Geodesic
On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 425-439

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The authors discuss a scheme proposed by V. P. Maslov for constructing combined (with respect to smoothness and a small parameter $h$) asymptotics of the solution of the Cauchy problem for $h$-pseudodifferential equations. The exposition is carried out by means of examples of equations for the oscillations of a crystal lattice and for water waves. The main attention is given to the isolation of the leading term of the asymptotics. A number of estimates are proved for the remainders in formulas for the action of an $h$-pseudodifferential operator on the exponential function, with respect to smoothness and the parameter. Bibliography: 9 titles 
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     author = {V. G. Danilov and P. N. Zhevandrov},
     title = {On {Maslov's} method for constructing combined asymptotics for $h$-pseudodifferential equations},
     journal = {Izvestiya. Mathematics },
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     volume = {34},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a10/}
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V. G. Danilov; P. N. Zhevandrov. On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 425-439. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a10/