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Romanyuk, Anatolii Sergiiovych

Author ID: romanyuk.anatolii-sergiiovych Recent zbMATH articles by "Romanyuk, Anatolii Sergiiovych"
Published as: Romanyuk, A. S.; Romanyuk, Anatolii Sergiiovych; Romanyuk, Anatolii S.
Documents Indexed: 64 Publications since 1987, including 1 Book and 1 Additional arXiv Preprint
Co-Authors: 18 Co-Authors with 16 Joint Publications
844 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 309 times in 114 Documents Cited by Year
Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\). Zbl 0782.42022
Romanyuk, A. S.
20
1991
Diameters and best approximation of the classes \(B^r_{p,\theta}\) of periodic functions of several variables. Zbl 1240.42028
Romanyuk, A. S.
18
2011
Best \(M\)-term trigonometric approximations of Besov classes of periodic functions of several variables. Zbl 1066.42001
Romanyuk, A. S.
17
2003
Best approximations and widths of classes of periodic functions of several variables. Zbl 1173.41012
Romanyuk, A. S.
15
2008
Linear widths of the Besov classes of periodic functions of many variables. II. Zbl 0998.41019
Romanyuk, A. S.
14
2001
Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \). Zbl 1436.42005
Romanyuk, A. S.; Romanyuk, V. S.
13
2019
Trigonometric and orthoprojection widths of classes of periodic functions of many variables. Zbl 1224.41086
Romanyuk, A. S.; Romanyuk, V. S.
11
2009
Linear widths of the Besov classes of periodic functions of many variables. I. Zbl 0991.41017
Romanyuk, A. S.
11
2001
Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables. Zbl 1224.42005
Romanyuk, A. S.; Romanyuk, V. S.
10
2010
Approximation characteristics of classes of periodic functions of several variables. (Аппроксимативные характеристики классов периодичестих функций многих переменных.) Zbl 1324.42001
Romanyuk, A. S.
10
2012
On estimates of the Kolmogorov widths of the classes \(B_{p,\theta}^r\) in the space \(L_q\). Zbl 1005.42005
Romanyuk, A. S.
10
2001
Kolmogorov and trigonometric widths of the Besov classes \(B^r_{p,\theta}\) of multivariate periodic functions. Zbl 1147.46026
Romanyuk, A. S.
9
2006
Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric. Zbl 1219.41006
Romanyuk, A. S.
9
2007
Estimation of the entropy numbers and Kolmogorov widths for the Nikol’skii-Besov classes of periodic functions of many variables. Zbl 1388.46028
Romanyuk, A. S.
9
2016
Approximation of the classes \(B^r_{p,\theta}\) of periodic functions of several variables by linear methods, and best approximations. Zbl 1074.46024
Romanyuk, A. S.
8
2004
Estimates of approximation characteristics of the Besov classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space \(L_q\). II. Zbl 1005.42004
Romanyuk, A. S.
8
2001
On Kolmogorov widths of classes \(B^ r_{p,\theta}\) of periodic functions of many variables with low smoothness in space \(L_ p\). Zbl 0883.42017
Romanyuk, A. S.
7
1994
Bilinear approximations and Kolmogorov widths of periodic Besov classes. Zbl 1199.46085
Romanyuk, A. S.
7
2009
Approximation of classes of periodic functions of several variables. Zbl 1020.42012
Romanyuk, A. S.
7
2002
Estimates for approximation characteristics of the Besov classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space \(L_q\). I. Zbl 1005.42003
Romanyuk, A. S.
7
2001
Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables. Zbl 1490.41014
Romanyuk, A. S.
7
2017
Approximation of the isotropic classes \(B^r_{p,\theta}\) of periodic functions of several variables in the space \(L_q\). Zbl 1199.46084
Romanyuk, A. S.
6
2008
The best trigonometric approximations and the Kolmogorov diameters of the Besov classes of functions of many variables. Zbl 0819.42010
Romanyuk, A. S.
6
1993
Approximative characteristics of the isotropic classes of periodic functions of many variables. Zbl 1224.42022
Romanyuk, A. S.
5
2009
On the best approximations and Kolmogorov width of Besov classes of periodic functions of several variables. Zbl 0907.41023
Romanyuk, A. S.
5
1995
Best trigonometric and bilinear approximations of functions of several variables of the classes \(B_{p,\theta}^ r\). I. Zbl 0793.42009
Romanyuk, A. S.
5
1992
Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes \(B_{p,\theta}^r\). Zbl 1101.41027
Romanyuk, A. S.
4
2006
On best trigonometric and bilinear approximation of Besov classes of functions of many variables. Zbl 0887.42018
Romanyuk, A. S.
4
1995
On approximation of classes of periodic functions of several variables. Zbl 0773.42015
Romanyuk, A. S.
4
1992
Entropy numbers and widths for the Nikol’skii-Besov classes of functions of many variables in the space \(L_{\infty}\). Zbl 1438.41044
Romanyuk, A. S.
4
2019
Estimation of some approximating characteristics of the classes of periodic functions of one and many variables. Zbl 1523.42005
Romanyuk, A. S.; Romanyuk, V. S.
4
2020
Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\). Zbl 1498.41027
Romanyuk, A. S.; Yanchenko, S. Ya.
4
2022
Best bilinear approximations of functions from Nikol’skii-Besov classes. Zbl 1257.41015
Romanyuk, A. S.; Romanyuk, V. S.
4
2012
Approximation of classes of functions of many variables by their orthogonal projections onto subspaces of trigonometric polynomials. Zbl 0937.41017
Romanyuk, A. S.
3
1996
The best trigonometric and bilinear approximations for functions of many variables from the classes \(B^ r_{p,\theta}\). II. Zbl 0819.42011
Romanyuk, A. S.
3
1993
Kolmogorov widths of the Besov classes \(B_{p,\theta}^r\) in the metric of the space \(L_\infty\). Zbl 1151.41310
Romanyuk, A. S.
3
2005
Best trigonometric and bilinear approximations of classes of functions of several variables. Zbl 1286.42008
Romanyuk, A. S.
3
2013
Approximation of classes of periodic functions of several variables. Zbl 0782.42023
Romanyuk, A. S.
2
1992
Best bilinear approximations for the classes of functions of many variables. Zbl 1309.41016
Romanyuk, A. S.; Romanyuk, V. S.
2
2014
Approximation of classes \(B_{p,\theta}^r\) by linear methods and best approximations. Zbl 1006.42014
Romanyuk, A. S.
2
2002
Estimates of the entropy numbers and \(\varepsilon\)-entropy of the Nikol’skii-Besov classes of periodic functions of several variables. Zbl 1313.41046
Romanyuk, A. S.
2
2014
Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions. Zbl 1519.42003
Romanyuk, A. S.; Romanyuk, V. S.; Pozharska, K. V.; Hembars’ka, S. B.
2
2023
Trigonometric widths of the classes \(B_{p,\theta}^{r}\) of functions of many variables in the space \(L_{q}\). Zbl 0942.42005
Romanyuk, A. S.
1
1998
On the problem of linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables. Zbl 1309.41014
Romanyuk, A. S.
1
2014
Trigonometric and linear widths for the classes of periodic multivariate functions. Zbl 1499.41091
Romanyuk, A. S.
1
2017
Kolmogorov widths and bilinear approximations of the classes of periodic functions of one and many variables. Zbl 1426.41034
Romanyuk, A. S.
1
2018
Approximation of the classes of periodic functions of one and many variables from the Nikol’skii-Besov and Sobolev spaces. Zbl 1526.42004
Romanyuk, A. S.; Yanchenko, S. Ya.
1
2022
Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions. Zbl 1519.42003
Romanyuk, A. S.; Romanyuk, V. S.; Pozharska, K. V.; Hembars’ka, S. B.
2
2023
Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\). Zbl 1498.41027
Romanyuk, A. S.; Yanchenko, S. Ya.
4
2022
Approximation of the classes of periodic functions of one and many variables from the Nikol’skii-Besov and Sobolev spaces. Zbl 1526.42004
Romanyuk, A. S.; Yanchenko, S. Ya.
1
2022
Estimation of some approximating characteristics of the classes of periodic functions of one and many variables. Zbl 1523.42005
Romanyuk, A. S.; Romanyuk, V. S.
4
2020
Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \). Zbl 1436.42005
Romanyuk, A. S.; Romanyuk, V. S.
13
2019
Entropy numbers and widths for the Nikol’skii-Besov classes of functions of many variables in the space \(L_{\infty}\). Zbl 1438.41044
Romanyuk, A. S.
4
2019
Kolmogorov widths and bilinear approximations of the classes of periodic functions of one and many variables. Zbl 1426.41034
Romanyuk, A. S.
1
2018
Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables. Zbl 1490.41014
Romanyuk, A. S.
7
2017
Trigonometric and linear widths for the classes of periodic multivariate functions. Zbl 1499.41091
Romanyuk, A. S.
1
2017
Estimation of the entropy numbers and Kolmogorov widths for the Nikol’skii-Besov classes of periodic functions of many variables. Zbl 1388.46028
Romanyuk, A. S.
9
2016
Best bilinear approximations for the classes of functions of many variables. Zbl 1309.41016
Romanyuk, A. S.; Romanyuk, V. S.
2
2014
Estimates of the entropy numbers and \(\varepsilon\)-entropy of the Nikol’skii-Besov classes of periodic functions of several variables. Zbl 1313.41046
Romanyuk, A. S.
2
2014
On the problem of linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables. Zbl 1309.41014
Romanyuk, A. S.
1
2014
Best trigonometric and bilinear approximations of classes of functions of several variables. Zbl 1286.42008
Romanyuk, A. S.
3
2013
Approximation characteristics of classes of periodic functions of several variables. (Аппроксимативные характеристики классов периодичестих функций многих переменных.) Zbl 1324.42001
Romanyuk, A. S.
10
2012
Best bilinear approximations of functions from Nikol’skii-Besov classes. Zbl 1257.41015
Romanyuk, A. S.; Romanyuk, V. S.
4
2012
Diameters and best approximation of the classes \(B^r_{p,\theta}\) of periodic functions of several variables. Zbl 1240.42028
Romanyuk, A. S.
18
2011
Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables. Zbl 1224.42005
Romanyuk, A. S.; Romanyuk, V. S.
10
2010
Trigonometric and orthoprojection widths of classes of periodic functions of many variables. Zbl 1224.41086
Romanyuk, A. S.; Romanyuk, V. S.
11
2009
Bilinear approximations and Kolmogorov widths of periodic Besov classes. Zbl 1199.46085
Romanyuk, A. S.
7
2009
Approximative characteristics of the isotropic classes of periodic functions of many variables. Zbl 1224.42022
Romanyuk, A. S.
5
2009
Best approximations and widths of classes of periodic functions of several variables. Zbl 1173.41012
Romanyuk, A. S.
15
2008
Approximation of the isotropic classes \(B^r_{p,\theta}\) of periodic functions of several variables in the space \(L_q\). Zbl 1199.46084
Romanyuk, A. S.
6
2008
Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric. Zbl 1219.41006
Romanyuk, A. S.
9
2007
Kolmogorov and trigonometric widths of the Besov classes \(B^r_{p,\theta}\) of multivariate periodic functions. Zbl 1147.46026
Romanyuk, A. S.
9
2006
Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes \(B_{p,\theta}^r\). Zbl 1101.41027
Romanyuk, A. S.
4
2006
Kolmogorov widths of the Besov classes \(B_{p,\theta}^r\) in the metric of the space \(L_\infty\). Zbl 1151.41310
Romanyuk, A. S.
3
2005
Approximation of the classes \(B^r_{p,\theta}\) of periodic functions of several variables by linear methods, and best approximations. Zbl 1074.46024
Romanyuk, A. S.
8
2004
Best \(M\)-term trigonometric approximations of Besov classes of periodic functions of several variables. Zbl 1066.42001
Romanyuk, A. S.
17
2003
Approximation of classes of periodic functions of several variables. Zbl 1020.42012
Romanyuk, A. S.
7
2002
Approximation of classes \(B_{p,\theta}^r\) by linear methods and best approximations. Zbl 1006.42014
Romanyuk, A. S.
2
2002
Linear widths of the Besov classes of periodic functions of many variables. II. Zbl 0998.41019
Romanyuk, A. S.
14
2001
Linear widths of the Besov classes of periodic functions of many variables. I. Zbl 0991.41017
Romanyuk, A. S.
11
2001
On estimates of the Kolmogorov widths of the classes \(B_{p,\theta}^r\) in the space \(L_q\). Zbl 1005.42005
Romanyuk, A. S.
10
2001
Estimates of approximation characteristics of the Besov classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space \(L_q\). II. Zbl 1005.42004
Romanyuk, A. S.
8
2001
Estimates for approximation characteristics of the Besov classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space \(L_q\). I. Zbl 1005.42003
Romanyuk, A. S.
7
2001
Trigonometric widths of the classes \(B_{p,\theta}^{r}\) of functions of many variables in the space \(L_{q}\). Zbl 0942.42005
Romanyuk, A. S.
1
1998
Approximation of classes of functions of many variables by their orthogonal projections onto subspaces of trigonometric polynomials. Zbl 0937.41017
Romanyuk, A. S.
3
1996
On the best approximations and Kolmogorov width of Besov classes of periodic functions of several variables. Zbl 0907.41023
Romanyuk, A. S.
5
1995
On best trigonometric and bilinear approximation of Besov classes of functions of many variables. Zbl 0887.42018
Romanyuk, A. S.
4
1995
On Kolmogorov widths of classes \(B^ r_{p,\theta}\) of periodic functions of many variables with low smoothness in space \(L_ p\). Zbl 0883.42017
Romanyuk, A. S.
7
1994
The best trigonometric approximations and the Kolmogorov diameters of the Besov classes of functions of many variables. Zbl 0819.42010
Romanyuk, A. S.
6
1993
The best trigonometric and bilinear approximations for functions of many variables from the classes \(B^ r_{p,\theta}\). II. Zbl 0819.42011
Romanyuk, A. S.
3
1993
Best trigonometric and bilinear approximations of functions of several variables of the classes \(B_{p,\theta}^ r\). I. Zbl 0793.42009
Romanyuk, A. S.
5
1992
On approximation of classes of periodic functions of several variables. Zbl 0773.42015
Romanyuk, A. S.
4
1992
Approximation of classes of periodic functions of several variables. Zbl 0782.42023
Romanyuk, A. S.
2
1992
Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\). Zbl 0782.42022
Romanyuk, A. S.
20
1991
all top 5

Cited by 69 Authors

20 Romanyuk, Anatolii Sergiiovych
9 Stasyuk, Serhii A.
8 Hembars’ka, Svitlana Borysivna
7 Romanyuk, Viktor Sergiiovych
6 Sickel, Winfried
6 Solich, Kateryna Vasylivna
6 Ullrich, Tino
5 Akishev, Gabdolla Akishevich
5 Bazarkhanov, Daurenbek Bolysbekovich
5 Fedunyk-Yaremchuk, Oksana Volodymyrivna
4 Duan, Liqin
4 Liu, Yongping
4 Myronyuk, V. V.
4 Pozharska, Kateryna Vitaliivna
4 Yanchenko, Serhii Ya.
3 Bekmaganbetov, Kuanysh Abdrakhmanovich
3 Derev’yanko, N. V.
3 Hembars’kyi, Mykhailo Vitaliiovych
3 Jiang, Yanjie
3 Nguyen, Van Kien
3 Shkapa, Viktoriya V.
3 Temlyakov, Vladimir Nikolaevich
2 Byrenheid, Glenn
2 Fang, Gensun
2 Gensun, Fang
2 Guanggui, Chen
2 Toleugazy, Yerzhan
2 Yanchenko, Sergii Yakovych
1 Anh, Vo V.
1 Balgimbayeva, Sholpan A.
1 Bilenko, V. I.
1 Bozhonok, K. V.
1 Cobos, Fernando
1 Dinh Dũng
1 Dzyadyk, S. Yu.
1 Hansen, Markus
1 Kervenev, K. E.
1 Kolomoitsev, Yurii S.
1 Konograi, A. F.
1 Konohrai, A. F.
1 Kühn, Thomas
1 Leonenko, Nikolai N.
1 Li, Rensuo
1 Malykhin, Yuriĭ Vyacheslavovich
1 Mayer, Sebastian A.
1 Petersen, Martin R.
1 Radchenko, O. Ya.
1 Romanyuk, Ihor A.
1 Ronto, Andrei
1 Rontó, Miklós
1 Sakhno, Lyudmyla Mykhaĭlivna
1 Schneider, Reinhold
1 Serdyuk, Anatoly S.
1 Shchobak, Nataliya N.
1 Smirnov, T. I.
1 Stepanyuk, Tetiana A.
1 Sun, Yongsheng
1 Suzuki, Taiji
1 Tsuji, Kazuma
1 Uschmajew, André
1 Vlasyk, Hanna M.
1 Wang, Kai
1 Wang, Yali
1 Xu, Guiqiao
1 Yanchenko, Ya.
1 Ye, Peixin
1 Zaderei, P. V.
1 Zamrii, Iryna V.
1 Zhou, Yinying

Citations by Year