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Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\). (English. Ukrainian original) Zbl 07491010

Ukr. Math. J. 73, No. 8, 1278-1298 (2022); translation from Ukr. Mat. Zh. 73, No. 8, 1102-1119 (2021).
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Some inequalities between the best polynomial approximations and averaged finite-difference norms in space \(L_2\). (English. Russian original) Zbl 07457379

Russ. Math. 65, No. 10, 69-81 (2021); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2021, No. 10, 78-91 (2021).
MSC:  41A17 41A44
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Widths of functional classes defined by the majorants of generalized moduli of smoothness in the spaces \(\mathcal{S}^p\). (English. Ukrainian original) Zbl 07441695

Ukr. Math. J. 73, No. 6, 841-858 (2021); translation from Ukr. Mat. Zh. 73, No. 6, 723-737 (2021).
MSC:  41A46 41A17 41A25
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Kolmogorov widths of the intersection of two finite-dimensional balls. (English. Russian original) Zbl 1479.41018

Russ. Math. 65, No. 7, 17-23 (2021); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2021, No. 7, 23-29 (2021).
MSC:  41A45 46B45
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Sharp inequalities between the best root-mean-square approximations of analytic functions in the disk and some smoothness characteristics in the Bergman space. (English. Russian original) Zbl 1477.41006

Math. Notes 110, No. 2, 248-260 (2021); translation from Mat. Zametki 110, No. 2, 266-281 (2021).
MSC:  41A17 30E10 41A25
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Sharp inequalities of Jackson-Stechkin type and widths of classes of functions in \(L_2\). (Russian. English translation) Zbl 1474.42012

Ufim. Mat. Zh. 13, No. 1, 56-68 (2021); translation in Ufa Math. J. 13, No. 1, 56-67 (2021).
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Kolmogorov widths of intersections of weighted Sobolev classes on an interval with conditions on the zeroth and first derivatives. (English. Russian original) Zbl 1460.41014

Izv. Math. 85, No. 1, 1-23 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 1, 3-26 (2021).
MSC:  41A46
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Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii-Besov spaces. (English. Ukrainian original) Zbl 1462.42002

J. Math. Sci., New York 252, No. 4, 508-525 (2021); translation from Ukr. Mat. Visn. 17, No. 3, 372-395 (2020).
MSC:  42A10 41A46 42B10
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Adaptive low-rank approximations for operator equations: accuracy control and computational complexity. (English) Zbl 1478.65105

Brenner, Susanne C. (ed.) et al., 75 years of mathematics of computation. Symposium celebrating 75 years of mathematics of computation, Institute for Computational and Experimental Research in Mathematics, ICERM, Providence, RI, USA, November 1–3, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 754, 1-44 (2020).
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Infinitely many minimal surfaces in low dimensions [after F. C. Marques, A. A. Neves et A. Song]. (Infinité d’hypersurfaces minimales en basses dimensions [d’après F. C. Marques, A. A. Neves et A. Song].) (French. English summary) Zbl 1476.53013

Séminaire Bourbaki. Volume 2018/2019, Exposés 1151–1165. Avec table par noms d’auteurs de 1948 à 2018/19. Paris: Société Mathématique de France (SMF). Astérisque 422, 499-543, Exp. No. 1165 (2020).
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Nonlinear spline approximation in BMO\((\mathbb{R})\). (English) Zbl 1460.41005

Draganov, Borislav (ed.) et al., Constructive theory of functions. Proceedings of the 13th international conference, Sozopol, Bulgaria, June 2–8, 2019. Dedicated to the memory of Blagovest Sendov. Sofia: Prof. Marin Drinov Academic Publishing House. 73-112 (2020).
MSC:  41A15 41A17 41A46
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Optimal subspaces for mean square approximation of classes of differentiable functions on a segment. (English. Russian original) Zbl 1458.41005

Vestn. St. Petersbg. Univ., Math. 53, No. 3, 270-281 (2020); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 3, 404-417 (2020).
MSC:  41A15
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Linear and Kolmogorov widths of the classes \(B_{p,\theta}^{\Omega}\) of periodic functions of one and several variables. (English. Ukrainian original) Zbl 1448.41024

J. Math. Sci., New York 249, No. 5, 720-732 (2020); translation from Ukr. Mat. Visn. 17, No. 2, 171-187 (2020).
MSC:  41A46 42B35
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On the estimates of the values of various widths of classes of functions of two variables in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp ( - x^2 - y^2)\). (English. Ukrainian original) Zbl 1462.46031

J. Math. Sci., New York 248, No. 2, 217-232 (2020); translation from Ukr. Mat. Visn. 17, No. 1, 94-102 (2020).
MSC:  46E30 41A46
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Kolmogorov widths of weighted Sobolev classes on an interval with conditions on the zeroth and first derivatives. (English. Russian original) Zbl 1473.41007

Math. Notes 107, No. 3, 522-524 (2020); translation from Mat. Zametki 107, No. 3, 470-472 (2020).
MSC:  41A46
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On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space. (English. Russian original) Zbl 1443.41009

Russ. Math. 64, No. 2, 66-83 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 2, 74-92 (2020).
MSC:  41A17 41A10 43A50
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