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
2024
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
2023
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
2018
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
2017
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
2016
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
2015
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
2014
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
2016
46.
E. E. Dikarev, D. M. Polyakov, “Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space”, J. Math. Sci., 213:6 (2016), 823–831
2025