Chernyshev, V. L.; Nazaikinskii, V. E.; Tsvetkova, A. V. Lattice equations and semiclassical asymptotics. (English) Zbl 1528.81142 Russ. J. Math. Phys. 30, No. 2, 152-164 (2023). MSC: 81Q20 58J37 81R30 14M17 05C05 81Q30 PDFBibTeX XMLCite \textit{V. L. Chernyshev} et al., Russ. J. Math. Phys. 30, No. 2, 152--164 (2023; Zbl 1528.81142) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Homogenization of the Cauchy problem for the wave equation with rapidly varying coefficients and initial conditions. (English) Zbl 1501.35031 Manuilov, Vladimir M. (ed.) et al., Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6–9, 2018. Cham: Birkhäuser. Trends Math., 77-102 (2021). MSC: 35B27 35L05 35L15 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, in: Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6--9, 2018. Cham: Birkhäuser. 77--102 (2021; Zbl 1501.35031) 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.; Minenkov, D. S.; Nazaikinskii, V. E. Representation of Bessel functions by the Maslov canonical operator. (English. Russian original) Zbl 1471.81033 Theor. Math. Phys. 208, No. 2, 1018-1037 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 196-217 (2021). MSC: 81Q20 81S08 33C10 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 208, No. 2, 1018--1037 (2021; Zbl 1471.81033); translation from Teor. Mat. Fiz. 208, No. 2, 196--217 (2021) 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. Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. (English. Russian original) Zbl 1450.35119 Comput. Math. Math. Phys. 60, No. 8, 1348-1360 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394-1407 (2020). MSC: 35G10 35Q35 35Q41 35Q61 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Comput. Math. Math. Phys. 60, No. 8, 1348--1360 (2020; Zbl 1450.35119); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394--1407 (2020) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. (English. Russian original) Zbl 1441.81091 Theor. Math. Phys. 201, No. 3, 1742-1770 (2019); translation from Teor. Mat. Fiz. 201, No. 3, 382-414 (2019). MSC: 81Q10 81Q20 33C10 34L40 34E10 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 201, No. 3, 1742--1770 (2019; Zbl 1441.81091); translation from Teor. Mat. Fiz. 201, No. 3, 382--414 (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
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
Minenkov, D. S.; Nazaĭkinskiĭ, V. E.; Chernyshev, V. L. On the Bose-Maslov statistics in the case of infinitely many degrees of freedom. (English. Russian original) Zbl 1357.11095 Dokl. Math. 93, No. 3, 326-328 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 468, No. 6, 618-621 (2016). Reviewer: Piotr Garbaczewski (Opole) MSC: 11N80 11P70 11P82 11B75 81Q35 82C20 PDFBibTeX XMLCite \textit{D. S. Minenkov} et al., Dokl. Math. 93, No. 3, 326--328 (2016; Zbl 1357.11095); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 468, No. 6, 618--621 (2016) Full Text: DOI
Maslov, V. P.; Nazaikinskii, V. E. Disinformation theory for bosonic computational media. (English) Zbl 1349.82022 Math. Notes 99, No. 6, 895-900 (2016). MSC: 82B30 81P45 PDFBibTeX XMLCite \textit{V. P. Maslov} and \textit{V. E. Nazaikinskii}, Math. Notes 99, No. 6, 895--900 (2016; Zbl 1349.82022) 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
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E. Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. (English. Russian original) Zbl 1323.81031 Theor. Math. Phys. 180, No. 2, 894-916 (2014); translation from Teor. Mat. Fiz. 180, No. 2, 162-188 (2014). MSC: 81Q05 35C05 35Q41 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 180, No. 2, 894--916 (2014; Zbl 1323.81031); translation from Teor. Mat. Fiz. 180, No. 2, 162--188 (2014) Full Text: DOI
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya. New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. (English. Russian original) Zbl 1298.81091 Theor. Math. Phys. 177, No. 3, 1579-1605 (2013); translation from Teor. Mat. Fiz. 177, No. 3, 355-386 (2013). MSC: 81Q20 81Q05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 177, No. 3, 1579--1605 (2013; Zbl 1298.81091); translation from Teor. Mat. Fiz. 177, No. 3, 355--386 (2013) Full Text: DOI arXiv
Dobrokhotov, Sergey; Minenkov, Dmitrii; Nazaikinskii, Vladimir; Tirozzi, Brunello Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. (English) Zbl 1263.35154 Karlovich, Yuri I. (ed.) et al., Operator theory, pseudo-differential equations, and mathematical physics. The Vladimir Rabinovich anniversary volume. Dedicated to his 70th birthday. Basel: Birkhäuser (ISBN 978-3-0348-0536-0/hbk; 978-3-0348-0537-7/ebook). Operator Theory: Advances and Applications 228, 95-125 (2013). MSC: 35L15 35L05 81Q20 35Q35 PDFBibTeX XMLCite \textit{S. Dobrokhotov} et al., Oper. Theory: Adv. Appl. 228, 95--125 (2013; Zbl 1263.35154) Full Text: DOI arXiv
Katsnelson, M. I.; Nazaikinskii, V. E. The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions. (English. Russian original) Zbl 1282.82064 Theor. Math. Phys. 172, No. 3, 1263-1277 (2012); translation from Teor. Mat. Fiz. 172, No. 3, 437-453 (2012). MSC: 82D80 81Q05 37B30 PDFBibTeX XMLCite \textit{M. I. Katsnelson} and \textit{V. E. Nazaikinskii}, Theor. Math. Phys. 172, No. 3, 1263--1277 (2012; Zbl 1282.82064); translation from Teor. Mat. Fiz. 172, No. 3, 437--453 (2012) Full Text: DOI arXiv Link
Maslov, V. P.; Nazaikinskii, V. E. On the distribution of integer random variables related by a certain linear inequality. I. (English) Zbl 1150.82017 Math. Notes 83, No. 2, 211-237 (2008); translation from Mat. Zametki 83, No. 2, 232-263 (2008). MSC: 82B05 60K35 62P35 81P20 82C05 82C41 PDFBibTeX XMLCite \textit{V. P. Maslov} and \textit{V. E. Nazaikinskii}, Math. Notes 83, No. 2, 211--237 (2008; Zbl 1150.82017); translation from Mat. Zametki 83, No. 2, 232--263 (2008) Full Text: DOI
Nazaikinskii, V. E.; Schulze, B. W.; Sternin, B. Y. Quantization methods in differential equations. (English) Zbl 1079.81040 Differential and Integral Equations and Their Applications 3. London: Taylor & Francis (ISBN 0-415-27364-1). xii, 356 p. (2002). MSC: 58J40 58-02 35B40 35Q40 35Q60 47G30 81Q05 81Q20 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} et al., Quantization methods in differential equations. London: Taylor \& Francis (2002; Zbl 1079.81040)
Nazaikinskii, V. E. Semiclassical Lefschetz formulas on smooth and singular manifolds. (English) Zbl 1059.58503 Russ. J. Math. Phys. 6, No. 2, 202-213 (1999). MSC: 58J20 58J40 81Q20 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 6, No. 2, 202--213 (1999; Zbl 1059.58503)
Nazaikinskii, V. E.; Shatalov, V. E.; Sternin, B. Yu. Methods of noncommutative analysis: theory and applications. (English) Zbl 0876.47015 de Gruyter Studies in Mathematics. 22. Berlin: Walter de Gruyter. x, 373 p. (1995). Reviewer: A.Kondrat’ev (Pensacola) MSC: 47A60 47-02 35-02 47-XX 44-XX 81R50 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} et al., Methods of noncommutative analysis: theory and applications. Berlin: Walter de Gruyter (1995; Zbl 0876.47015)
Maslov, V. P.; Nazaĭkinskiĭ, V. E. Algebras with general commutation relations and their applications. I: Pseudodifferential equations with increasing coefficients. (English. Russian original) Zbl 0482.58028 J. Sov. Math. 15, 167-273 (1981); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 13, 5-144 (1979). MSC: 58J40 35B40 47A60 35S05 81Q10 81S05 PDFBibTeX XMLCite \textit{V. P. Maslov} and \textit{V. E. Nazaĭkinskiĭ}, J. Sov. Math. 15, 167--273 (1979; Zbl 0482.58028); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 13, 5--144 (1979) Full Text: DOI
Karasev, M. V.; Nazaĭkinskiĭ, V. E. On the quantization of rapidly oscillating symbols. (English) Zbl 0417.47025 Math. USSR, Sb. 34, 737-764 (1978). MSC: 47G10 47A60 35S10 81T05 PDFBibTeX XMLCite \textit{M. V. Karasev} and \textit{V. E. Nazaĭkinskiĭ}, Math. USSR, Sb. 34, 737--764 (1978; Zbl 0417.47025) Full Text: DOI