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Asymptotics of solutions of differential equations on complex varieties. (English. Russian original) Zbl 0693.58027
Math. USSR, Sb. 65, No. 2, 385-422 (1990); translation from Mat. Sb., Nov. Ser. 137(179), No. 3(11), 381-416 (1988).
This paper deals with global asymptotics of the solutions of partial differential equations on complex manifolds. The same problem was considered and solved in the sixties on real manifolds by using the machinery of the classical pseudodifferential operators and the Fourier- Maslov integral operators / the method of Maslov’s canonical operator. The paper under consideration is an analogue of Maslov’s theory on complex manifolds. To develop the new theory an analogue of the classical Fourier transformation is introduced by the authors in the class of multivalued analytic functions. In the last §4 interesting results concerning the asymptotic expansion of the solutions of some classes of linear partial differential equations having holomorphic coefficients are proved.
Reviewer: P.Popivanov
MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
35B40 Asymptotic behavior of solutions to PDEs
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