Abstract:
On the basis of the stationary phase method for oscillatory integrals with complex phase function, the authors prove the coincidence of Fourier integral operators and Maslov's canonical operator.
Bibliography: 17 titles.
\Bibitem{DanLe 79}
\by V.~G.~Danilov, Le Vu An'
\paper On Fourier integral operators
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 3
\pages 293--334
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This publication is cited in the following 9 articles:
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions”, Math. Notes, 103:5 (2018), 33–43
K.J.A. Reijnders, D.S. Minenkov, M.I. Katsnelson, S.Yu. Dobrokhotov, “Electronic optics in graphene in the semiclassical approximation”, Annals of Physics, 397 (2018), 65
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. Math., 81:2 (2017), 286–328
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Maslov's canonical operator in arbitrary coordinates on the Lagrangian manifold”, Dokl. Math., 93:1 (2016), 99
S. Yu. Dobrokhotov, G. N. Makrakis, V. E. Nazaikinskii, “Maslov's canonical operator, Hörmander's formula, and localization of the Berry–Balazs solution in the theory of wave beams”, Theoret. and Math. Phys., 180:2 (2014), 894–916
Dobrokhotov S., Zhevandrov P., “Asymptotic Expansions and the Maslov Canonical Operator in the Linear Theory of Water Waves. I. Main Constructions and Equations for Surface Gravity Waves”, Russ. J. Math. Phys., 10:1 (2003), 1–31
M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205
V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42
V. E. Nazaikinskii, V. G. Oshmyan, B. Yu. Sternin, V. E. Shatalov, “Fourier integral operators and the canonical operator”, Russian Math. Surveys, 36:2 (1981), 93–161
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