Homogenization Method for Problems on Quasiclassical Asymptotics

The homogenization method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations. Algebras of locally averaged functions are studied, a homogenization theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation.