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Found 23 Documents (Results 1–23)

Uniformization and semiclassical asymptotics for a class of equations degenerating on the boundary of a manifold. (English. Russian original) Zbl 1512.35066

J. Math. Sci., New York 270, No. 4, 507-530 (2023); translation from Probl. Mat. Anal. 122, 5-24 (2023).
MSC:  35B40 53D12 76B15
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Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides. (English. Russian original) Zbl 1519.35061

Theor. Math. Phys. 214, No. 1, 1-23 (2023); translation from Teor. Mat. Fiz. 214, No. 1, 3-29 (2023).
MSC:  35C20 35S05 53D12
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Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. (English. Russian original) Zbl 1492.81056

Russ. Math. Surv. 76, No. 5, 745-819 (2021); translation from Usp. Mat. Nauk 76, No. 5, 3-80 (2021).
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Fock quantization of canonical transformations and semiclassical asymptotics for degenerate problems. (English) Zbl 1472.81099

Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 – July 6, 2019. Cham: Birkhäuser. Trends Math., 187-195 (2020).
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Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. (English. Russian original) Zbl 1483.53094

Math. Notes 108, No. 3, 318-338 (2020); translation from Mat. Zametki 108, No. 3, 334-359 (2020).
MSC:  53D12 41A60
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Maslov’s canonical operator in problems on localized asymptotic solutions of hyperbolic equations and systems. (English. Russian original) Zbl 1432.35025

Math. Notes 106, No. 3, 402-411 (2019); translation from Mat. Zametki 106, No. 3, 424-435 (2019).
MSC:  35B40 58J40 53D12
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Asymptotic eigenfunctions of the operator \(\nabla D(x)\nabla\) defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls. (English. Russian original) Zbl 1418.37094

Differ. Equ. 55, No. 5, 644-657 (2019); translation from Differ. Uravn. 55, No. 5, 660-672 (2019).
MSC:  37J35 37J05 37D50 53D12 53D25 35P05
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Analogue of Maslov’s canonical operator for localized functions and its applications to the description of rapidly decaying asymptotic solutions of hyperbolic equations and systems. (English. Russian original) Zbl 1407.35028

Dokl. Math. 97, No. 2, 177-180 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 479, No. 6, 611-615 (2018).
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New integral representations of the Maslov canonical operator in singular charts. (English. Russian original) Zbl 1369.81033

Izv. Math. 81, No. 2, 286-328 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 2, 53-96 (2017).
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Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. (English. Russian original) Zbl 1345.53083

Dokl. Math. 93, No. 1, 99-102 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 6, 641-644 (2016).
MSC:  53D12 81Q20
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Fourier integrals and a new representation of Maslov’s canonical operator near caustics. (English) Zbl 1320.81058

Khruslov, E. (ed.) et al., Spectral theory and differential equations: V. A. Marchenko’s 90th anniversary collection. Providence, RI: American Mathematical Society (AMS); (ISBN 978-1-4704-1683-6/hbk). Translations. Series 2. American Mathematical Society 233; Advances in the Mathematical Sciences 66, 95-115 (2014).
MSC:  81Q20 35S30 53D12
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The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary. (English. Russian original) Zbl 1330.53108

Math. Notes 96, No. 2, 248-260 (2014); translation from Mat. Zametki 96, No. 2, 261-276 (2014).
MSC:  53D12 35L05
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Quantization of canonical transformations on manifolds with conic singularities. (English. Russian original) Zbl 0971.53049

Dokl. Math. 60, No. 1, 73-76 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 367, No. 4, 447-450 (1999).
MSC:  53D50
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Wave packet transform in symplectic geometry and asymptotic quantization. (English) Zbl 0915.58108

Komrakov, B. P. (ed.) et al., Lie groups and Lie algebras. Their representations, generalisations and applications. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 433, 47-69 (1998).
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Contact geometry and linear differential equations. (English. Russian original) Zbl 0826.58037

Russ. Math. Surv. 48, No. 3, 93-132 (1993); translation from Usp. Mat. Nauk 48, No. 3(291), 97-134 (1993).
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