Persons: Sakbaev Vsevolod Zhanovich, List of publications

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Sakbaev Vsevolod Zhanovich

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2016
1.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. Math., 80:6 (2016), 1131–1158

2026
2.	Vsevolod Sakbaev, Igor Volovich, “Measures and trajectory properties in oscillator systems”, Ann. Funct. Anal., 17:1 (2026), 10, 29 pp., arXiv: 2506.18093
3.	A. M. Bikchentaev, V. Zh. Sakbaev, “On the variance of measurable operators”, Theoret. and Math. Phys., 227:2 (2026), 903–923
4.	S. V. Dzhenzher, V. Zh. Sakbaev, “Limit theorems for the evolution of quantum pure states”, Comput. Math. Math. Phys., 66:5 (2026), 927–932
5.	V. M. Busovikov, V. Zh. Sakbaev, “Measurability of curved bars on a Hilbert space”, Comput. Math. Math. Phys., 66:5 (2026), 816–825
6.	O. V. Besov, G. E. Ivanov, V. Zh. Sakbaev, Zh. Vychisl. Mat. Mat. Fiz., 66:5 (2026), 663–665

2025
7.	Yu. N. Orlov, V. Zh. Sakbaev, “Feynman–Kac formulas for solutions of nonstationarily perturbed evolution equations”, Comput. Math. Math. Phys., 65:1 (2025), 109–128
8.	R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Stochastic control modeling for the problem of random motion”, Mat. Model., 37:3 (2025), 113–126
9.	Grigori Amosov, Vsevolod Sakbaev, “On dynamics of quantum states generated by averaging of random shifts”, Adv. Oper. Theory, 10 (2025), 51, 20 pp.	1 ^[x]
10.	Yu. N. Orlov, V. Zh. Sakbaev, “Diffusion of quantum states generated by a classical random walk”, Modern Methods of Theory of Boundary Value Problems. Pontryagin Readings — XXXV, CMFD, 71, no. 2, PFUR, M., 2025, 275–286
11.	V. M. Busovikov, Yu. N. Orlov, V. Zh. Sakbaev, “Function Spaces and Boundary Value Problems in Domains of a Hilbert Space”, Proc. Steklov Inst. Math., 331 (2025), 57–69

2024
12.	V. M. Busovikov, Yu. N. Orlov, V. Zh. Sakbaev, “Unitary representation of walks along random vector fields and the Kolmogorov–Fokker–Planck equation in a Hilbert space”, Theoret. and Math. Phys., 218:2 (2024), 205–221
13.	G. G. Amosov, A. M. Bikchentaev, V. Zh. Sakbaev, “On Extreme Points of Sets in Operator Spaces and State Spaces”, Proc. Steklov Inst. Math., 324 (2024), 4–17
14.	R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Generalized Coherent States and Random Shift Operators”, Proc. Steklov Inst. Math., 324 (2024), 115–122
15.	Vsevolod Sakbaev, Igor Volovich, “Analogues of Jacobi and Weyl theorems for infinite-dimensional tori”, J. Stoch. Anal., 5:1 (2024), 4, 16 pp.

2023
16.	Vsevolod Zh. Sakbaev, “Flows in infinite-dimensional phase space equipped with a finitely-additive invariant measure”, Mathematics, 11:5 (2023), 1161, 49 pp.	9 ^[x]
17.	V. M. Busovikov, V. Zh. Sakbaev, “Direct limit of shift-invariant measures on a Hilbert space”, Lobachevskii J. Math., 44:6 (2023), 1998–2006	5 ^[x]
18.	R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Averaging of random affine transformations of functions domain”, Ufa Math. J., 15:2 (2023), 55–64

2022
19.	R. Sh. Kalmetiev, Yu. N. Orlov, V. Zh. Sakbaev, “Chernoff iterations as an averaging method for random affine transformations”, Comput. Math. Math. Phys., 62:6 (2022), 996–1006
20.	J. E. Gough, Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Markov approximations of the evolution of quantum systems”, Dokl. Math., 105:2 (2022), 92–96
21.	K. Yu. Zamana, V. Zh. Sakbaev, “Compositions of independent random operators and related differential equations”, Keldysh Institute preprints, 2022
22.	V. A. Glazatov, V. Zh. Sakbaev, “Measures on Hilbert space invariant with respect to Hamiltonian flows”, Ufa Math. J., 14:2 (2022), 3–21
23.	V. M. Busovikov, V. Zh. Sakbaev, “Invariant measures for Hamiltonian flows anddiffusion in infinitely dimensional phase spaces”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2243018, 15 pp.	7 ^[x]
24.	V. A. Glazatov, V. Zh. Sakbaev, “On the Koopman representation of Hamiltonian flows in infinite dimensional spaces with invariant measure”, Keldysh Institute preprints, 2022
25.	O. N. Ageev, Ya. B. Vorobets, B. Weiss, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, L. S. Efremova, A. Yu. Zhirov, E. V. Zhuzhoma, B. S. Kashin, V. N. Kolokoltsov, A. V. Kochergin, L. M. Lerman, I. V. Mykytyuk, V. I. Oseledets, A. Yu. Plakhov, O. V. Pochinka, V. V. Ryzhikov, V. Zh. Sakbaev, A. G. Sergeev, Ya. G. Sinai, A. T. Tagi-Zade, S. V. Tikhonov, J.-P. Thouvenot, A. Ya. Helemskii, A. I. Shafarevich, “Anatolii Mikhailovich Stepin (obituary)”, Russian Math. Surveys, 77:2 (2022), 361–367
26.	Dokl. Math., 106:2 (2022), 402–403

2021
27.	V. M. Busovikov, D. V. Zavadsky, V. Zh. Sakbaev, “Quantum Systems with Infinite-Dimensional Coordinate Space and the Fourier Transform”, Proc. Steklov Inst. Math., 313 (2021), 27–40
28.	V. Zh. Sakbaev, O. G. Smolyanov, “Lebesgue–Feynman measures on infinite dimensional spaces”, Internat. J. Theoret. Phys., 60 (2021), 650–654	2 ^[x]
29.	J. E. Gough, Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Random quantization of Hamiltonian systems”, Dokl. Math., 103:3 (2021), 122–126

2020
30.	V. M. Busovikov, V. Zh. Sakbaev, “Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups”, Izv. Math., 84:4 (2020), 694–721
31.	A. D. Grekhneva, V. Zh. Sakbaev, “Dynamics of a set of quantum states generated by a nonlinear Liouville–von Neumann equation”, Comput. Math. Math. Phys., 60 (2020), 1337–1347
32.	V. M. Busovikov, V. Zh. Sakbaev, “Shift-Invariant Measures on Hilbert and Related Function Spaces”, J. Math. Sci., 249:6 (2020), 864–884
33.	V. M. Busovikov, V. Zh. Sakbaev, “Dirichlet Problem for Poisson Equation on the Rectangle in Infinite Dimensional Hilbert Space”, Appl. Math. Nonlinear Sci., 5:2 (2020), 329–344	3 ^[x]
34.	Yu. N. Orlov, V. Zh. Sakbaev, D. V. Zavadsky, “Operator random walks and quantum oscillator”, Lobachevskii J. Math., 41:4 (2020), 676–685	4 ^[x]
35.	K. Yu. Zamana, V. Zh. Sakbaev, O. G. Smolyanov, “Stochastic processes on the group of orthogonal matrices and evolution equations describing them”, Comput. Math. Math. Phys., 60:10 (2020), 1686–1700
36.	V. Zh. Sakbaev, N. V. Tsoy, “Analogue of Chernoff theorem for cylindrical pseudomeasures”, Lobachevskii J. Math., 41:12 (2020), 2369–2382	7 ^[x]

2019
37.	D. V. Zavadsky, V. Zh. Sakbaev, “Diffusion on a Hilbert Space Equipped with a Shift- and Rotation-Invariant Measure”, Proc. Steklov Inst. Math., 306 (2019), 102–119
38.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Randomizes hamiltonian mechanics”, Dokl. Akad. Nauk, 486:6 (2019), 635–658
39.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman Formulas and the Law of Large Numbers for Random One-Parameter Semigroups”, Proc. Steklov Inst. Math., 306 (2019), 196–211
40.	L.S. Efremova, A.D. Grekhneva, V.Zh. Sakbaev., “Phase Flows Generated by Cauchy Problem for Nonlinear Schrödinger Equation and Dynamical Mappings of Quantum States”, Lobachevski Journal of Mathematics, 40:10 (2019), 1455-1469	6 ^[x]

2018
41.	Yu. N. Orlov, V. Zh. Sakbaev, “Feynman–Chernoff Iterations and Their Applications in Quantum Dynamics”, Proc. Steklov Inst. Math., 301 (2018), 197–206
42.	I. V. Volovich, V. Zh. Sakbaev, “On Quantum Dynamics on $C^*$-Algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38

2021
43.	V. Zh. Sakbaev, “Transformation Semigroups of the Space of Functions That Are Square Integrable with respect to a Translation-Invariant Measure on a Banach Space”, J. Math. Sci. (N. Y.), 252:1 (2021), 72–89

2018
44.	V. Zh. Sakbaev, D. V. Zavadsky, “Shift-invariant measures on infinite-dimensional spaces: integrable functions and random walks”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 384–391
45.	V. Zh. Sakbaev, O. G. Smolyanov, “Feynman calculus for random operator-valued functions and their applications”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 373–383	2 ^[x]

2019
46.	V. Zh. Sakbaev, “Random walks and measures on Hilbert space that are invariant with respect to shifts and rotations”, Journal of Mathematical Sciences, 241:4 (2019), 469–500

2017
47.	V. Zh. Sakbaev, I. V. Volovich, “Self-adjoint approximations of the degenerate Schrödinger operator”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 39–52, arXiv: 1701.02777	5 ^[x]
48.	V. Zh. Sakbaev, “Averaging of random walks and shift-invariant measures on a Hilbert space”, Theoret. and Math. Phys., 191:3 (2017), 886–909

2016
49.	V. Zh. Sakbaev, “On the law of large numbers for compositions of independent random semigroups”, Russian Math. (Iz. VUZ), 60:10 (2016), 72–76
50.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. Math., 80:6 (2016), 1131–1158
51.	G. G. Amosov, V. Zh. Sakbaev, “Geometrical properties of systems of vector states and representing of states in the form of Pettis integrals”, St. Petersburg Math. J., 27:4 (2016), 589–597

2015
52.	A. Yaakbarieh, V. Zh. Sakbaev, “Correctness of a problem with initial conditions for parabolic differential-difference equations with shifts of time argument”, Russian Math. (Iz. VUZ), 59:4 (2015), 13–19
53.	L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Equivalence by Chernoff and evolution equations for density matrix and Wigner function for linear quantization”, Keldysh Institute preprints, 2015, 66–28
54.	L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Feynman formulas for averaging of semigroups, generating by the operators of Schrödinger type”, Keldysh Institute preprints, 2015, 57–23
55.	L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598

2014
56.	M. H. Numan Elsheikh, J. O. Ogun, Yu. N. Orlov, R. V. Pleshakov, V. Zh. Sakbaev, “Averaging of random semigroups and the ambiguity of quantization of Hamiltonian systems”, Keldysh Institute preprints, 2014, 19–28
57.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman formulas as a method of averaging random Hamiltonians”, Proc. Steklov Inst. Math., 285 (2014), 222–232
58.	I. V. Volovich, V. Zh. Sakbaev, “Universal boundary value problem for equations of mathematical physics”, Proc. Steklov Inst. Math., 285 (2014), 56–80
59.	V. Sakbaev, “On dynamical properties of a one-parameter family of transformations arising in averaging of semigroups”, Journal of Mathematical Sciences, 202:6 (2014), 869–886

2013
60.	G. G. Amosov, V. Zh. Sakbaev, “On Analogs of Spectral Decomposition of a Quantum State”, Math. Notes, 93:3 (2013), 351–359
61.	V. Zh. Sakbaev, “Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation”, Proc. Steklov Inst. Math., 283 (2013), 165–180
62.	V. Zh. Sakbaev, “Blow-up of solutions of Cauchy problem for nonlinear Schrödinger equation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(30) (2013), 159–171

2016
63.	V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459

2012
64.	J. O. Ogun, Yu. N. Orlov, V. Zh. Sakbaev, “On the data space transformation for initial Cauchy problem with blow-up solutions”, Keldysh Institute preprints, 2012, 87–31
65.	Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian”, Theoret. and Math. Phys., 172:1 (2012), 987–1000
66.	G. G. Amosov, V. Zh. Sakbaev, O. G. Smolyanov, “Linear and nonlinear liftings of states of quantum systems”, Russ. J. Math. Phys., 19:4 (2012), 417–427	2 ^[x]

2011
67.	V. Z. Sakbaev, “The set of quantum states and its averaged dynamic transformations”, Russian Math. (Iz. VUZ), 55:10 (2011), 41–50
68.	V. Zh. Sakbaev, “On the dynamics of the quantum states set for a system with degenerated Hamiltonian”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2(23) (2011), 200–220

2010
69.	V. Zh. Sakbaev, “Averaging of quantum dynamical semigroups”, Theoret. and Math. Phys., 164:3 (2010), 1215–1221

2009
70.	L. V. Korobenko, V. Zh. Sakbaev, “Formulation and well-posedness of the Cauchy problem for a diffusion equation with discontinuous degenerating coefficients”, Comput. Math. Math. Phys., 49:6 (2009), 1037–1053

2008
71.	V. Zh. Sakbaev, “Spectral Aspects of Regularization of the Cauchy Problem for a Degenerate Equation”, Proc. Steklov Inst. Math., 261 (2008), 253–261
72.	V. Zh. Sakbaev, “On the Cauchy problem for the Schrödinger equation degenerating outside a segment: properties of solutions and spectral aspects of the regularization”, Journal of Mathematical Sciences, 153:5 (2008), 562–590
73.	V. Zh. Sakbaev, “On the dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line”, J. Math. Sci., 151:1 (2008), 2741–2753

2006
74.	V. Zh. Sakbaev, “Set-valued mappings specified by regularization of the Schrödinger equation with degeneration”, Comput. Math. Math. Phys., 46:4 (2006), 651–665

2004
75.	G. G. Amosov, V. Zh. Sakbaev, “On Self-Adjoint Extensions of Schrödinger Operators Degenerating on a Pair of Half-Lines and the Corresponding Markovian Cocycles”, Math. Notes, 76:3 (2004), 315–322
76.	V. Zh. Sakbaev, “Functionals on solutions of the Cauchy problem for the Schrödinger equation with degeneration on a half-line”, Comput. Math. Math. Phys., 44:9 (2004), 1573–1591
77.	V. Zh. Sakbaev, “On the Cauchy Problem for the Schrödinger Equation with Generator of Variable Type”, Differ. Equ., 40:2 (2004), 241–255

2003
78.	V. V. Vlasov, V. Zh. Sakbaev, “Correct solvability of differential equations with aftereffect in the scale of Sobolev spaces”, Russian Math. (Iz. VUZ), 47:4 (2003), 6–14

2002
79.	V. Zh. Sakbaev, “On the formulation of the Cauchy problem for the Schrödinger equation that degenerates on a half-space”, Comput. Math. Math. Phys., 42:11 (2002), 1636–1646

2001
80.	V. Zh. Sakbaev, “The Cauchy Problem for the Average Field Equation Describing a Model of a Magnetic Solid”, Math. Notes, 70:3 (2001), 392–402
81.	V. V. Vlasov, V. Zh. Sakbaev, “The Correct Solvability of Some Differential-Difference Equations in the Scale of Sobolev Spaces”, Differ. Equ., 37:9 (2001), 1252–1260

2000
82.	V. V. Vlasov, V. Zh. Sakbaev, “Well-Defined Solvability of Some Differential-Difference Equations in Sobolev Spaces”, Math. Notes, 68:6 (2000), 794–797

1999
83.	V. Zh. Sakbaev, “On the well-posedness of the Cauchy problem for the mean field equations describing a solid magnet”, Comput. Math. Math. Phys., 39:6 (1999), 933–950

1995
84.	P. E. Zhidkov, V. Zh. Sakbaev, “On the existence of a countable set of solutions of a certain nonlinear boundary value problem”, Differ. Equ., 31:4 (1995), 585–593

1994
85.	P. E. Zhidkov, V. Zh. Sakbaev, “On a nonlinear ordinary differential equation”, Math. Notes, 55:4 (1994), 351–357