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.
I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a third-order differential operator”, St. Petersburg Math. J., 31:4 (2020), 585–606 https://www.ams.org/journals/spmj/2020-31-04/S1061-0022-2020-01616-6/
7.
A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602
8.
A. V. Zvyagin, D. M. Polyakov, “On the solvability of the Jeffreys–Oldroyd-alpha model”, Differential Equations, 52:6 (2016), 761–766
9.
D. M. Polyakov, “Method of Similar Operators in Spectral Analysis of a Fourth-Order Nonself-Adjoint Operator”, Differential Equations, 51:3 (2015), 421–425
10.
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.
D. M. Polyakov, “Nonlocal perturbation of a periodic problem for a second-order differential operator”, Differential Equation, 57:1 (2021), 11–18
13.
D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comp. Math. Math. Phys., 60:7 (2020), 1163–1184
14.
D. M. Polyakov, “On the spectral characteristics of non-self-adjoint fourth-order operators with matrix coefficients”, Math. Notes, 105:4 (2019), 630–635
15.
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
16.
D. M. Polyakov, “Formula for regularized trace of a second order differential operator with involution”, J. Math. Sci., 251:5 (2020), 748–759
D. M. Polyakov, “Spectral properties of an even-order differential operator”, Differential Equations, 52:8 (2016), 1098–1103
18.
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
19.
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 estimates for fourth-order differential operator with periodic coefficients”, Russian Math. (Iz. VUZ), 66:7 (2022), 76–81
21.
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
22.
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
23.
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
E. E. Dikarev, D. M. Polyakov, “Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space”, J. Math. Sci., 213:6 (2016), 823–831
26.
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
27.
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
28.
D. M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math. Meth. Appl. Sci., 46:5 (2023), 5483–5504
29.
D. M. Polyakov, “On the Bari basis property for even-order differential operators with involution”, Tamkang J. Math., 54:4 (2023), 339–351
30.
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
31.
D. M. Polyakov, “Eigenvalue asymptotics and a trace formula for a fourth-order differential operator”, Complex Anal. Oper. Theory, 17:8 (2023), 121
32.
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
35.
D. M. Polyakov, “Estimates of spectral gap lengths for Schrodinger and Dirac operators”, Differential Equations, 56:5 (2020), 585–594
36.
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
37.
D. M. Polyakov, “Spectral asymptotics of a non-self-adjoint fourth-order operator with periodic boundary conditions”, TMF (to appear)
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