Edit Profile (opens in new tab) Romanyuk, Anatolii Sergiiovych Co-Author Distance Author ID: romanyuk.anatolii-sergiiovych Published as: Romanyuk, A. S.; Romanyuk, Anatolii Sergiiovych; Romanyuk, Anatolii S. more...less 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 all top 5 Co-Authors 48 single-authored 11 Romanyuk, Viktor Sergiiovych 5 Yanchenko, Serhii Ya. 2 Lukovsky, Ivan Oleksandrovych 2 Makarov, Volodymyr Leonidovych 2 Motornyĭ, Vitaliĭ Pavlovych 2 Samoĭlenko, Anatoliĭ Mykhaĭlovych 2 Serdyuk, Anatoly S. 2 Zaderei, P. V. 1 Golub, Anatoly P. 1 Hembars’ka, Svitlana Borysivna 1 Konovalov, V. M. 1 Mytropol’skyĭ, Yuriĭ Oleksiĭovych 1 Pozharska, Kateryna Vitaliivna 1 Rukasov, Vladimir I. 1 Savchuk, Viktor V. 1 Shevchuk, Igor Oleksandrovych 1 Shidlich, Andrii 1 Sokolenko, Igor V. all top 5 Serials 19 Ukrainian Mathematical Journal 18 Ukraïns’kyĭ Matematychnyĭ Zhurnal 5 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 4 Mathematical Notes 3 Sbornik: Mathematics 2 Analysis Mathematica 2 Izvestiya: Mathematics 1 Mathematische Nachrichten 1 Journal of Mathematical Sciences (New York) 1 Ukraïns’kyĭ Matematychnyĭ Visnyk 1 Carpathian Mathematical Publications all top 5 Fields 54 Approximations and expansions (41-XX) 46 Harmonic analysis on Euclidean spaces (42-XX) 21 Functional analysis (46-XX) 2 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 Cited in 26 Serials 43 Ukrainian Mathematical Journal 14 Journal of Mathematical Sciences (New York) 8 Journal of Approximation Theory 6 Journal of Complexity 5 Mathematical Notes 5 Proceedings of the Steklov Institute of Mathematics 3 Analysis Mathematica 3 Constructive Approximation 2 Mathematische Nachrichten 2 Science in China. Series A 2 Doklady Mathematics 2 Acta Mathematica Sinica. English Series 2 Carpathian Mathematical Publications 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Siberian Mathematical Journal 1 Chinese Science Bulletin 1 Matematychni Studiï 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Sarajevo Journal of Mathematics 1 Electronic Journal of Statistics 1 Eurasian Mathematical Journal 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Advances in Operator Theory 1 Ural Mathematical Journal all top 5 Cited in 16 Fields 95 Approximations and expansions (41-XX) 73 Harmonic analysis on Euclidean spaces (42-XX) 34 Functional analysis (46-XX) 8 Numerical analysis (65-XX) 4 Operator theory (47-XX) 2 Ordinary differential equations (34-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year