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Tikhonov, Sergei Yur'evich

Statistics Math-Net.Ru
Total publications: 20
Scientific articles: 20
Presentations: 11

Number of views:
This page:3074
Abstract pages:5204
Full texts:1704
References:657
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:
  1. F. Dai, Z. Ditzian, S. Tikhonov, “Sharp Jackson inequalities”, J. Approx. Theory, 151:1 (2008), 86–112  crossref  mathscinet  zmath
  2. S. Tikhonov, “Trigonometric series with general monotone coefficients”, J. Math. Anal. Appl., 326:1 (2007), 721–735  crossref  mathscinet  zmath
  3. B. V. Simonov, S. Yu. Tikhonov, “Teoremy vlozheniya v konstruktivnoi teorii priblizhenii”, Matem. sb., 199:9 (2008), 107–148  mathnet
  4. Z. Ditzian, S. Tikhonov, “Ul'yanov and Nikol'skii-type inequalitie”, J. Approx. Theory, 133:3 (2005), 100–133  crossref  mathscinet  zmath
  5. S. Tikhonov, “Weak Type Inequalities for Moduli of Smoothness: The Case of Limit Value Parameters”, J. Fourier Anal. Appl., 16 (2010), 590–608

http://www.mathnet.ru/eng/person15876
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
2019
1. 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  mathnet  mathscinet  elib; Russian Math. Surveys, 74:4 (2019), 579–630  isi  scopus
2. M. I. Dyachenko, A. B. Mukanov, S. Yu. Tikhonov, “Smoothness of functions and Fourier coefficients”, Mat. Sb., 210:7 (2019),  94–119  mathnet  elib; Sb. Math., 210:7 (2019), 994–1018  isi  scopus
2017
3. 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  mathnet  mathscinet  isi  scopus
2015
4. 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  mathnet  elib; Funct. Anal. Appl., 49:3 (2015), 226–229  isi  scopus
2013
5. M. I. Dyachenko, E. D. Nursultanov, S. Yu. Tikhonov, “Global and local smoothness of the Hilbert transforms”, Tr. Mat. Inst. Steklova, 280 (2013),  175–187  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 280 (2013), 169–180  isi  elib  scopus
2012
6. M. I. Dyachenko, S. Tikhonov, “Trigonometric series with lacunary-monotone coefficients”, Eurasian Math. J., 3:2 (2012),  31–52  mathnet  mathscinet  zmath
2010
7. M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes”, Tr. Mat. Inst. Steklova, 269 (2010),  204–214  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 269 (2010), 197–207  isi  elib  scopus
2009
8. 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, 3,  17–25  mathnet  mathscinet  zmath
2008
9. B. V. Simonov, S. Yu. Tikhonov, “Embedding theorems in constructive approximation”, Mat. Sb., 199:9 (2008),  107–148  mathnet  mathscinet  zmath  elib; Sb. Math., 199:9 (2008), 1367–1407  isi  elib  scopus
10. M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “An inequality of P. L. Ul’yanov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, 3,  33–36  mathnet  mathscinet  zmath
2007
11. S. Yu. Tikhonov, “On the Uniform Convergence of Trigonometric Series”, Mat. Zametki, 81:2 (2007),  304–310  mathnet  mathscinet  zmath  elib; Math. Notes, 81:2 (2007), 268–274  isi  scopus
2005
12. S. Yu. Tikhonov, “On two theorems of Lorentz”, Izv. RAN. Ser. Mat., 69:1 (2005),  165–178  mathnet  mathscinet  zmath  elib; Izv. Math., 69:1 (2005), 163–175  isi  scopus
13. S. Yu. Tikhonov, “On the Integrability of Trigonometric Series”, Mat. Zametki, 78:3 (2005),  476–480  mathnet  mathscinet  zmath  elib; Math. Notes, 78:3 (2005), 437–442  isi  scopus
14. 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  mathnet  mathscinet  zmath  elib; Math. Notes, 77:1 (2005), 90–107  isi  scopus
2004
15. S. Yu. Tikhonov, “Generalized Lipschitz Classes and Fourier Coefficients”, Mat. Zametki, 75:6 (2004),  947–951  mathnet  mathscinet  zmath  elib; Math. Notes, 75:6 (2004), 885–889  isi
16. 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, 5,  18–26  mathnet  mathscinet  zmath
17. Z. Ditzian, S. Yu. Tikhonov, “Remark on the order of approximation by Steklov means”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2004, 3,  57–58  mathnet  mathscinet  zmath
2003
18. 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”, Tr. Mat. Inst. Steklova, 243 (2003),  244–256  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 243 (2003), 234–246
2002
19. S. Yu. Tikhonov, “Fourier coefficients of functions in the Besov–Nikolskii class”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 6,  26–35  mathnet  mathscinet  zmath
20. S. Yu. Tikhonov, “Estimates for the moduli of smoothness of a transformed Fourier series”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 5,  58–61  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Гладкость функций в теории приближений
S. Yu. Tikhonov
Seminar on Theory of Functions of Real Variables
November 8, 2019 18:30
2. 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
3. Некоторые неравенства для тригонометрических полиномов
S. Yu. Tikhonov
Seminar on Approximation Theory
April 20, 2017 10:30
4. 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
5. Теоремы Винера для положительно определённых функций
S. Yu. Tikhonov
Seminar on Approximation Theory
March 3, 2016 10:30
6. 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
7. 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
8. Оценки модулей гладкости в одной и разных метриках
S. Yu. Tikhonov
Seminar on Approximation Theory
October 2, 2014 10:30
9. 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
10. 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
11. 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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