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
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for Schrödinger operator perturbed by translation operator”, Izv. Math., 89:3 (2025), 442–460
2.
D. M. Polyakov, “Mixed problem for even-order differential equations with an involution”, Vladikavkaz Math. J., 27:2 (2025), 128–135;
3.
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
4.
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
5.
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
6.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
D. M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math. Meth. Appl. Sci., 46:5 (2023), 5483–5504
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, “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
17.
D. M. Polyakov, “Eigenvalue asymptotics and a trace formula for a fourth-order differential operator”, Complex Anal. Oper. Theory, 17:8 (2023), 121
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
D. M. Polyakov, “On the spectral characteristics of non-self-adjoint fourth-order operators with matrix coefficients”, Math. Notes, 105:4 (2019), 630–635
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
31.
I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28
32.
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
33.
D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485
34.
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
35.
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
36.
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
37.
A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602
38.
A. V. Zvyagin, D. M. Polyakov, “On the solvability of the Jeffreys–Oldroyd-alpha model”, Differential Equations, 52:6 (2016), 761–766
39.
D. M. Polyakov, “Spectral properties of an even-order differential operator”, Differential Equations, 52:8 (2016), 1098–1103
40.
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
41.
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
42.
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
43.
D. M. Polyakov, “Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients”, Siberian Math. J., 56:1 (2015), 138–154
44.
D. M. Polyakov, “Method of Similar Operators in Spectral Analysis of a Fourth-Order Nonself-Adjoint Operator”, Differential Equations, 51:3 (2015), 421–425
45.
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
46.
E. E. Dikarev, D. M. Polyakov, “Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space”, J. Math. Sci., 213:6 (2016), 823–831
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
