01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
9.04.1977
E-mail:
Keywords:
selections from multi-valued mappings,
approximation by generalised rational functions,
pseudodimension.
Subject:
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.
Ravnomernaya nepreryvnost operatorov obobschennogo ratsionalnogo priblizheniya // Sovremennye problemy teorii funktsii i ikh prilozheniya (tezisy dokladov 10-i Saratovskoi zimnei shkoly, 2000 g.), s. 120–121.
Nepreryvnost operatorov obobschennogo ratsionalnogo priblizheniya v prostranstvakh $L_p$ // Sovremennye problemy teorii funktsii i ikh prilozheniya (tezisy dokladov 11-i Saratovskoi zimnei shkoly, 2002 g.), s. 177–179.
A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Uspekhi Mat. Nauk, 78:3(471) (2023), 3–52; Russian Math. Surveys, 78:3 (2023), 399–442
T. I. Zaitseva, Yu. V. Malykhin, K. S. Ryutin, “On Recovery of Regular Ridge Functions”, Mat. Zametki, 109:2 (2021), 307–311; Math. Notes, 109:2 (2021), 307–311
A. S. Rubtsova, K. S. Ryutin, V. N. Temlyakov, “On the fixed volume discrepancy of the Korobov point sets”, Mat. Sb., 212:8 (2021), 151–164; Sb. Math., 212:8 (2021), 1180–1192
2020
5.
K. S. Ryutin, “Integer Sampling Matrices with Small Entries Ensuring Vector Recovery”, Mat. Zametki, 107:2 (2020), 317–320; Math. Notes, 107:2 (2020), 363–366
K. S. Ryutin, “Recovery of sparse integer vectors from linear measurements”, Uspekhi Mat. Nauk, 74:6(450) (2019), 167–168; Russian Math. Surveys, 74:6 (2019), 1129–1131
B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Trudy Mat. Inst. Steklova, 303 (2018), 155–168; Proc. Steklov Inst. Math., 303 (2018), 140–153
Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Mat. Zametki, 101:1 (2017), 85–90; Math. Notes, 101:1 (2017), 94–99
Yu. V. Malykhin, K. S. Ryutin, “Concentration of the $L_1$-norm of trigonometric polynomials and entire functions”, Mat. Sb., 205:11 (2014), 95–124; Sb. Math., 205:11 (2014), 1620–1649
Yu. V. Malykhin, K. S. Ryutin, “On the concentration of measure and the $L^1$-norm”, J. Approx. Theory, 175 (2013), 77–82
11.
S. V. Konyagin, Yu. V. Malykhin, C. S. Rjutin, “On Exact Recovery of Sparse Vectors from Linear Measurements”, Mat. Zametki, 94:1 (2013), 122–129; Math. Notes, 94:1 (2013), 107–114
C. S. Rjutin, “Continuity of Operators of Generalized Rational Approximation in the Space $L_1[0;1]$”, Mat. Zametki, 73:1 (2003), 148–153; Math. Notes, 73:1 (2003), 142–147
C. S. Rjutin, “A Lower Bound for Pseudodimension in Terms of Topological Dimension”, Mat. Zametki, 70:1 (2001), 155–156; Math. Notes, 70:1 (2001), 143–144
2000
16.
C. S. Rjutin, “Lipshitz retractions and the operator of generalized rational approximation”, Fundam. Prikl. Mat., 6:4 (2000), 1205–1220
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
2018
18.
B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Trudy Mat. Inst. Steklova, 303 (2018), 7–16; Proc. Steklov Inst. Math., 303 (2018), 1–9
2014
19.
S. V. Konyagin, Yu. V. Malykhin, K. S. Ryutin, “Letter to the Editor”, Mat. Zametki, 96:3 (2014), 480; Math. Notes, 96:3 (2014), 462
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
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