A general theorem on the existance of lipshitz retractions on certain surfaces was proved.<br> As a corollary, a lipshitz $\varepsilon$-selection on the set of generalised rational functions was constructed. Several results, concerning the problem of existance of continuous selections from the operator of generalised rational approximation in $L_p$, $0<p\le\infty$ spaces were obtained. It was proved that pseudodimension of any set is greater or equal than its topological dimension.
Main publications:
Lipshitsevost retraktsii i operator obobschennogo ratsionalnogo priblizheniya // Fundament. i prikl. matem., 2000, # 4, s. 1205–1220.
Ravnomernaya nepreryvnost obobschennykh ratsionalnykh priblizhenii // Matematicheskie zametki, 2002, t. 71, # 2, s. 261–270.
Otsenka snizu psevdorazmernosti cherez topologicheskuyu // Matematicheskie zametki, 2001, t. 70, # 1, s. 155–156.
A. A. Vasil'eva, A. V. Gorshkov, M. P. Zapletin, L. V. Lokutsievskiy, G. G. Magaril-Il'yaev, K. Yu. Osipenko, K. S. Ryutin, A. V. Fursikov, “Main recent research results of the staff of the Chair of General Problems of Control”, Moscow University Mathematics Bulletin, 79:6 (2024), 351–359
2023
5.
A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
2022
6.
Yuri Malykhin, Konstantin Ryutin, Tatyana Zaitseva, “Recovery of regular ridge functions on the ball”, Constr. Approx., 56 (2022), 687–708 , arXiv: 2102.13203
Teoriya priblizhenii, funktsionalnyi analiz i prilozheniya, Sbornik statei. K 70-letiyu akademika Borisa Sergeevicha Kashina, Trudy MIAN, 319, ed. S. V. Konyagin, M. I. Dyachenko, V. N. Temlyakov, M. R. Gabdullin, K. S. Ryutin, MIAN, M., 2022 , 328 pp.
2021
8.
T. I. Zaitseva, Yu. V. Malykhin, K. S. Ryutin, “On Recovery of Regular Ridge Functions”, Math. Notes, 109:2 (2021), 307–311
9.
A. S. Rubtsova, K. S. Ryutin, V. N. Temlyakov, “On the fixed volume discrepancy of the Korobov point sets”, Sb. Math., 212:8 (2021), 1180–1192
2020
10.
K. S. Ryutin, “Integer Sampling Matrices with Small Entries Ensuring Vector Recovery”, Math. Notes, 107:2 (2020), 363–366
11.
A. R. Alimov, A. A. Vasil'eva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 70–71
2019
12.
K. S. Ryutin, “Recovery of sparse integer vectors from linear measurements”, Russian Math. Surveys, 74:6 (2019), 1129–1131
2018
13.
B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Proc. Steklov Inst. Math., 303 (2018), 140–153
14.
Garmonicheskii analiz, teoriya priblizhenii i teoriya chisel, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Sergeya Vladimirovicha Konyagina, Trudy MIAN, 303, ed. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, I. D. Shkredov, K. S. Ryutin, MAIK «Nauka/Interperiodika», M., 2018 , 287 pp.
15.
B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9
2017
16.
Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Math. Notes, 101:1 (2017), 94–99
2014
17.
Yu. V. Malykhin, K. S. Ryutin, “Concentration of the $L_1$-norm of trigonometric polynomials and entire functions”, Sb. Math., 205:11 (2014), 1620–1649
18.
S. V. Konyagin, Yu. V. Malykhin, K. S. Ryutin, “Letter to the Editor”, Math. Notes, 96:3 (2014), 462
2013
19.
Yu. V. Malykhin, K. S. Ryutin, “On the concentration of measure and the $L^1$-norm”, J. Approx. Theory, 175 (2013), 77–82
20.
S. V. Konyagin, Yu. V. Malykhin, C. S. Rjutin, “On Exact Recovery of Sparse Vectors from Linear Measurements”, Math. Notes, 94:1 (2013), 107–114
2010
21.
C. S. Rjutin, “On Uniformly Continuous Almost Best Generalized Rational Approximation Operators”, Math. Notes, 87:1 (2010), 141–145
2003
22.
C. S. Rjutin, “Continuity of Operators of Generalized Rational Approximation in the Space $L_1[0;1]$”, Math. Notes, 73:1 (2003), 142–147
2002
23.
C. S. Rjutin, “Uniform Continuity of Generalized Rational Approximations”, Math. Notes, 71:2 (2002), 236–244
2001
24.
C. S. Rjutin, “A Lower Bound for Pseudodimension in Terms of Topological Dimension”, Math. Notes, 70:1 (2001), 143–144
2000
25.
C. S. Rjutin, “Lipshitz retractions and the operator of generalized rational approximation”, Fundam. Prikl. Mat., 6:4 (2000), 1205–1220
An extremal problem for integer sparse recovery S. V. Konyagin, K. S. Rjutin XVI International Conference «Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history» dedicated to the 80th anniversary of the birth of Professor Michel Desa May 13, 2019 15:00
On the concentration of $L_1$ norm Yu. V. Malykhin, K. S. Ryutin International conference "Nonlinear Approximations and Applications" dedicated to the 60th birthday of Professor V. N. Temlyakov November 1, 2013 17:00
Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, ed. S. V. Konyagin, M. I. Dyachenko, V. N. Temlyakov, M. R. Gabdullin, K. S. Ryutin, 2022, 328 с. http://mi.mathnet.ru/book1903
Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, ed. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, I. D. Shkredov, K. S. Ryutin, 2018, 287 с. http://mi.mathnet.ru/book1734
2025
