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## Tikhonov, Sergey Yur’evich

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 Author ID: tikhonov.sergey-yu Published as: Tikhonov, S.; Tikhonov, S. Yu.; Tikhonov, Sergej Yu.; Tikhonov, Sergey; Tikhonov, Sergey Yu.; Tikhonov, Sergeĭ Yur’evich External Links: MGP · Math-Net.Ru · Wikidata · dblp
 Documents Indexed: 105 Publications since 2002, including 3 Books
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#### Co-Authors

 23 single-authored 15 Gorbachëv, Dmitriĭ Viktorovich 13 D’yachenko, Mikhaĭl Ivanovich 13 Simonov, Boris Vital’evich 12 Nursultanov, Erlan D. 9 Liflyand, Elijah 9 Potapov, Mikhaĭl Konstantinovich 6 Dai, Feng 4 Ditzian, Zeev 4 Ruzhansky, Michael V. 3 De Carli, Laura 3 Ivanov, Valeriy Ivanovich 3 Mukanov, Askhat Birlesovich 2 Ivanov, Valeriĭ Ivanovich 2 Stepanov, Vladimir Dmitrievich 2 Temlyakov, Vladimir Nikolaevich 2 Tleukhanova, Nazerke Tulekovna 2 Trebels, Walter 2 Zeltser, Maria 1 Abell, Martha L. 1 Ash, J. Marshall 1 Bondarenko, Andriy V. 1 Erlan, Nursultanov 1 Feng, Han 1 Ganzburg, Michael Iosifovich 1 Glazyrina, Polina Yu. 1 Gogatishvili, Amiran 1 Iacob, Emil 1 Kolesnikov, Alexander V. 1 Kolomoitsev, Yurii S. 1 Mhaskar, Hrushikesh N. 1 Opic, Bohumír 1 Prymak, Andriy V. 1 Stokolos, Alex 1 Taylor, Sharon 1 Tung, James 1 Zhu, Jiehua
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#### Serials

 9 Journal of Approximation Theory 7 Journal of Mathematical Analysis and Applications 5 The Journal of Fourier Analysis and Applications 4 Mathematical Notes 4 Proceedings of the American Mathematical Society 4 Constructive Approximation 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal d’Analyse Mathématique 3 Moscow University Mathematics Bulletin 3 Studia Mathematica 3 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Acta Mathematica Hungarica 2 Revista Matemática Iberoamericana 2 Calculus of Variations and Partial Differential Equations 2 Bulletin des Sciences Mathématiques 2 Sbornik: Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Proceedings of the Steklov Institute of Mathematics 2 Applied and Numerical Harmonic Analysis 1 Analysis Mathematica 1 Russian Mathematical Surveys 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 Acta Scientiarum Mathematicarum 1 Canadian Journal of Mathematics 1 Functional Analysis and its Applications 1 Indiana University Mathematics Journal 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Real Analysis Exchange 1 Zeitschrift für Analysis und ihre Anwendungen 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Potential Analysis 1 ETNA. Electronic Transactions on Numerical Analysis 1 Izvestiya: Mathematics 1 Doklady Mathematics 1 Mathematical Inequalities & Applications 1 Journal of the European Mathematical Society (JEMS) 1 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 1 Surveys in Approximation Theory (SAT) 1 Complex Variables and Elliptic Equations 1 Jaen Journal on Approximation 1 Eurasian Mathematical Journal 1 Advanced Courses in Mathematics – CRM Barcelona
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#### Fields

 76 Harmonic analysis on Euclidean spaces (42-XX) 31 Approximations and expansions (41-XX) 30 Real functions (26-XX) 30 Functional analysis (46-XX) 7 Special functions (33-XX) 7 Integral transforms, operational calculus (44-XX) 5 Partial differential equations (35-XX) 5 Operator theory (47-XX) 4 Sequences, series, summability (40-XX) 4 Numerical analysis (65-XX) 3 General and overarching topics; collections (00-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral equations (45-XX)

#### Citations contained in zbMATH

81 Publications have been cited 677 times in 300 Documents Cited by Year
Trigonometric series with general monotone coefficients. Zbl 1106.42003
Tikhonov, S.
2007
Ul’yanov and Nikol’skii-type inequalities. Zbl 1069.41014
Ditzian, Z.; Tikhonov, S.
2005
A concept of general monotonicity and applications. Zbl 1223.26017
Liflyand, E.; Tikhonov, S.
2011
Best approximation and moduli of smoothness: Computation and equivalence theorems. Zbl 1215.42002
Tikhonov, Sergey
2008
Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Zbl 1169.42001
Dyachenko, Mikhail; Tikhonov, Sergey
2009
Extended solution of Boas’ conjecture on Fourier transforms. Zbl 1151.42002
Liflyand, Elijah; Tikhonov, Sergey
2008
The Fourier transforms of general monotone functions. Zbl 1297.42009
Liflyand, E.; Tikhonov, S.
2009
Sharp Jackson inequalities. Zbl 1136.41003
Dai, F.; Ditzian, Z.; Tikhonov, S.
2008
Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Zbl 1356.35022
Nursultanov, Erlan; Ruzhansky, Michael; Tikhonov, Sergey
2016
Mixed moduli of smoothness in $$L_{p}$$: a survey. Zbl 1285.26008
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2013
Sharp Ul’yanov-type inequalities using fractional smoothness. Zbl 1215.26011
Simonov, Boris; Tikhonov, Sergey
2010
Net spaces and boundedness of integral operators. Zbl 1248.46025
Nursultanov, Erlan; Tikhonov, Sergey
2011
Embedding theorems in constructive approximation. Zbl 1172.46023
Simonov, B. V.; Tikhonov, S. Yu.
2008
Trigonometric series of Nikol’skii classes. Zbl 1121.42006
Tikhonov, S.
2007
A sharp Remez inequality for trigonometric polynomials. Zbl 1280.41011
Nursultanov, E.; Tikhonov, S.
2013
Weighted Fourier inequalities: Boas’ conjecture in $${\mathbb{R}}^{n}$$. Zbl 1246.42011
Gorbachev, D.; Liflyand, E.; Tikhonov, S.
2011
Pitt’s inequalities and uncertainty principle for generalized Fourier transform. Zbl 1404.42019
Gorbachev, Dmitry V.; Ivanov, Valerii I.; Tikhonov, Sergey Yu.
2016
On generalized Lipschitz classes and Fourier series. Zbl 1065.26005
Tikhonov, Sergey
2004
Convolution inequalities in Lorentz spaces. Zbl 1235.44012
Nursultanov, Erlan; Tikhonov, Sergey
2011
Convergence of trigonometric series with general monotone coefficients. Zbl 1141.42004
Dyachenko, Mikhail; Tikhonov, Sergey
2007
Positive $$L^p$$-bounded Dunkl-type generalized translation operator and its applications. Zbl 1416.42007
Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu.
2019
Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010
Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter
2014
Moduli of smoothness of functions and their derivatives. Zbl 1141.26005
Ditzian, Z.; Tikhonov, S.
2007
Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates. Zbl 1252.42011
Gorbachev, Dmitry; Tikhonov, Sergey
2012
Weak type inequalities for moduli of smoothness: The case of limit value parameters. Zbl 1217.41015
Tikhonov, Sergey
2010
On $$L_1$$-convergence of Fourier series. Zbl 1257.42009
Tikhonov, Sergey
2008
On the integrability of trigonometric series. Zbl 1136.42003
Tikhonov, S. Yu.
2005
On sharp constants in Bernstein-Nikolskii inequalities. Zbl 1370.41023
Ganzburg, Michael I.; Tikhonov, Sergey Yu.
2017
Nikolskii inequality and functional classes on compact Lie groups. Zbl 1339.46038
Nursultanov, E. D.; Ruzhansky, M. V.; Tikhonov, S. Yu.
2015
Extending tests for convergence of number series. Zbl 1216.40001
Liflyand, E.; Tikhonov, S.; Zeltser, M.
2011
Weighted Paley-Wiener theorem on the Hilbert transform. Zbl 1210.42019
Liflyand, Elijah; Tikhonov, Sergey
2010
General monotone sequences and convergence of trigonometric series. Zbl 1167.42303
Dyachenko, M.; Tikhonov, S.
2008
A Hardy-Littlewood theorem for multiple series. Zbl 1283.42031
Dyachenko, Mikhail; Tikhonov, Sergey
2008
On the uniform convergence of trigonometric series. Zbl 1183.42005
Tikhonov, S. Yu.
2007
Smoothness conditions and Fourier series. Zbl 1124.26002
Tikhonov, Sergey
2007
On moduli of smoothness of fractional order. Zbl 1108.26004
Tikhonov, S.
2005
Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $$L^2$$. Zbl 1334.42020
Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu.
2016
On embeddings of function classes defined by constructive characteristics. Zbl 1115.46029
Simonov, Boris V.; Tikhonov, Sergey Yu.
2006
Pitt inequalities and restriction theorems for the Fourier transform. Zbl 1381.42018
De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey
2017
Pitt and Boas inequalities for Fourier and Hankel transforms. Zbl 1307.44004
De Carli, L.; Gorbachev, D.; Tikhonov, S.
2013
Two-sided weighted Fourier inequalities. Zbl 1278.42006
Liflyand, Elijah; Tikhonov, Sergey
2012
Uniform convergence and integrability of Fourier integrals. Zbl 1201.42003
Dyachenko, Mikhail; Liflyand, Elijah; Tikhonov, Sergey
2010
Embedding results in questions of strong approximation by Fourier series. Zbl 1121.42005
Tikhonov, Sergey
2006
Strong approximation of Fourier series and embedding theorems. Zbl 1120.42002
Tikhonov, Sergey
2005
Wiener’s problem for positive definite functions. Zbl 1402.42011
Gorbachev, D. V.; Tikhonov, S. Yu.
2018
Constructive characteristics of mixed moduli of smoothness of positive orders. Zbl 1298.41020
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2012
Two power-weight inequalities for the Hilbert transform on the cones of monotone functions. Zbl 1237.44005
Stepanov, Vladimir D.; Tikhonov, Sergey Yu.
2011
Ulyanov-type inequalities and generalized Liouville derivatives. Zbl 1213.26010
Tikhonov, Sergey; Trebels, Walter
2011
Relations between mixed moduli of smoothness, and embedding theorems for Nikol’skii classes. Zbl 1213.46032
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2010
Wiener’s positive Fourier coefficients theorem in variants of $$L^p$$ spaces. Zbl 1204.42012
Ash, J. M.; Tikhonov, S.; Tung, J.
2010
Weighted norm inequalities for integral transforms. Zbl 1410.42013
Gorbachev, Dmitry; Liflyand, Elijah; Tikhonov, Sergey
2018
Weighted norm inequalities for convolution and Riesz potential. Zbl 1307.31017
Nursultanov, Erlan; Tikhonov, Sergey
2015
Two-weight inequalities for the Hilbert transform of monotone functions. Zbl 1253.26034
Stepanov, V. D.; Tikhonov, S. Yu.
2011
Relations between moduli of smoothness in different metrics. Zbl 1304.41010
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2009
Norm inequalities for convolution operators. Zbl 1184.42005
Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke
2009
Characteristics of Besov-Nikol’skiĭ class of functions. Zbl 1114.42002
Tikhonov, Sergey
2005
On the Besov and Besov-Nikol’skiĭ classes and on estimates for the mixed moduli of smoothness of fractional derivatives. Zbl 1089.46024
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2003
Properties of moduli of smoothness in $$L_p (\mathbb{R}^d)$$. Zbl 1450.41004
Kolomoitsev, Yurii; Tikhonov, Sergey
2020
Smoothness and asymptotic properties of functions with general monotone Fourier coefficients. Zbl 1412.42005
Dyachenko, M. I.; Tikhonov, S. Yu.
2018
Remez-type and Nikol’skii-type inequalities: general relations and the hyperbolic cross polynomials. Zbl 1381.41015
Temlyakov, V.; Tikhonov, S.
2017
Reverse Hölder’s inequality for spherical harmonics. Zbl 1366.33009
Dai, Feng; Feng, Han; Tikhonov, Sergey
2016
Weak monotonicity concept and its applications. Zbl 1334.40004
Tikhonov, S.; Zeltser, M.
2014
Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084
2012
Relations for moduli of smoothness in various metrics: functions with restrictions on the Fourier coefficients. Zbl 1204.42007
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2009
An inequality of P. L. Ul’yanov. Zbl 1212.26029
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2008
Doubling condition at the origin for non-negative positive definite functions. Zbl 1412.42024
Gorbachev, Dmitry; Tikhonov, Sergey
2019
Hardy-Littlewood and Pitt’s inequalities for Hausdorff operators. Zbl 1409.42006
Dyachenko, M.; Nursultanov, E.; Tikhonov, S.
2018
Weighted fractional Bernstein’s inequalities and their applications. Zbl 1350.26022
Dai, Feng; Tikhonov, Sergey
2016
Some problems in Fourier analysis and approximation theory. Zbl 1343.42001
Ruzhansky, Michael; Tikhonov, Sergey
2016
Transformation of Fourier series using power and weakly oscillating sequences. Zbl 1094.42005
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2005
Integral norm discretization and related problems. Zbl 07179262
Dai, F.; Prymak, A.; Temlyakov, V. N.; Tikhonov, S. Yu.
2019
Uniform convergence of trigonometric series with general monotone coefficients. Zbl 1427.42003
Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey
2019
Norm convolution inequalities in Lebesgue spaces. Zbl 1404.44010
Erlan, Nursultanov; Tikhonov, Sergey; Tleukhanova, Nazerke
2018
Bernstein inequalities with nondoubling weights. Zbl 1362.26014
Bondarenko, Andrii; Tikhonov, Sergey
2017
Jacobi weights, fractional integration, and sharp Ulyanov inequalities. Zbl 1321.41011
Glazyrina, Polina; Tikhonov, Sergey
2015
Regularity of the Monge-Ampère equation in Besov’s spaces. Zbl 1290.35098
Kolesnikov, Alexander V.; Tikhonov, Sergey Yu.
2014
Addendum to “Trigonometric series of Nikol’skii classes”. Zbl 1212.42011
Tikhonov, S.
2008
On two theorems of Lorentz. Zbl 1077.42004
Tikhonov, S. Yu.
2005
Remark on the order of approximation by Steklov means. Zbl 1084.41013
Ditzian, Z.; Tikhonov, S. Yu.
2004
Estimates for the moduli of smoothness of a transformed Fourier series. Zbl 1119.42301
Tikhonov, S. Yu.
2002
Moduli of smoothness and the interrelation of some classes of functions. Zbl 1129.46307
Tikhonov, Sergey Yu.
2002
Properties of moduli of smoothness in $$L_p (\mathbb{R}^d)$$. Zbl 1450.41004
Kolomoitsev, Yurii; Tikhonov, Sergey
2020
Positive $$L^p$$-bounded Dunkl-type generalized translation operator and its applications. Zbl 1416.42007
Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu.
2019
Doubling condition at the origin for non-negative positive definite functions. Zbl 1412.42024
Gorbachev, Dmitry; Tikhonov, Sergey
2019
Integral norm discretization and related problems. Zbl 07179262
Dai, F.; Prymak, A.; Temlyakov, V. N.; Tikhonov, S. Yu.
2019
Uniform convergence of trigonometric series with general monotone coefficients. Zbl 1427.42003
Dyachenko, Mikhail; Mukanov, Askhat; Tikhonov, Sergey
2019
Wiener’s problem for positive definite functions. Zbl 1402.42011
Gorbachev, D. V.; Tikhonov, S. Yu.
2018
Weighted norm inequalities for integral transforms. Zbl 1410.42013
Gorbachev, Dmitry; Liflyand, Elijah; Tikhonov, Sergey
2018
Smoothness and asymptotic properties of functions with general monotone Fourier coefficients. Zbl 1412.42005
Dyachenko, M. I.; Tikhonov, S. Yu.
2018
Hardy-Littlewood and Pitt’s inequalities for Hausdorff operators. Zbl 1409.42006
Dyachenko, M.; Nursultanov, E.; Tikhonov, S.
2018
Norm convolution inequalities in Lebesgue spaces. Zbl 1404.44010
Erlan, Nursultanov; Tikhonov, Sergey; Tleukhanova, Nazerke
2018
On sharp constants in Bernstein-Nikolskii inequalities. Zbl 1370.41023
Ganzburg, Michael I.; Tikhonov, Sergey Yu.
2017
Pitt inequalities and restriction theorems for the Fourier transform. Zbl 1381.42018
De Carli, Laura; Gorbachev, Dmitry; Tikhonov, Sergey
2017
Remez-type and Nikol’skii-type inequalities: general relations and the hyperbolic cross polynomials. Zbl 1381.41015
Temlyakov, V.; Tikhonov, S.
2017
Bernstein inequalities with nondoubling weights. Zbl 1362.26014
Bondarenko, Andrii; Tikhonov, Sergey
2017
Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Zbl 1356.35022
Nursultanov, Erlan; Ruzhansky, Michael; Tikhonov, Sergey
2016
Pitt’s inequalities and uncertainty principle for generalized Fourier transform. Zbl 1404.42019
Gorbachev, Dmitry V.; Ivanov, Valerii I.; Tikhonov, Sergey Yu.
2016
Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $$L^2$$. Zbl 1334.42020
Gorbachev, D. V.; Ivanov, V. I.; Tikhonov, S. Yu.
2016
Reverse Hölder’s inequality for spherical harmonics. Zbl 1366.33009
Dai, Feng; Feng, Han; Tikhonov, Sergey
2016
Weighted fractional Bernstein’s inequalities and their applications. Zbl 1350.26022
Dai, Feng; Tikhonov, Sergey
2016
Some problems in Fourier analysis and approximation theory. Zbl 1343.42001
Ruzhansky, Michael; Tikhonov, Sergey
2016
Nikolskii inequality and functional classes on compact Lie groups. Zbl 1339.46038
Nursultanov, E. D.; Ruzhansky, M. V.; Tikhonov, S. Yu.
2015
Weighted norm inequalities for convolution and Riesz potential. Zbl 1307.31017
Nursultanov, Erlan; Tikhonov, Sergey
2015
Jacobi weights, fractional integration, and sharp Ulyanov inequalities. Zbl 1321.41011
Glazyrina, Polina; Tikhonov, Sergey
2015
Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010
Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter
2014
Weak monotonicity concept and its applications. Zbl 1334.40004
Tikhonov, S.; Zeltser, M.
2014
Regularity of the Monge-Ampère equation in Besov’s spaces. Zbl 1290.35098
Kolesnikov, Alexander V.; Tikhonov, Sergey Yu.
2014
Mixed moduli of smoothness in $$L_{p}$$: a survey. Zbl 1285.26008
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2013
A sharp Remez inequality for trigonometric polynomials. Zbl 1280.41011
Nursultanov, E.; Tikhonov, S.
2013
Pitt and Boas inequalities for Fourier and Hankel transforms. Zbl 1307.44004
De Carli, L.; Gorbachev, D.; Tikhonov, S.
2013
Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates. Zbl 1252.42011
Gorbachev, Dmitry; Tikhonov, Sergey
2012
Two-sided weighted Fourier inequalities. Zbl 1278.42006
Liflyand, Elijah; Tikhonov, Sergey
2012
Constructive characteristics of mixed moduli of smoothness of positive orders. Zbl 1298.41020
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2012
Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084
2012
A concept of general monotonicity and applications. Zbl 1223.26017
Liflyand, E.; Tikhonov, S.
2011
Net spaces and boundedness of integral operators. Zbl 1248.46025
Nursultanov, Erlan; Tikhonov, Sergey
2011
Weighted Fourier inequalities: Boas’ conjecture in $${\mathbb{R}}^{n}$$. Zbl 1246.42011
Gorbachev, D.; Liflyand, E.; Tikhonov, S.
2011
Convolution inequalities in Lorentz spaces. Zbl 1235.44012
Nursultanov, Erlan; Tikhonov, Sergey
2011
Extending tests for convergence of number series. Zbl 1216.40001
Liflyand, E.; Tikhonov, S.; Zeltser, M.
2011
Two power-weight inequalities for the Hilbert transform on the cones of monotone functions. Zbl 1237.44005
Stepanov, Vladimir D.; Tikhonov, Sergey Yu.
2011
Ulyanov-type inequalities and generalized Liouville derivatives. Zbl 1213.26010
Tikhonov, Sergey; Trebels, Walter
2011
Two-weight inequalities for the Hilbert transform of monotone functions. Zbl 1253.26034
Stepanov, V. D.; Tikhonov, S. Yu.
2011
Sharp Ul’yanov-type inequalities using fractional smoothness. Zbl 1215.26011
Simonov, Boris; Tikhonov, Sergey
2010
Weak type inequalities for moduli of smoothness: The case of limit value parameters. Zbl 1217.41015
Tikhonov, Sergey
2010
Weighted Paley-Wiener theorem on the Hilbert transform. Zbl 1210.42019
Liflyand, Elijah; Tikhonov, Sergey
2010
Uniform convergence and integrability of Fourier integrals. Zbl 1201.42003
Dyachenko, Mikhail; Liflyand, Elijah; Tikhonov, Sergey
2010
Relations between mixed moduli of smoothness, and embedding theorems for Nikol’skii classes. Zbl 1213.46032
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2010
Wiener’s positive Fourier coefficients theorem in variants of $$L^p$$ spaces. Zbl 1204.42012
Ash, J. M.; Tikhonov, S.; Tung, J.
2010
Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Zbl 1169.42001
Dyachenko, Mikhail; Tikhonov, Sergey
2009
The Fourier transforms of general monotone functions. Zbl 1297.42009
Liflyand, E.; Tikhonov, S.
2009
Relations between moduli of smoothness in different metrics. Zbl 1304.41010
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2009
Norm inequalities for convolution operators. Zbl 1184.42005
Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke
2009
Relations for moduli of smoothness in various metrics: functions with restrictions on the Fourier coefficients. Zbl 1204.42007
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2009
Best approximation and moduli of smoothness: Computation and equivalence theorems. Zbl 1215.42002
Tikhonov, Sergey
2008
Extended solution of Boas’ conjecture on Fourier transforms. Zbl 1151.42002
Liflyand, Elijah; Tikhonov, Sergey
2008
Sharp Jackson inequalities. Zbl 1136.41003
Dai, F.; Ditzian, Z.; Tikhonov, S.
2008
Embedding theorems in constructive approximation. Zbl 1172.46023
Simonov, B. V.; Tikhonov, S. Yu.
2008
On $$L_1$$-convergence of Fourier series. Zbl 1257.42009
Tikhonov, Sergey
2008
General monotone sequences and convergence of trigonometric series. Zbl 1167.42303
Dyachenko, M.; Tikhonov, S.
2008
A Hardy-Littlewood theorem for multiple series. Zbl 1283.42031
Dyachenko, Mikhail; Tikhonov, Sergey
2008
An inequality of P. L. Ul’yanov. Zbl 1212.26029
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2008
Addendum to “Trigonometric series of Nikol’skii classes”. Zbl 1212.42011
Tikhonov, S.
2008
Trigonometric series with general monotone coefficients. Zbl 1106.42003
Tikhonov, S.
2007
Trigonometric series of Nikol’skii classes. Zbl 1121.42006
Tikhonov, S.
2007
Convergence of trigonometric series with general monotone coefficients. Zbl 1141.42004
Dyachenko, Mikhail; Tikhonov, Sergey
2007
Moduli of smoothness of functions and their derivatives. Zbl 1141.26005
Ditzian, Z.; Tikhonov, S.
2007
On the uniform convergence of trigonometric series. Zbl 1183.42005
Tikhonov, S. Yu.
2007
Smoothness conditions and Fourier series. Zbl 1124.26002
Tikhonov, Sergey
2007
On embeddings of function classes defined by constructive characteristics. Zbl 1115.46029
Simonov, Boris V.; Tikhonov, Sergey Yu.
2006
Embedding results in questions of strong approximation by Fourier series. Zbl 1121.42005
Tikhonov, Sergey
2006
Ul’yanov and Nikol’skii-type inequalities. Zbl 1069.41014
Ditzian, Z.; Tikhonov, S.
2005
On the integrability of trigonometric series. Zbl 1136.42003
Tikhonov, S. Yu.
2005
On moduli of smoothness of fractional order. Zbl 1108.26004
Tikhonov, S.
2005
Strong approximation of Fourier series and embedding theorems. Zbl 1120.42002
Tikhonov, Sergey
2005
Characteristics of Besov-Nikol’skiĭ class of functions. Zbl 1114.42002
Tikhonov, Sergey
2005
Transformation of Fourier series using power and weakly oscillating sequences. Zbl 1094.42005
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2005
On two theorems of Lorentz. Zbl 1077.42004
Tikhonov, S. Yu.
2005
On generalized Lipschitz classes and Fourier series. Zbl 1065.26005
Tikhonov, Sergey
2004
Remark on the order of approximation by Steklov means. Zbl 1084.41013
Ditzian, Z.; Tikhonov, S. Yu.
2004
On the Besov and Besov-Nikol’skiĭ classes and on estimates for the mixed moduli of smoothness of fractional derivatives. Zbl 1089.46024
Potapov, M. K.; Simonov, B. V.; Tikhonov, S. Yu.
2003
Estimates for the moduli of smoothness of a transformed Fourier series. Zbl 1119.42301
Tikhonov, S. Yu.
2002
Moduli of smoothness and the interrelation of some classes of functions. Zbl 1129.46307
Tikhonov, Sergey Yu.
2002
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#### Cited in 103 Serials

 25 Journal of Mathematical Analysis and Applications 21 Journal of Approximation Theory 16 Acta Mathematica Hungarica 16 The Journal of Fourier Analysis and Applications 15 Analysis Mathematica 13 Mathematical Notes 10 Moscow University Mathematics Bulletin 9 Ukrainian Mathematical Journal 8 Constructive Approximation 7 Journal of Mathematical Sciences (New York) 7 Proceedings of the Steklov Institute of Mathematics 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Journal of Pseudo-Differential Operators and Applications 5 Eurasian Mathematical Journal 4 Proceedings of the American Mathematical Society 4 Doklady Mathematics 4 Journal of Inequalities and Applications 3 Journal d’Analyse Mathématique 3 Journal of Functional Analysis 3 Mathematische Nachrichten 3 Bulletin des Sciences Mathématiques 3 Abstract and Applied Analysis 3 Mediterranean Journal of Mathematics 3 Complex Variables and Elliptic Equations 3 Chebyshevskiĭ Sbornik 3 Transactions of A. Razmadze Mathematical Institute 2 Russian Mathematical Surveys 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Monatshefte für Mathematik 2 Siberian Mathematical Journal 2 The Journal of Geometric Analysis 2 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 2 Indagationes Mathematicae. New Series 2 Russian Mathematics 2 Integral Transforms and Special Functions 2 Mathematical Inequalities & Applications 2 Analysis and Applications (Singapore) 2 Complex Analysis and Operator Theory 2 Journal of Function Spaces 1 Bulletin of the Australian Mathematical Society 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Linear and Multilinear Algebra 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Colloquium Mathematicum 1 Demonstratio Mathematica 1 Functional Analysis and its Applications 1 Indiana University Mathematics Journal 1 Journal of Multivariate Analysis 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Journal of Integral Equations and Applications 1 International Journal of Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Expositiones Mathematicae 1 Computational Statistics and Data Analysis 1 Potential Analysis 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 St. Petersburg Mathematical Journal 1 Turkish Journal of Mathematics 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Bernoulli 1 Sbornik: Mathematics 1 Acta Mathematica Sinica. English Series 1 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 1 Communications on Pure and Applied Analysis 1 Computational Methods and Function Theory 1 Journal of the Institute of Mathematics of Jussieu 1 Analysis in Theory and Applications 1 International Journal of Wavelets, Multiresolution and Information Processing 1 The Australian Journal of Mathematical Analysis and Applications 1 Journal of Fixed Point Theory and Applications 1 Journal of Mathematical Inequalities 1 Discrete and Continuous Dynamical Systems. Series S 1 Tbilisi Mathematical Journal 1 Science China. Mathematics 1 Symmetry 1 Analysis and Mathematical Physics 1 Forum of Mathematics, Sigma 1 Journal of Classical Analysis 1 Problemy Analiza. Issues of Analysis 1 Journal of Linear and Topological Algebra 1 European Journal of Mathematics 1 Advances in Operator Theory ...and 3 more Serials
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#### Cited in 31 Fields

 187 Harmonic analysis on Euclidean spaces (42-XX) 83 Approximations and expansions (41-XX) 72 Real functions (26-XX) 68 Functional analysis (46-XX) 30 Operator theory (47-XX) 26 Integral transforms, operational calculus (44-XX) 16 Sequences, series, summability (40-XX) 15 Special functions (33-XX) 14 Partial differential equations (35-XX) 13 Abstract harmonic analysis (43-XX) 12 Functions of a complex variable (30-XX) 9 Topological groups, Lie groups (22-XX) 8 Numerical analysis (65-XX) 4 Integral equations (45-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistics (62-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 $$K$$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Computer science (68-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

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