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Quasi-invertibility of functions of ordered operators in the theory of pseudodifferential equations. (English. Russian original) Zbl 0402.35094
J. Sov. Math. 7, 695-795 (1977); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 6, 5-132 (1976).

##### MSC:
 35S99 Pseudodifferential operators and other generalizations of partial differential operators 53A55 Differential invariants (local theory), geometric objects 47Gxx Integral, integro-differential, and pseudodifferential operators
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##### References:
 [1] V. M. Babich and V. S. Buldyrev, Asymptotic Methods for Short-Wave Diffraction Problems. Calibration Problems [in Russian], Nauka, Moscow (1972). [2] B. Blombergen, Nonlinear Optics [Russian translation], Mir, Moscow (1973). [3] V. G. Danilov, ?Mesh functions and Kotel’nikov’s theorem,? Moscow Institute of Electronic and Mechanical Engineering, Moscow (1974). [4] S. Yu. Dobrokhotov and V. P. Maslov, ?Some applications of the theory of the complex germ to equations with a small parameter,? in: Progress in Science and Technology. Contemporary Problems of Mathematics [in Russian], Vol. 5, VINITI Akad. Nauk SSSR, Moscow (1975), pp. 141?211. [5] V. V. Kucherenko, ?Asymptotic solutions of equations with complex characteristics,? Matem. Sb.,95, No. 2, 163?213 (1974). · Zbl 0311.35007 [6] V. V. Kucherenko, ?Asymptotics of the solution of the system $$A\left( {x,---ih \frac{\partial }{{\partial x}}} \right)u = 0$$ for h?0 in the case of characteristics of variable multiplicity,? Izv. Akad. Nauk SSSR, Ser. Matem.,38, No. 3, 625?662 (1974). [7] V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973). [8] V. P. Maslov, ?The canonical operator on a Lagrangian manifold with a complex germ and a regularizer for pseudodifferential operators and difference schemes,? Dokl. Akad. Nauk SSSR,195, No. 3, 551?554 (1970). · Zbl 0217.41902 [9] F. Treves, ?Hypoelliptic partial differential equations of principal type. Sufficient conditions and necessary conditions,? Commun. Pure and Appl. Math.,24, No. 5, 631?670 (1971). · Zbl 0234.35019 · doi:10.1002/cpa.3160240504
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