Ryutin, Konstantin Sergeevich

Statistics Math-Net.Ru
Total publications: 16
Scientific articles: 13
Presentations: 17

Number of views:
This page:1605
Abstract pages:5241
Full texts:1450
Candidate of physico-mathematical sciences
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 9.04.1977
Keywords: selections from multi-valued mappings, approximation by generalised rational functions, pseudodimension.


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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. T. I. Zaitseva, Yu. V. Malykhin, K. S. Ryutin, “On Recovery of Regular Ridge Functions”, Mat. Zametki, 109:2 (2021),  307–311  mathnet  mathscinet  elib; Math. Notes, 109:2 (2021), 307–311  isi  scopus
2. 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  mathnet  mathscinet  elib; Sb. Math., 212:8 (2021), 1180–1192  isi  scopus
3. K. S. Ryutin, “Integer Sampling Matrices with Small Entries Ensuring Vector Recovery”, Mat. Zametki, 107:2 (2020),  317–320  mathnet  mathscinet  elib; Math. Notes, 107:2 (2020), 363–366  isi  scopus
4. K. S. Ryutin, “Recovery of sparse integer vectors from linear measurements”, Uspekhi Mat. Nauk, 74:6(450) (2019),  167–168  mathnet  mathscinet  elib; Russian Math. Surveys, 74:6 (2019), 1129–1131  isi  scopus
5. B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Trudy Mat. Inst. Steklova, 303 (2018),  155–168  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 303 (2018), 140–153  isi  scopus
6. 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  mathnet  mathscinet  elib; Math. Notes, 101:1 (2017), 94–99  isi  scopus
7. 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  mathnet  mathscinet  zmath  elib; Sb. Math., 205:11 (2014), 1620–1649  isi  scopus
8. Yu. V. Malykhin, K. S. Ryutin, “On the concentration of measure and the $L^1$-norm”, J. Approx. Theory, 175 (2013),  77–82  mathnet  mathscinet  zmath  isi  scopus
9. 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  mathnet  mathscinet  zmath  elib; Math. Notes, 94:1 (2013), 107–114  isi  elib  scopus
10. C. S. Rjutin, “On Uniformly Continuous Almost Best Generalized Rational Approximation Operators”, Mat. Zametki, 87:1 (2010),  147–150  mathnet  mathscinet  zmath; Math. Notes, 87:1 (2010), 141–145  isi  scopus
11. C. S. Rjutin, “Continuity of Operators of Generalized Rational Approximation in the Space $L_1[0;1]$”, Mat. Zametki, 73:1 (2003),  148–153  mathnet  mathscinet  zmath; Math. Notes, 73:1 (2003), 142–147  isi
12. C. S. Rjutin, “Uniform Continuity of Generalized Rational Approximations”, Mat. Zametki, 71:2 (2002),  261–270  mathnet  mathscinet  zmath  elib; Math. Notes, 71:2 (2002), 236–244  isi  scopus
13. C. S. Rjutin, “A Lower Bound for Pseudodimension in Terms of Topological Dimension”, Mat. Zametki, 70:1 (2001),  155–156  mathnet  mathscinet  zmath; Math. Notes, 70:1 (2001), 143–144  isi
14. C. S. Rjutin, “Lipshitz retractions and the operator of generalized rational approximation”, Fundam. Prikl. Mat., 6:4 (2000),  1205–1220  mathnet  mathscinet  zmath

15. 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, 4,  70–71  mathnet
16. 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  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 303 (2018), 1–9  isi  scopus
17. S. V. Konyagin, Yu. V. Malykhin, K. S. Ryutin, “Letter to the Editor”, Mat. Zametki, 96:3 (2014),  480  mathnet  mathscinet  zmath  elib; Math. Notes, 96:3 (2014), 462  isi  elib  scopus

Presentations in Math-Net.Ru
1. Several problems of Compressed Sensing
K. Ryutin
Approximation and discretization
September 1, 2021 16:00   
2. О проклятии размерностей для восстановления регулярных ридж-функций
K. S. Ryutin

August 9, 2021 18:00
3. Recovery of integer sparse vectors in terms of universal measurement matrices
S. V. Konyagin, K. S. Ryutin
International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday
January 22, 2020 11:50   
4. Целочисленные матрицы измерений с малыми элементами
K. S. Ryutin
Contemporary Problems in Number Theory
November 21, 2019 12:45
5. Целочисленные матрицы измерений с малыми элементами
K. S. Ryutin
Seminar on Theory of Functions of Real Variables
November 15, 2019 18:30
6. 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
7. Поперечники по Колмогорову и аппроксимативный ранг
K. S. Ryutin
Differential equations, analysis and control: theory and applications
December 10, 2018 18:30
8. Поперечник по Колмогорову и аппроксимативный ранг
Yu. V. Malykhin, B. S. Kashin, K. S. Ryutin
Seminar on Approximation Theory
October 4, 2018 10:30
9. Поперечники произведения октаэдров
Yu. V. Malykhin, K. S. Ryutin
Seminar on Approximation Theory
November 3, 2016 10:30
10. Поперечники классов гладких функций нескольких переменных
Yu. V. Malykhin, K. S. Ryutin
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
April 27, 2016 16:00   
11. О концентрации $L^1$-нормы
Yu. V. Malykhin, K. S. Ryutin
Knots and Representation Theory
October 14, 2014 18:30
12. Концентрация $L_1$ нормы для тригонометрических полиномов и целых функций
Yu. V. Malykhin, K. S. Ryutin
Traditional winter session MIAN–POMI devoted to the topic "Harmonic Analysis and Theory of Functions"
December 23, 2013 12:15   
13. On the concentration of the $L_1$-norm
Yu. V. Malykhin, K. S. Ryutin
Discrete and Computational Geometry
December 11, 2013 13:00
14. 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   
15. Концентрация нормы для тригонометрических полиномов и целых функций
Yu. V. Malykhin, C. S. Rjutin
Seminar on Approximation Theory
October 3, 2013 10:30
16. О некоторых модификациях размерности Вапника–Червоненкиса
C. S. Rjutin
Contemporary Problems in Number Theory
May 17, 2012 12:45
17. О размерностях Вапника–Червоненкиса
C. S. Rjutin
Seminar on Approximation Theory
April 26, 2012 10:30

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