Geodesic
Asymptotics of the solution of the system $A(x,-ih\frac\partial{\partial x})$ as~$h\to0$ in the case of characteristics of variable multiplicity
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 631-666.

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In this paper we develop a new asymptotic method for pseudodifferential operators in the case of characteristics of variable multiplicity; the $N$th term of the asymptotics is expressed in terms of an $N$-dimensional integral of a rapidly oscillating function of $(N+n)$ arguments, where $n$ is the dimension of the space ($x=x_1,\dots,x_n$). 
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V. V. Kucherenko. Asymptotics of the solution of the system $A(x,-ih\frac\partial{\partial x})$ as~$h\to0$ in the case of characteristics of variable multiplicity. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 631-666. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a10/

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