01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
13.10.1990
E-mail:
Keywords:
perturbation, asymptotics, spectrum, non-self-adjoint operator, spectral gaps, eigenvalue, spectral decompositions, basis, fourth-order differential operator, existence theorem, alpha-models in hydrodynamics
UDC:
517.9, 517.927
Subject:
Spectral analysis of differential operators, Harmonic analysis of semigroups, hydrodynamics.
Main publications:
A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43
D. M. Polyakov, “Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions”, St. Petersburg Mathematical Journal, 27:5 (2016), 789–811
A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43
2.
D. M. Polyakov, “Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions”, St. Petersburg Mathematical Journal, 27:5 (2016), 789–811
3.
D. M. Polyakov, “Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients”, Siberian Math. J., 56:1 (2015), 138–154
4.
A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 1–10
5.
I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28
6.
A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602
7.
D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comp. Math. Math. Phys., 60:7 (2020), 1163–1184
D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential–difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260 , 33 pp. https://www.mdpi.com/2227-7390/11/20/4260
A. V. Zvyagin, V. G. Zvyagin, D. M. Polyakov, “Dissipative solvability of an alpha model of fluid flow with memory”, Comp. Math. Math. Phys., 59:7 (2019), 1185–1198
11.
D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485
12.
A. V. Zvyagin, D. M. Polyakov, “On the solvability of the Jeffreys–Oldroyd-alpha model”, Differential Equations, 52:6 (2016), 761–766
13.
D. M. Polyakov, “Method of Similar Operators in Spectral Analysis of a Fourth-Order Nonself-Adjoint Operator”, Differential Equations, 51:3 (2015), 421–425
14.
D. M. Polyakov, “Nonlocal perturbation of a periodic problem for a second-order differential operator”, Differential Equation, 57:1 (2021), 11–18
15.
D. M. Polyakov, “On the spectral characteristics of non-self-adjoint fourth-order operators with matrix coefficients”, Math. Notes, 105:4 (2019), 630–635
16.
A. V. Zvyagin, V. G. Zvyagin, D. M. Polyakov, “On solvability of one alpha-model of fluid motion with memory”, Russian Math. (Iz. VUZ), 62:6 (2018), 69–74
17.
D. M. Polyakov, “Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation”, Monatsh. Math., 202 (2023), 171–212 , arXiv: https://arxiv.org/abs/2202.03764
D. M. Polyakov, “Spectral properties of an even-order differential operator”, Differential Equations, 52:8 (2016), 1098–1103
21.
D. M. Polyakov, “On spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions”, Russian Math. (Iz. VUZ), 59:5 (2015), 64–68
22.
D. M. Polyakov, “The spectral properties of a two-term fourth-order operator with a spectral parameter in the boundary condition”, Siberian Math. J., 64:3 (2023), 649–669
23.
D. I. Borisov, D. M. Polyakov, “Asymptotics for eigenvalues of Schrödinger operator with small translation and Dirichlet condition”, Dokl. Math., 109:3 (2024), 227–231
24.
D. I. Borisov, D. M. Polyakov, “Uniform asymptotics for eigenvalues of model Schrödinger operator with small translation”, Ufa Math. J., 16:3 (2024), 1–20
25.
D. M. Polyakov, “Spectral estimates for fourth-order differential operator with periodic coefficients”, Russian Math. (Iz. VUZ), 66:7 (2022), 76–81
26.
I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a fourth-order differential operator with matrix coefficients”, Differential Equations, 54:4 (2018), 450–467
27.
E. E. Dikarev, D. M. Polyakov, “Harmonic Analysis of Some Classes of Linear Operators on a Real Banach Space”, Math. Notes, 97:5 (2015), 684–693
28.
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for Schrödinger operator perturbed by translation operator”, Izv. Math., 89:3 (2025), 442–460
29.
D. M. Polyakov, “Asymptotics of the eigenvalues of a two-term fourth-order operator with boundary conditions dependent on the spectral parameter”, Bol. Soc. Mat. Mex., 30 (2024), 25
D. M. Polyakov, “Spectral asymptotics of a non-self-adjoint fourth-order operator with periodic boundary conditions”, Theoret. and Math. Phys., 221:1 (2024), 1615–1632
31.
D. M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math. Meth. Appl. Sci., 46:5 (2023), 5483–5504
E. E. Dikarev, D. M. Polyakov, “Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space”, J. Math. Sci., 213:6 (2016), 823–831
35.
D. M. Polyakov, “Mixed problem for even-order differential equations with an involution”, Vladikavkaz Math. J., 27:2 (2025), 128–135;
36.
D. I. Borisov, D. M. Polyakov, “Uniform spectral asymptotics for Schrödinger operator with translation in free term and periodic boundary condition”, Russ. J. Math. Phys., 32:3 (2025), 434–450
37.
D. M. Polyakov, “Asymptotics of the spectrum for a fourth-order differential operator with a spectral parameter in two boundary conditions”, Differential Equations, 61:6 (2025), 755–768
38.
D. M. Polyakov, “Some asymptotical properties for a fourth-order differential equation with a spectral parameter in three boundary conditions”, Lobachevskii J. Math., 46:7 (2025), 3181–3197
39.
D. I. Borisov, D. M. Polyakov, “Uniform spectral asymptotics for Schrödinger operator on segment with delta-interaction”, Russ. J. Math. Phys., 31:2 (2024), 149–161
40.
D. M. Polyakov, “Asymptotic behavior of eigenvalues of fourth-order differential operators with spectral parameter in the boundary conditions”, Electr. J. Differ. Eq., 2024:62 (2024), 1–30
41.
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for nonlocal one-dimensional Schrodinger operator with Neumann condition and translation in free term”, Lobachevskii J. Math., 45:12 (2024), 6476–6482
42.
D. M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, Asympt. Anal., 130 (2022), 477–503
A. G. Baskakov, D. M. Polyakov, “Fourier method for a mixed problem with the Hill operator”, Differential Equations, 56:6 (2020), 679–684
45.
D. M. Polyakov, “Estimates of spectral gap lengths for Schrodinger and Dirac operators”, Differential Equations, 56:5 (2020), 585–594
46.
A. V. Zvyagin, D. M. Polyakov, “Investigation of the dissipative solvability for alpha-maxwell model”, Taurida Journal of Computer Science Theory and Mathematics, 2018, no. 4, 67–89
47.
A. O. Vatulyan, M. I. Karyakin, A. G. Kusraev, I. Kh. Musin, Yu. S. Nalbandjan, D. M. Polyakov, D. A. Polyakova, R. S. Yulmukhametov, “Abanin Alexander Vasil'evich (on his 70's anniversary)”, Vladikavkaz. Mat. Zh., 27:1 (2025), 150–153
48.
V. Bobkov, A. Gladkov, G. V. Grishina, A. A. Kovalevsky, L. M. Kozhevnikova, A. G. Kusraev, Z. A. Kusraeva, E. Yu. Panov, D. M. Polyakov, “Anatolii Fedorovich Tedeev (on his 70's anniversary)”, Vladikavkaz. Mat. Zh., 27:2 (2025), 148–149
