harmonic analysis; theory of orthogonal series; theory of generalized integrals; martingale theory
Main publications:
M. G. Plotnikov, “O mnozhestvakh edinstvennosti dlya kratnykh ryadov Uolsha”, Matem. zametki, 81:2 (2007), 265–279
M. G. Plotnikov, “Kvazimery, khausdorfovy $p$-mery i ryady Uolsha i Khaara”, Izv. RAN. Ser. matem., 74:4 (2010), 157–188
M. G. Plotnikov, “Kvazimery na gruppe $G^m$, mnozhestva Dirikhle i problemy edinstvennosti dlya kratnykh ryadov Uolsha”, Matem. sb., 201:12 (2010), 131–156
M.G. Plotnikov, “Q-measures on the dyadic group and uniqueness sets for Haar series”, Methods of Fourier Analysis and Approximation Theory, Michael Ruzhansky, Sergey Tikhonov (eds.), Applied and Numerical Harmonic Analysis, Springer International Publ. Switzerland, 2016, 71–83
M. Plotnikov, “V-sets in the products of zero-dimensional compact abelian groups”, European J. Math., 5:1 (2019), 223–240
M. G. Plotnikov, “Uniqueness sets of positive measure for the trigonometric system”, Izv. RAN. Ser. Mat., 86:6 (2022), 161–186; Izv. Math., 86:6 (2022), 1179–1203
2.
M. G. Plotnikov, V. S. Astashonok, “Recovery of Functions on $p$-Adic Groups”, Mat. Zametki, 112:6 (2022), 867–878; Math. Notes, 112:6 (2022), 955–964
2021
3.
M. G. Plotnikov, “Recovery of integrable functions and trigonometric series”, Mat. Sb., 212:6 (2021), 109–125; Sb. Math., 212:6 (2021), 843–858
M. G. Plotnikov, “$\lambda$-Convergence of Multiple Walsh–Paley Series and Sets of Uniqueness”, Mat. Zametki, 102:2 (2017), 292–301; Math. Notes, 102:2 (2017), 268–276
M. G. Plotnikov, Yu. A. Plotnikova, “Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a Haar system”, Mat. Sb., 207:3 (2016), 137–152; Sb. Math., 207:3 (2016), 444–457
M. G. Plotnikov, Ju. A. Plotnikova, “Martingales and Theorems of Cantor–Young–Bernstein and de la Vallée Poussin”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(2) (2014), 569–574
7.
M. G. Plotnikov, “Multiple Walsh Series and Zygmund Sets”, Mat. Zametki, 95:5 (2014), 750–762; Math. Notes, 95:5 (2014), 686–696
M. G. Plotnikov, “Quasi-measures, Hausdorff $p$-measures and Walsh and Haar series”, Izv. RAN. Ser. Mat., 74:4 (2010), 157–188; Izv. Math., 74:4 (2010), 819–848
M. G. Plotnikov, “Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series”, Mat. Sb., 201:12 (2010), 131–156; Sb. Math., 201:12 (2010), 1837–1862
M. G. Plotnikov, “Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series”, Mat. Zametki, 86:4 (2009), 601–611; Math. Notes, 86:4 (2009), 567–576
2007
13.
M. G. Plotnikov, “On multiple Walsh series convergent over cubes”, Izv. RAN. Ser. Mat., 71:1 (2007), 61–78; Izv. Math., 71:1 (2007), 57–73
M. G. Plotnikov, “Several properties of generalized multivariate integrals
and theorems of the du Bois-Reymond type for Haar series”, Mat. Sb., 198:7 (2007), 63–90; Sb. Math., 198:7 (2007), 967–991
M. G. Plotnikov, “On the boundary of existence of uniqueness for two-dimensional Haar series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, no. 7, 57–64; Russian Math. (Iz. VUZ), 50:7 (2006), 54–61
M. G. Plotnikov, “On the reconstruction of the coefficients of two-dimensional Haar series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 2, 45–53; Russian Math. (Iz. VUZ), 49:2 (2005), 42–50
M. G. Plotnikov, “On the Mawhin integral and its application to Haar series”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 4, 63–66
2016
24.
B. I. Golubov, B. S. Kashin, T. P. Lukashenko, M. G. Plotnikov, M. A. Skopina, A. P. Solodov, A. M. Stepin, N. N. Kholshchevnikova, “Valentin Anatol'evich Skvortsov (on his 80th birthday)”, Uspekhi Mat. Nauk, 71:1(427) (2016), 184–186; Russian Math. Surveys, 71:1 (2016), 175–177
Presentations in Math-Net.Ru
1.
О проблемах единственности для рядов по ортогональным системам M. G. Plotnikov XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 30, 2024 15:00
2.
О восстановлении интегрируемых функций A. D. Kashina, M. G. Plotnikov XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 29, 2024 18:10
3.
Множества единственности для подсистем системы Виленкина-Крестенсона A. D. Kazakova, M. G. Plotnikov XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 28, 2024 18:20