Geodesic
Averaging method for problems on quasiclassical asymptotics
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 53-76

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The averaging 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, an averaging theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation.
Keywords: averaging methods, rapidly oscillating coefficients, quasiclassical asymptotics, algebras of locally averaged functions. 
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     title = {Averaging method for problems on quasiclassical asymptotics},
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S. Yu. Dobrokhotov; V. E. Nazaikinskii. Averaging method for problems on quasiclassical asymptotics. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 53-76. http://geodesic.mathdoc.fr/item/CMFD_2024_70_1_a4/