Asymptotic methods in differential equations and mathematical physics, asymptotic methods in statistics of many-particle systems, elliptic operators, index theory
Main publications:
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of Maslov's canonical operator in singular charts”, Izv. RAN. Ser. Mat., 81:2 (2017), 53–96
D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators”, Funktsional. Anal. i Prilozhen., 50:4 (2016), 55–75; Funct. Anal. Appl., 50:4 (2016), 291–307
V. E. Nazaikinskii, “The Maslov Canonical Operator on Lagrangian Manifolds in the Phase Space Corresponding to a Wave Equation Degenerating on the Boundary”, Mat. Zametki, 96:2 (2014), 261–276; Math. Notes, 96:2 (2014), 248–260
M. I. Katsnel'son, V. E. Nazaikinskii, “The Aharonov–Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions”, TMF, 172:3 (2012), 437–453; Theoret. and Math. Phys., 172:3 (2012), 1263–1277
V. E. Nazaikinskii, B. Yu. Sternin, “The Index Locality Principle in Elliptic Theory”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 37–52; Funct. Anal. Appl., 35:2 (2001), 111–123
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Averaging method for problems on quasiclassical asymptotics”, CMFD, 70:1 (2024), 53–76
2023
2.
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Nonlinear Effects and Run-up of Coastal Waves Generated by Billiards with Semi-rigid Walls in the Framework of Shallow Water Theory”, Trudy Mat. Inst. Steklova, 322 (2023), 111–123; Proc. Steklov Inst. Math., 322 (2023), 105–117
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides”, TMF, 214:1 (2023), 3–29; Theoret. and Math. Phys., 214:1 (2023), 1–23
V. E. Nazaikinskii, “On an elliptic operator degenerating on the boundary”, Funktsional. Anal. i Prilozhen., 56:4 (2022), 109–112; Funct. Anal. Appl., 56:4 (2022), 324–326
D. S. Minenkov, V. E. Nazaikinskii, T. W. Hilberdink, V. L. Chernyshev, “Restricted partions: the polynomial case”, Funktsional. Anal. i Prilozhen., 56:4 (2022), 80–92; Funct. Anal. Appl., 56:4 (2022), 299–309
V. E. Nazaikinskii, “Canonical Operator on Punctured Lagrangian Manifolds and Commutation with Pseudodifferential Operators: Local Theory”, Mat. Zametki, 112:5 (2022), 733–751; Math. Notes, 112:5 (2022), 709–725
7.
A. Baldare, V. E. Nazaikinskii, A. Yu. Savin, E. Schrohe, “$C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators”, Mat. Zametki, 111:5 (2022), 692–716; Math. Notes, 111:5 (2022), 701–721
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves”, Algebra i Analiz, 33:2 (2021), 5–34; St. Petersburg Math. J., 33:2 (2022), 185–205
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Uspekhi Mat. Nauk, 76:5(461) (2021), 3–80; Russian Math. Surveys, 76:5 (2021), 745–819
S. Yu. Dobrokhotov, D. S. Minenkov, V. E. Nazaikinskii, “Representations of Bessel functions via the Maslov canonical operator”, TMF, 208:2 (2021), 196–217; Theoret. and Math. Phys., 208:2 (2021), 1018–1037
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp”, Mat. Zametki, 108:3 (2020), 334–359; Math. Notes, 108:3 (2020), 318–338
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Uniformization of Equations with Bessel-Type Boundary Degeneration and Semiclassical Asymptotics”, Mat. Zametki, 107:5 (2020), 780–786; Math. Notes, 107:5 (2020), 847–853
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1394–1407; Comput. Math. Math. Phys., 60:8 (2020), 1348–1360
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “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”, Differ. Uravn., 55:5 (2019), 660–672; Differ. Equ., 55:5 (2019), 644–657
V. E. Nazaikinskii, A. I. Shafarevich, “Maslov's Canonical Operator in Problems on Localized Asymptotic Solutions of Hyperbolic Equations and Systems”, Mat. Zametki, 106:3 (2019), 424–435; Math. Notes, 106:3 (2019), 402–411
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Asymptotics, Related to Billiards with Semi-Rigid Walls, of Eigenfunctions of the $\nabla D(x)\nabla$ Operator in Dimension 2 and Trapped Coastal Waves”, Mat. Zametki, 105:5 (2019), 792–797; Math. Notes, 105:5 (2019), 789–794
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Nonstandard Lagrangian Singularities and Asymptotic Eigenfunctions of the Degenerating Operator $-\frac{d}{dx}D(x)\frac{d}{dx}$”, Trudy Mat. Inst. Steklova, 306 (2019), 83–99; Proc. Steklov Inst. Math., 306 (2019), 74–89
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems”, TMF, 201:3 (2019), 382–414; Theoret. and Math. Phys., 201:3 (2019), 1742–1770
Anatoly Anikin, Sergey Dobrokhotov, Vladimir Nazaikinskii, “Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time”, Zh. Mat. Fiz. Anal. Geom., 14:4 (2018), 393–405
V. L. Chernyshev, D. S. Minenkov, V. E. Nazaikinskii, “Typical Shape of Elements in an Arithmetical Semigroup
with Exponentially Growing Prime Counting Function
and Deviations from the Bose–Einstein Distribution”, Math. Notes, 104:6 (2018), 939–942
21.
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem”, Mat. Zametki, 104:4 (2018), 483–504; Math. Notes, 104:4 (2018), 471–488
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions”, Mat. Zametki, 103:5 (2018), 680–692; Math. Notes, 103:5 (2018), 33–43
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. RAN. Ser. Mat., 81:2 (2017), 53–96; Izv. Math., 81:2 (2017), 286–328
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “On the Asymptotics of a Bessel-Type Integral Having Applications in Wave Run-Up Theory”, Mat. Zametki, 102:6 (2017), 828–835; Math. Notes, 102:6 (2017), 756–762
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Punctured Lagrangian manifolds and asymptotic solutions of linear water wave equations with localized initial conditions”, Mat. Zametki, 101:6 (2017), 936–943; Math. Notes, 101:6 (2017), 1053–1060
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Uniform Asymptotics of the Boundary Values of the Solution in a Linear Problem on the Run-Up of Waves on a Shallow Beach”, Mat. Zametki, 101:5 (2017), 700–715; Math. Notes, 101:5 (2017), 802–814
D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators”, Funktsional. Anal. i Prilozhen., 50:4 (2016), 55–75; Funct. Anal. Appl., 50:4 (2016), 291–307
V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics”, Mat. Zametki, 100:6 (2016), 855–867; Math. Notes, 100:6 (2016), 828–834
S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Characteristics with Singularities and the Boundary Values of the Asymptotic Solution of the Cauchy Problem for a Degenerate Wave Equation”, Mat. Zametki, 100:5 (2016), 710–731; Math. Notes, 100:5 (2016), 695–713
D. S. Minenkov, V. E. Nazaikinskii, “Remark on the Inverse Abstract Prime Number Theorem”, Mat. Zametki, 100:4 (2016), 627–629; Math. Notes, 100:4 (2016), 633–635
V. P. Maslov, V. E. Nazaikinskii, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds”, Math. Notes, 100:3 (2016), 421–428
V. P. Maslov, V. E. Nazaikinskii, “Bose–Einstein Distribution as a Problem of Analytic Number Theory: The Case of Less than Two Degrees of Freedom”, Math. Notes, 100:2 (2016), 245–255
V. E. Nazaikinskii, “Relative Index Theorem in $K$-Homology”, Funktsional. Anal. i Prilozhen., 49:4 (2015), 85–90; Funct. Anal. Appl., 49:4 (2015), 311–314
V. E. Nazaikinskii, “The Maslov Canonical Operator on Lagrangian Manifolds in the Phase Space Corresponding to a Wave Equation Degenerating on the Boundary”, Mat. Zametki, 96:2 (2014), 261–276; Math. Notes, 96:2 (2014), 248–260
V. E. Nazaikinskii, “On the Representation of Localized Functions in $\mathbb R^2$ by Maslov's Canonical Operator”, Mat. Zametki, 96:1 (2014), 88–100; Math. Notes, 96:1 (2014), 99–109
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”, TMF, 180:2 (2014), 162–188; Theoret. and Math. Phys., 180:2 (2014), 894–916
S. Yu. Dobrokhotov, G. N. Makrakis, V. E. Nazaikinskii, T. Ya. Tudorovskii, “New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics”, TMF, 177:3 (2013), 355–386; Theoret. and Math. Phys., 177:3 (2013), 1579–1605
V. E. Nazaikinskii, “Phase Space Geometry for a Wave Equation Degenerating on the Boundary of the Domain”, Mat. Zametki, 92:1 (2012), 153–156; Math. Notes, 92:1 (2012), 144–148
M. I. Katsnel'son, V. E. Nazaikinskii, “The Aharonov–Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions”, TMF, 172:3 (2012), 437–453; Theoret. and Math. Phys., 172:3 (2012), 1263–1277
S. Yu. Dobrokhotov, V. E. Nazaĭkinskiĭ, B. Tirozzi, “Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data”, Algebra i Analiz, 22:6 (2010), 67–90; St. Petersburg Math. J., 22:6 (2011), 895–911
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in $K$-theory on manifolds with edges”, CMFD, 34 (2009), 109–120; Journal of Mathematical Sciences, 170:2 (2010), 238–250
46.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Atiyah–Bott index on stratified manifolds”, CMFD, 34 (2009), 100–108; Journal of Mathematical Sciences, 170:2 (2010), 229–237
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, CMFD, 29 (2008), 131–164; Journal of Mathematical Sciences, 164:4 (2010), 603–636
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Satisfying Two Linear Relations”, Mat. Zametki, 84:1 (2008), 69–98; Math. Notes, 84:1 (2008), 73–99
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III”, Mat. Zametki, 83:6 (2008), 880–898; Math. Notes, 83:6 (2008), 804–820
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by Two Linear Inequalities: I”, Mat. Zametki, 83:4 (2008), 559–580; Math. Notes, 83:4 (2008), 512–529
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. II”, Mat. Zametki, 83:3 (2008), 381–401; Math. Notes, 83:3 (2008), 345–363
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. I”, Mat. Zametki, 83:2 (2008), 232–263; Math. Notes, 83:2 (2008), 211–237
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. RAN. Ser. Mat., 71:6 (2007), 91–118; Izv. Math., 71:6 (2007), 1167–1192
V. P. Maslov, V. E. Nazaikinskii, “Tunnel Canonical Operator in Thermodynamics”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 12–29; Funct. Anal. Appl., 40:3 (2006), 173–187
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Mat. Sb., 196:9 (2005), 23–58; Sb. Math., 196:9 (2005), 1271–1305
V. E. Nazaikinskii, B. Yu. Sternin, “Operator Algebras on Manifolds with Isolated Singularities”, Differ. Uravn., 39:1 (2003), 92–104; Differ. Equ., 39:1 (2003), 99–111
V. E. Nazaikinskii, B. Yu. Sternin, “The Index Locality Principle in Elliptic Theory”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 37–52; Funct. Anal. Appl., 35:2 (2001), 111–123
V. E. Nazaikinskii, B. Schulze, B. Yu. Sternin, “The index of Fourier integral operators on manifolds with conical singularities”, Izv. RAN. Ser. Mat., 65:2 (2001), 127–154; Izv. Math., 65:2 (2001), 329–355
V. Nazaikinskii, B. Sternin, V. Shatalov, B.-W. Schulze, “Spectral boundary value problems and elliptic equations on manifolds with singularities”, Differ. Uravn., 34:5 (1998), 695–708; Differ. Equ., 34:5 (1998), 696–710
V. E. Nazaikinskii, B. Yu. Sternin, V. E. Shatalov, “Contact geometry and linear differential equations”, Uspekhi Mat. Nauk, 48:3(291) (1993), 97–134; Russian Math. Surveys, 48:3 (1993), 93–132
V. E. Nazaikinskii, B. Yu. Sternin, V. E. Shatalov, “Application of Maslov's operator method to a diffraction problem”, Dokl. Akad. Nauk SSSR, 317:4 (1991), 832–834; Dokl. Math., 43:2 (1991), 547–549
63.
V. E. Nazaikinskii, B. Yu. Sternin, V. E. Shatalov, “Local solvability of differential equations in spaces of multivalued analytic functions”, Differ. Uravn., 27:1 (1991), 103–114; Differ. Equ., 27:1 (1991), 82–91
1981
64.
V. P. Maslov, V. E. Nazaikinskii, “Asymptotics for equations with singularities in the characteristics”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 1049–1087; Math. USSR-Izv., 19:2 (1982), 315–347
V. E. Nazaikinskii, V. G. Oshmyan, B. Yu. Sternin, V. E. Shatalov, “Fourier integral operators and the canonical operator”, Uspekhi Mat. Nauk, 36:2(218) (1981), 81–140; Russian Math. Surveys, 36:2 (1981), 93–161
V. P. Maslov, V. E. Nazaikinskii, “Algebras with general commutation relations and their applications. I. Pseudodifferential equations with increasing coefficients”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 13 (1979), 5–144; J. Soviet Math., 15:3 (1981), 167–273
M. V. Karasev, V. E. Nazaikinskii, “On the quantization of rapidly oscillating symbols”, Mat. Sb. (N.S.), 106(148):2(6) (1978), 183–213; Math. USSR-Sb., 34:6 (1978), 737–764
I. V. Kurdyumov, M. V. Mosolova, V. E. Nazaikinskii, “A computational algorithm for a quadratic programming problem of large dimension”, Zh. Vychisl. Mat. Mat. Fiz., 18:5 (1978), 1119–1128; U.S.S.R. Comput. Math. Math. Phys., 18:5 (1978), 45–55
2024
69.
S. O. Gorchinskiy, V. G. Danilov, S. Yu. Dobrokhotov, V. V. Kozlov, V. E. Nazaikinskii, N. N. Nefedov, D. O. Orlov, S. A. Stepin, I. A. Taimanov, D. V. Treschev, N. A. Tyurin, A. T. Fomenko, S. E. Yakush, “Andrei Igorevich Shafarevich (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 79:3(477) (2024), 185–188; Russian Math. Surveys, 79:3 (2024), 553–556
Efficient asymptotic solutions of equations with localized right-hand sides V. E. Nazaikinskii VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 15, 2023 13:20
On the singular trace of the main operations of field theory V. E. Nazaikinskii III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 12, 2023 12:00
12.
Effective asymptotics of linear (pseudo)differential equations with localized right hand sides S. Yu. Dobrokhotov, V. E. Nazaikinskii III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 10, 2023 10:00
The current status of the theory of the canonical operator V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich International Conference Dedicated to the 100th Anniversary of the Birthday
of V. S. Vladimirov (Vladimirov-100) January 12, 2023 11:00
Efficient semiclassical asymptotics V. E. Nazaikinskii Mathematical Physics, Dynamical Systems and Infinite-Dimensional
Analysis – 2021 July 9, 2021 19:00