Persons: Tikhonov, Sergei Yur'evich

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Tikhonov, Sergei Yur'evich

Candidate of physico-mathematical sciences (2003)

Speciality:

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

E-mail:

Keywords:

Fourier series/transforms, inequalities in approximation theory, function spaces, integral operators, embedding theorems.

UDC:

517, 517.5, 517.518.23, 517.518.83

MSC:

41, 42

Subject:

Harmonic analysis, approximation theory.

Biography

1999: MS, Lomonosov Moscow State University;
2003: PhD, Lomonosov Moscow State University.

Students: Diana Darbaeva (MS), co-directed with E. Nursultanov (http://enu.kz/professors/prepodavateli/nursultanov);
Ainur Jumabayeva (PhD), co-directed with N. Tleukhanova (http://enu.kz/professors/prepodavateli/tleukhanova).

Main publications:

F. Dai, Z. Ditzian, S. Tikhonov, “Sharp Jackson inequalities”, J. Approx. Theory, 151:1 (2008), 86–112
S. Tikhonov, “Trigonometric series with general monotone coefficients”, J. Math. Anal. Appl., 326:1 (2007), 721–735
B. V. Simonov, S. Yu. Tikhonov, “Teoremy vlozheniya v konstruktivnoi teorii priblizhenii”, Matem. sb., 199:9 (2008), 107–148
Z. Ditzian, S. Tikhonov, “Ul'yanov and Nikol'skii-type inequalitie”, J. Approx. Theory, 133:3 (2005), 100–133
S. Tikhonov, “Weak Type Inequalities for Moduli of Smoothness: The Case of Limit Value Parameters”, J. Fourier Anal. Appl., 16 (2010), 590–608

https://www.mathnet.ru/eng/person15876

List of publications on Google Scholar

	Publications in Math-Net.Ru	Citations
	2023
1.	F. Dai, A. Prymak, A. Yu. Shadrin, V. N. Temlyakov, S. Yu. Tikhonov, “On the cardinality of lower sets and universal discretization”, J. Complexity, 76 (2023), 101726–16	1
	2022
2.	M. I. Dyachenko, S. Yu. Tikhonov, “Piecewise General Monotone Functions and the Hardy–Littlewood Theorem”, Trudy Mat. Inst. Steklova, 319 (2022), 120–133 ; Proc. Steklov Inst. Math., 319 (2022), 110–123
	2021
3.	F. Dai, A. Prymak, A. Shadrin, V. Temlyakov, S. Tikhonov, “Sampling discretization of integral norms”, Constr. Approx., 54:3 (2021), 455–471	14
4.	F. Dai, A. Prymak, A. Shadrin, V. Temlyakov, S. Tikhonov, “Entropy numbers and Marcinkiewicz-type discretization”, J. Funct. Anal., 281:6 (2021), 109090–25	17
5.	A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, “Functions with general monotone Fourier coefficients”, Uspekhi Mat. Nauk, 76:6(462) (2021), 3–70 ; Russian Math. Surveys, 76:6 (2021), 951–1017	5
6.	Sergey Yu. Tikhonov, “Weighted Fourier Inequalities and Boundedness of Variation”, Trudy Mat. Inst. Steklova, 312 (2021), 294–312 ; Proc. Steklov Inst. Math., 312 (2021), 282–300	2
	2019
7.	F. Dai, A. Prymak, V. N. Temlyakov, S. Yu. Tikhonov, “Integral norm discretization and related problems”, Uspekhi Mat. Nauk, 74:4(448) (2019), 3–58 ; Russian Math. Surveys, 74:4 (2019), 579–630	36
8.	M. I. Dyachenko, A. B. Mukanov, S. Yu. Tikhonov, “Smoothness of functions and Fourier coefficients”, Mat. Sb., 210:7 (2019), 94–119 ; Sb. Math., 210:7 (2019), 994–1018	10
	2017
9.	V. Temlyakov, S. Tikhonov, “Remez-Type and Nikol’skii-Type Inequalities: General Relations and the Hyperbolic Cross Polynomials”, Constr. Approx., 46:3 (2017), 593–615	8
	2015
10.	E. D. Nursultanov, M. V. Ruzhansky, S. Yu. Tikhonov, “Nikolskii Inequality and Functional Classes on Compact Lie Groups”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 83–87 ; Funct. Anal. Appl., 49:3 (2015), 226–229	13
	2013
11.	M. I. Dyachenko, E. D. Nursultanov, S. Yu. Tikhonov, “Global and local smoothness of the Hilbert transforms”, Trudy Mat. Inst. Steklova, 280 (2013), 175–187 ; Proc. Steklov Inst. Math., 280 (2013), 169–180
	2012
12.	M. I. Dyachenko, S. Tikhonov, “Trigonometric series with lacunary-monotone coefficients”, Eurasian Math. J., 3:2 (2012), 31–52	1
	2010
13.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes”, Trudy Mat. Inst. Steklova, 269 (2010), 204–214 ; Proc. Steklov Inst. Math., 269 (2010), 197–207	17
	2009
14.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Relations between moduli of smoothness in different metrics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2009, no. 3, 17–25	9
	2008
15.	B. V. Simonov, S. Yu. Tikhonov, “Embedding theorems in constructive approximation”, Mat. Sb., 199:9 (2008), 107–148 ; Sb. Math., 199:9 (2008), 1367–1407	41
16.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “An inequality of P. L. Ul’yanov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, no. 3, 33–36	2
	2007
17.	S. Yu. Tikhonov, “On the Uniform Convergence of Trigonometric Series”, Mat. Zametki, 81:2 (2007), 304–310 ; Math. Notes, 81:2 (2007), 268–274	20
	2005
18.	S. Yu. Tikhonov, “On two theorems of Lorentz”, Izv. RAN. Ser. Mat., 69:1 (2005), 165–178 ; Izv. Math., 69:1 (2005), 163–175	5
19.	S. Yu. Tikhonov, “On the Integrability of Trigonometric Series”, Mat. Zametki, 78:3 (2005), 476–480 ; Math. Notes, 78:3 (2005), 437–442	14
20.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Transformation of Fourier series using power and weakly oscillating sequences”, Mat. Zametki, 77:1 (2005), 99–116 ; Math. Notes, 77:1 (2005), 90–107	6
	2004
21.	S. Yu. Tikhonov, “Generalized Lipschitz Classes and Fourier Coefficients”, Mat. Zametki, 75:6 (2004), 947–951 ; Math. Notes, 75:6 (2004), 885–889	5
22.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Embedding theorems for Besov–Nikol'skii and Weyl–Nikol'skii classes in a mixed metric”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2004, no. 5, 18–26
23.	Z. Ditzian, S. Yu. Tikhonov, “Remark on the order of approximation by Steklov means”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2004, no. 3, 57–58
	2003
24.	M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “On the Besov and Besov–Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives”, Trudy Mat. Inst. Steklova, 243 (2003), 244–256 ; Proc. Steklov Inst. Math., 243 (2003), 234–246	6
	2002
25.	S. Yu. Tikhonov, “Fourier coefficients of functions in the Besov–Nikolskii class”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 6, 26–35
26.	S. Yu. Tikhonov, “Estimates for the moduli of smoothness of a transformed Fourier series”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 5, 58–61	1

	2021
27.	P. A. Borodin, M. I. Dyachenko, B. S. Kashin, T. P. Lukashenko, I. I. Mel'nikov, V. A. Sadovnichii, B. V. Simonov, V. A. Skvortsov, A. P. Solodov, V. N. Temlyakov, S. Yu. Tikhonov, V. M. Fedorov, “Mikhail Konstantinovich Potapov (on his 90th birthday)”, Uspekhi Mat. Nauk, 76:2(458) (2021), 185–186 ; Russian Math. Surveys, 76:2 (2021), 369–371

Presentations in Math-Net.Ru

1.	Truncated Besov spaces S. Yu. Tikhonov Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov May 30, 2023 12:30
2.	New estimates for the maximal functions S. Tikhonov Approximation and discretization September 1, 2021 11:00
3.	Принцип неопределенности Бургейна–Клозеля–Кахана и проблемы Логана D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov Seminar on Theory of Functions of Real Variables December 18, 2020 18:30
4.	Гладкость функций в теории приближений S. Yu. Tikhonov Seminar on Theory of Functions of Real Variables November 8, 2019 18:30
5.	Теоремы вложения и неравенства для преобразований Фурье S. Yu. Tikhonov Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics November 6, 2019 16:00
6.	Некоторые неравенства для тригонометрических полиномов S. Yu. Tikhonov Seminar on Approximation Theory April 20, 2017 10:30
7.	Теорема Харди–Литтлвуда и усреднение коэффициентов Фурье M. I. Dyachenko, E. D. Nursultanov, S. Yu. Tikhonov Seminar on Theory of Functions of Real Variables December 2, 2016 18:30
8.	Теоремы Винера для положительно определённых функций S. Yu. Tikhonov Seminar on Approximation Theory March 3, 2016 10:30
9.	Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $L^{2}$ D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 29, 2015 17:55
10.	Norm convolution inequalities in $L_p$ E. D. Nursultanov, S. Yu. Tikhonov, N. T. Tleukhanova International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 25, 2015 17:05
11.	Оценки модулей гладкости в одной и разных метриках S. Yu. Tikhonov Seminar on Approximation Theory October 2, 2014 10:30
12.	Весовое неравенство Бернштейна S. Yu. Tikhonov Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics October 1, 2014 16:00
13.	Sharp local inequalities for polynomials S. Yu. Tikhonov International conference "Nonlinear Approximations and Applications" dedicated to the 60th birthday of Professor V. N. Temlyakov October 30, 2013 17:15
14.	Весовые неравенства для преобразования Фурье S. Yu. Tikhonov Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics March 30, 2011

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