form A(e) = - d/dx g(x/e) d/dx + e(-2)V(x/e) with periodic coefficients. For the nonstationary Schrodinger equation with the Hamiltonian Ae and for the hyperbolic equation with the operator Ae, analogs of homogenization problems, related to the edges of the spectral bands of the operator A(e), are studied (the so-called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in L-2(R)-norm for small e are obtained.