Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., J. Math. Sci., New York 270, No. 4, 507--530 (2023; Zbl 1512.35066); translation from Probl. Mat. Anal. 122, 5--24 (2023) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 214, No. 1, 1--23 (2023; Zbl 1519.35061); translation from Teor. Mat. Fiz. 214, No. 1, 3--29 (2023) Full Text: DOI
Nazaikinskii, V. E.; Savin, A. Yu. On semiclassical asymptotics for nonlocal equations. (English) Zbl 1512.35412 Russ. J. Math. Phys. 29, No. 4, 568-575 (2022). MSC: 35P05 53D12 58J40 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} and \textit{A. Yu. Savin}, Russ. J. Math. Phys. 29, No. 4, 568--575 (2022; Zbl 1512.35412) Full Text: DOI
Nazaikinskii, V. E.; Tolchennikov, A. A. Constructive implementation of semiclassical asymptotic formulas in a neighborhood of a generic caustic cusp. (English) Zbl 1514.53119 Russ. J. Math. Phys. 29, No. 4, 558-567 (2022). MSC: 53D12 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} and \textit{A. A. Tolchennikov}, Russ. J. Math. Phys. 29, No. 4, 558--567 (2022; Zbl 1514.53119) Full Text: DOI
Nazaikinskii, V. E. Canonical operator on punctured Lagrangian manifolds and commutation with pseudodifferential operators: local theory. (English. Russian original) Zbl 1505.35378 Math. Notes 112, No. 5, 709-725 (2022); translation from Mat. Zametki 112, No. 5, 733-751 (2022). MSC: 35S05 53D12 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 112, No. 5, 709--725 (2022; Zbl 1505.35378); translation from Mat. Zametki 112, No. 5, 733--751 (2022) Full Text: DOI
Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 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). MSC: 81Q20 35L15 35L45 35S10 53D12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. Math. Surv. 76, No. 5, 745--819 (2021; Zbl 1492.81056); translation from Usp. Mat. Nauk 76, No. 5, 3--80 (2021) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Schafarevich, A. I. Canonical operator on punctured Lagrangian manifolds. (English) Zbl 1462.35480 Russ. J. Math. Phys. 28, No. 1, 22-36 (2021). MSC: 35S05 35Q35 53D12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 28, No. 1, 22--36 (2021; Zbl 1462.35480) Full Text: DOI
Dobrokhotov, Sergei; Nazaikinskii, Vladimir 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). MSC: 81Q20 35L80 81S10 53D12 53D22 PDFBibTeX XMLCite \textit{S. Dobrokhotov} and \textit{V. Nazaikinskii}, in: Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 -- July 6, 2019. Cham: Birkhäuser. 187--195 (2020; Zbl 1472.81099) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 108, No. 3, 318--338 (2020; Zbl 1483.53094); translation from Mat. Zametki 108, No. 3, 334--359 (2020) Full Text: DOI
Nazaikinskii, V. E.; Shafarevich, A. I. 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 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} and \textit{A. I. Shafarevich}, Math. Notes 106, No. 3, 402--411 (2019; Zbl 1432.35025); translation from Mat. Zametki 106, No. 3, 424--435 (2019) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. 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 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Differ. Equ. 55, No. 5, 644--657 (2019; Zbl 1418.37094); translation from Differ. Uravn. 55, No. 5, 660--672 (2019) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Efficient formulas for the Maslov canonical operator near a simple caustic. (English) Zbl 1406.81036 Russ. J. Math. Phys. 25, No. 4, 545-552 (2018). MSC: 81Q20 53D12 34L40 70H15 81-08 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 25, No. 4, 545--552 (2018; Zbl 1406.81036) Full Text: DOI
Nazaikinskii, V. E.; Shafarevich, A. I. 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). MSC: 35B40 53D20 47F05 53D12 35A18 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} and \textit{A. I. Shafarevich}, Dokl. Math. 97, No. 2, 177--180 (2018; Zbl 1407.35028); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 479, No. 6, 611--615 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds. (English) Zbl 1376.37114 Russ. J. Math. Phys. 24, No. 1, 127-133 (2017). MSC: 37K60 53D12 35S10 39A12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 24, No. 1, 127--133 (2017; Zbl 1376.37114) Full Text: DOI
Dobrokhotov, Sergei Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. 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). MSC: 81Q20 53D12 35C20 35S30 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Izv. Math. 81, No. 2, 286--328 (2017; Zbl 1369.81033); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 2, 53--96 (2017) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I. 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). Reviewer: Sönke Hansen (Paderborn) MSC: 53D12 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Dokl. Math. 93, No. 1, 99--102 (2016; Zbl 1345.53083); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 6, 641--644 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Makrakis, G.; Nazaikinskii, V. E. 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 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Transl., Ser. 2, Am. Math. Soc. 233, 95--115 (2014; Zbl 1320.81058) Full Text: arXiv
Nazaikinskii, V. E. 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). Reviewer: Chengbo Wang (Hangzhou) MSC: 53D12 35L05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 96, No. 2, 248--260 (2014; Zbl 1330.53108); translation from Mat. Zametki 96, No. 2, 261--276 (2014) Full Text: DOI
Nazaikinskii, V. E. On the representation of localized functions in \(\mathbb R^2\) by the Maslov canonical operator. (English. Russian original) Zbl 1320.53100 Math. Notes 96, No. 1, 99-109 (2014); translation from Mat. Zametki 96, No. 1, 88-100 (2014). MSC: 53D12 35L05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 96, No. 1, 99--109 (2014; Zbl 1320.53100); translation from Mat. Zametki 96, No. 1, 88--100 (2014) Full Text: DOI
Nazaikinskij, V. E.; Sternin, B. Yu.; Shatalov, V. E.; Schulze, B.-W. 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 PDFBibTeX XMLCite \textit{V. E. Nazaikinskij} et al., Dokl. Math. 60, No. 1, 447--450 (1999; Zbl 0971.53049); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 367, No. 4, 447--450 (1999)
Nazaikinskij, Vladimir; Sternin, Boris 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). Reviewer: Dmitry Kalinin (Kazan’) MSC: 58Z05 83C57 53B30 83C75 PDFBibTeX XMLCite \textit{V. Nazaikinskij} and \textit{B. Sternin}, Math. Appl., Dordr. 433, 47--69 (1998; Zbl 0915.58108)
Nazaĭkinskiĭ, V. E.; Sternin, B. Yu.; Shatalov, V. E. 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). Reviewer: J.Eichhorn (Greifswald) MSC: 58J40 37J55 58J60 53C15 PDFBibTeX XMLCite \textit{V. E. Nazaĭkinskiĭ} et al., Russ. Math. Surv. 48, No. 3, 1 (1993; Zbl 0826.58037); translation from Usp. Mat. Nauk 48, No. 3(291), 97--134 (1993) Full Text: DOI
Nazaĭkinskiĭ, V. E.; Shatalov, V. E.; Sternin, B. Yu. Contact geometry and linear differential equations. (English) Zbl 0813.58003 De Gruyter Expositions in Mathematics. 6. Berlin etc.: W. de Gruyter. ix, 216 p. (1992). Reviewer: W.Mozgawa (Lublin) MSC: 58-02 58J40 37J55 53D10 58C35 PDFBibTeX XMLCite \textit{V. E. Nazaĭkinskiĭ} et al., Contact geometry and linear differential equations. Berlin etc.: W. de Gruyter (1992; Zbl 0813.58003)