zbMATH — the first resource for mathematics

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).

35S99 Pseudodifferential operators and other generalizations of partial differential operators
53A55 Differential invariants (local theory), geometric objects
47Gxx Integral, integro-differential, and pseudodifferential operators
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.