Persons: Plotnikov, Mikhail Gennadevich

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Plotnikov, Mikhail Gennadevich

Doctor of physico-mathematical sciences (2011)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

E-mail:

Keywords:

sets of uniqueness; quasi-measures; dyadic group; zero-dimensional compact abelian groups; Haar, Walsh, Vilenkin systems; generalized integrals.

UDC:

517.518.113, 517.518.117, 517.518.126, 517.518.3, 517.518.36, 517.518, 517.521

MSC:

42C25, 26A39, 28C10

Subject:

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

https://www.mathnet.ru/eng/person16254

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/671710

https://elibrary.ru/author_items.asp?spin=9417-1290

https://orcid.org/0000-0001-5383-4832

	Publications in Math-Net.Ru	Citations
	2025
1.	A. D. Kazakova, M. G. Plotnikov, “Sets of uniqueness for subsystems of the trigonometric system”, Mat. Zametki, 117:1 (2025), 79–90 ; Math. Notes, 117:1 (2025), 75–84	1
2.	A. D. Kazakova, M. G. Plotnikov, “On lacunarity and uniqueness for $p$-adic analogs of Rademacher chaos”, Sibirsk. Mat. Zh., 66:5 (2025), 870–881 ; Siberian Math. J., 66:5 (2025), 1184–1194
3.	A. D. Kazakova, M. G. Plotnikov, “Subsystems of independent functions for the Walsh and Vilenkin–Chrestenson systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2025, no. 3, 76–80 ; Moscow University Mathematics Bulletin, 80:3 (2025), 202–206
	2024
4.	A. D. Kashina, M. G. Plotnikov, “Reconstruction of functions in Sobolev- and Korobov-type $p$-ary classes with small smoothness parameters”, Mat. Zametki, 116:5 (2024), 744–758 ; Math. Notes, 116:5 (2024), 1000–1013
	2022
5.	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	1
6.	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	1
	2021
7.	M. G. Plotnikov, “Recovery of integrable functions and trigonometric series”, Mat. Sb., 212:6 (2021), 109–125 ; Sb. Math., 212:6 (2021), 843–858	3
	2017
8.	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	7
	2016
9.	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	6
	2014
10.	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
11.	M. G. Plotnikov, “Multiple Walsh Series and Zygmund Sets”, Mat. Zametki, 95:5 (2014), 750–762 ; Math. Notes, 95:5 (2014), 686–696	3
	2012
12.	M. G. Plotnikov, “Coefficients of convergent multiple Haar series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 67–71 ; Russian Math. (Iz. VUZ), 56:1 (2012), 61–65	3
13.	M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Mat. Sb., 203:9 (2012), 67–82 ; Sb. Math., 203:9 (2012), 1295–1309	1
	2010
14.	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	6
15.	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	5
	2009
16.	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
17.	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	7
18.	M. G. Plotnikov, “On Uniqueness Sets for Multiple Walsh Series”, Mat. Zametki, 81:2 (2007), 265–279 ; Math. Notes, 81:2 (2007), 234–246	6
19.	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	4
	2006
20.	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	3
	2005
21.	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	1
22.	M. G. Plotnikov, “Uniqueness for multiple Haar series”, Mat. Sb., 196:2 (2005), 97–116 ; Sb. Math., 196:2 (2005), 243–261	4
	2004
23.	M. G. Plotnikov, “Uniqueness Questions for Some Classes of Haar Series”, Mat. Zametki, 75:3 (2004), 392–404 ; Math. Notes, 75:3 (2004), 360–371	2
24.	M. G. Plotnikov, “A certain Perron type integral”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2004, no. 2, 12–15
	2003
25.	M. G. Plotnikov, “Violation of the uniqueness for two-dimensional Haar series”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2003, no. 4, 20–24	6
	2001
26.	M. G. Plotnikov, “On the uniqueness of everywhere converging multiple Haar series”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 1, 23–28	4
	2000
27.	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

	2025
28.	M. I. Dyachenko, B. S. Kashin, T. P. Lukashenko, M. G. Plotnikov, A. P. Solodov, N. N. Kholshchevnikova, “Valentin Aleksandrovich Skvortsov (on his 90th birthday)”, Uspekhi Mat. Nauk, 80:6(486) (2025), 195–197
	2016
29.	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.	Khinchin's inequalities for systems of Rademacher chaos type and $\varepsilon$-uniqueness sets M. G. Plotnikov Seminar on Theory of Functions of Real Variables October 24, 2025 18:30
2.	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
3.	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
4.	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
5.	Восстановление и приближение интегрируемых функций M. G. Plotnikov November 10, 2022 15:00
6.	Uniqueness for rearrangements of the trigonometric system M. G. Plotnikov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 6, 2021 17:05
7.	Capacities of positive measure sets and recovery of functions M. Plotnikov Approximation and discretization September 1, 2021 15:30
8.	Восстановление суммируемых функций и смежные задачи M. G. Plotnikov Seminar on Theory of Functions of Real Variables April 9, 2021 18:30

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