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## Borodin, Petr A.

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 Author ID: borodin.petr-a Published as: Borodin, P. A.; Borodin, Petr A.; Borodin, Pëtr A.
 Documents Indexed: 39 Publications since 1994
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#### Co-Authors

 28 single-authored 2 Bednov, Borislav Borisovich 2 Chesnokova, Kseniya V. 2 Kosukhin, Oleg N. 1 Aptekarev, Alexander Ivanovich 1 Borodina, Yulia V. 1 Druzhinin, Yu. Yu. 1 Fomenko, Anatoliĭ Timofeevich 1 Kamo, S. O. 1 Kashin, Boris Sergeevich 1 Konyagin, Sergeĭ Vladimirovich 1 Kopecká, Eva 1 Nesterenko, Yuriĭ Valentinovich 1 Paramonov, Peter V. 1 Pokrovskii, Andrei Vladimirovich 1 Pyatyshev, I. A. 1 Sergeev, Armen Glebovich
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#### Serials

 13 Mathematical Notes 6 Moscow University Mathematics Bulletin 6 Sbornik: Mathematics 4 Izvestiya: Mathematics 3 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Analysis Mathematica 2 Russian Mathematical Surveys 1 Journal of Approximation Theory 1 Discrete Mathematics and Applications 1 Proceedings of the Steklov Institute of Mathematics
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#### Fields

 24 Approximations and expansions (41-XX) 18 Functional analysis (46-XX) 9 Functions of a complex variable (30-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Operator theory (47-XX) 3 Convex and discrete geometry (52-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 General topology (54-XX) 1 History and biography (01-XX) 1 Geometry (51-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

29 Publications have been cited 117 times in 89 Documents Cited by Year
Approximation by the simplest fractions on the real axis. Zbl 1101.41016
Borodin, P. A.; Kosukhin, O. N.
2005
Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements. Zbl 1201.94149
Borodina, Yu. V.; Borodin, P. A.
2010
Chebyshev polynomials for Julia sets. Zbl 0889.30025
Kamo, S. O.; Borodin, P. A.
1994
Banach spaces that realize minimal fillings. Zbl 1327.46013
Bednov, B. B.; Borodin, P. A.
2014
The Banach-Mazur theorem for spaces with asymmetric norm and its applications in convex analysis. Zbl 1014.46004
Borodin, P. A.
2001
An example of nonexistence of a Steiner point in a Banach space. Zbl 1211.46005
Borodin, P. A.
2010
Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line. Zbl 1413.42002
Borodin, P. A.; Konyagin, S. V.
2018
Approximation by simple partial fractions with constraints on the poles. II. Zbl 1354.30025
Borodin, Petr A.
2016
Approximation by simple partial fractions on the semi-axis. Zbl 1185.30038
Borodin, P. A.
2009
The linearity coefficient of metric projections onto a Chebyshev subspace. Zbl 1190.46017
Borodin, P. A.
2009
On the existence of an element with given deviations from an expanding system of subspaces. Zbl 1142.41011
Borodin, P. A.
2006
Approximation by sums of shifts of a single function on the circle. Zbl 1384.41016
Borodin, Petr A.
2017
Density of a semigroup in a Banach space. Zbl 1316.46015
Borodin, P. A.
2014
Approximation by simple partial fractions with constraints on the poles. Zbl 1273.41012
Borodin, P. A.
2012
On polynomials most deviating from zero on a domain boundary. Zbl 0914.30025
Borodin, P. A.
1997
On the convexity of $$N$$-Chebyshev sets. Zbl 1239.46013
Borodin, P. A.
2011
Convexity of 2-Chebyshev sets in a Hilbert space. Zbl 1212.52002
Borodin, P. A.
2008
Existence of Lipschitz selections of the Steiner map. Zbl 1404.41010
Bednov, Borislav B.; Borodin, Petr A.; Chesnokova, Kseniya V.
2018
Estimates of the distances to direct lines and rays from the poles of simplest fractions bounded in the norm of $$L_p$$ on these sets. Zbl 1163.26005
Borodin, P. A.
2007
An example of a bounded approximately compact set that is not compact. Zbl 0883.46008
Borodin, P. A.
1994
Approximation by sums of the form $$\sigma_k\lambda_k h(\lambda_kz)$$ in the disk. Zbl 1401.30039
Borodin, P. A.
2018
Examples of sets with given approximation properties in $$WCG$$-space. Zbl 1297.46053
Borodin, P. A.
2013
An example of non-approximatively-compact existence set with finite-valued metric projection. Zbl 1190.41016
Borodin, P. A.; Pyatyshev, I. A.
2009
A new proof of Blaschke’s ellipsoid theorem. Zbl 1052.51001
Borodin, P. A.
2003
Approximative properties of subspaces in $$c$$-type spaces. Zbl 1106.41300
Borodin, P. A.
2002
On convex approximate compact sets and the Efimov-Stechkin spaces. Zbl 0974.41011
Borodin, P. A.
1999
Linearity of metric projections on Chebyshev subspaces in $$L_1$$ and $$C$$. Zbl 0917.41018
Borodin, P. A.
1998
Quasiorthogonal sets and conditions for a Banach space to be a Hilbert space. Zbl 0908.46016
Borodin, P. A.
1997
Completeness of systems of successive primitives in the space $$C\Delta$$ and incomplete systems. Zbl 0981.42017
Borodin, P. A.
1995
Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line. Zbl 1413.42002
Borodin, P. A.; Konyagin, S. V.
2018
Existence of Lipschitz selections of the Steiner map. Zbl 1404.41010
Bednov, Borislav B.; Borodin, Petr A.; Chesnokova, Kseniya V.
2018
Approximation by sums of the form $$\sigma_k\lambda_k h(\lambda_kz)$$ in the disk. Zbl 1401.30039
Borodin, P. A.
2018
Approximation by sums of shifts of a single function on the circle. Zbl 1384.41016
Borodin, Petr A.
2017
Approximation by simple partial fractions with constraints on the poles. II. Zbl 1354.30025
Borodin, Petr A.
2016
Banach spaces that realize minimal fillings. Zbl 1327.46013
Bednov, B. B.; Borodin, P. A.
2014
Density of a semigroup in a Banach space. Zbl 1316.46015
Borodin, P. A.
2014
Examples of sets with given approximation properties in $$WCG$$-space. Zbl 1297.46053
Borodin, P. A.
2013
Approximation by simple partial fractions with constraints on the poles. Zbl 1273.41012
Borodin, P. A.
2012
On the convexity of $$N$$-Chebyshev sets. Zbl 1239.46013
Borodin, P. A.
2011
Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements. Zbl 1201.94149
Borodina, Yu. V.; Borodin, P. A.
2010
An example of nonexistence of a Steiner point in a Banach space. Zbl 1211.46005
Borodin, P. A.
2010
Approximation by simple partial fractions on the semi-axis. Zbl 1185.30038
Borodin, P. A.
2009
The linearity coefficient of metric projections onto a Chebyshev subspace. Zbl 1190.46017
Borodin, P. A.
2009
An example of non-approximatively-compact existence set with finite-valued metric projection. Zbl 1190.41016
Borodin, P. A.; Pyatyshev, I. A.
2009
Convexity of 2-Chebyshev sets in a Hilbert space. Zbl 1212.52002
Borodin, P. A.
2008
Estimates of the distances to direct lines and rays from the poles of simplest fractions bounded in the norm of $$L_p$$ on these sets. Zbl 1163.26005
Borodin, P. A.
2007
On the existence of an element with given deviations from an expanding system of subspaces. Zbl 1142.41011
Borodin, P. A.
2006
Approximation by the simplest fractions on the real axis. Zbl 1101.41016
Borodin, P. A.; Kosukhin, O. N.
2005
A new proof of Blaschke’s ellipsoid theorem. Zbl 1052.51001
Borodin, P. A.
2003
Approximative properties of subspaces in $$c$$-type spaces. Zbl 1106.41300
Borodin, P. A.
2002
The Banach-Mazur theorem for spaces with asymmetric norm and its applications in convex analysis. Zbl 1014.46004
Borodin, P. A.
2001
On convex approximate compact sets and the Efimov-Stechkin spaces. Zbl 0974.41011
Borodin, P. A.
1999
Linearity of metric projections on Chebyshev subspaces in $$L_1$$ and $$C$$. Zbl 0917.41018
Borodin, P. A.
1998
On polynomials most deviating from zero on a domain boundary. Zbl 0914.30025
Borodin, P. A.
1997
Quasiorthogonal sets and conditions for a Banach space to be a Hilbert space. Zbl 0908.46016
Borodin, P. A.
1997
Completeness of systems of successive primitives in the space $$C\Delta$$ and incomplete systems. Zbl 0981.42017
Borodin, P. A.
1995
Chebyshev polynomials for Julia sets. Zbl 0889.30025
Kamo, S. O.; Borodin, P. A.
1994
An example of a bounded approximately compact set that is not compact. Zbl 0883.46008
Borodin, P. A.
1994
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#### Cited by 70 Authors

 12 Borodin, Petr A. 8 Bednov, Borislav Borisovich 7 Komarov, Mikhaĭl Anatol’evich 5 Chesnokova, Kseniya V. 5 Popkov, Kirill A. 4 Alimov, Alexey R. 3 Filippov, Vadim Ivanovich 3 Romanov, Dmitry S. 3 Sánchez-Pérez, Enrique Alfonso 2 Aksoy, Asuman Güven 2 Almira, Jose María 2 Christiansen, Jacob Stordal 2 Chunaev, P. V. 2 Danchenko, Vladimir Il’ich 2 Druzhinin, Yu. Yu. 2 Ivanov, Aleksandr Olegovich 2 Jonard-Pérez, Natalia 2 Kayumov, Iigiz R. 2 Oikhberg, Timur 2 Pakhomova, A. S. 2 Peherstorfer, Franz 2 Schiefermayr, Klaus 2 Simon, Barry 2 Tsar’kov, Igor’ Germanovich 2 Tuzhilin, Alexey Avgustinovich 2 Zinchenko, Maxim 1 Alansari, Monairah 1 Alegre, Carmen 1 Alpan, Gökalp 1 Andrievskii, Vladimir V. 1 Baskakov, Anatoliĭ Grigor’evich 1 Beloshapka, I. V. 1 Borodina, Yulia V. 1 Burusheva, L. Sh. 1 Case, Caleb 1 Chunaev, Petr 1 Deutsch, Frank 1 Dyuzhina, N. A. 1 García-Raffi, Luis M. 1 Götz, Mario 1 Hundal, Hein S. 1 Kayumova, A. V. 1 Kočinac, Ljubiša D. R. 1 Konyagin, Sergeĭ Vladimirovich 1 Kosukhin, Oleg N. 1 Künzi, Hans-Peter A. 1 Laiyi, Zhu 1 Lewicki, Grzegorz 1 Liesen, Jörg 1 Luo, Zhenghua 1 Mustăţa, Costică 1 Nikolaeva, N. K. 1 Niţică, Viorel 1 Novak, Ya. V. 1 Peng, Qidi 1 Romaguera Bonilla, Salvador 1 Romanova, Elena Yu. 1 Sedletskiĭ, Anatoliĭ Mechislavovich 1 Sète, Olivier 1 Soltan, Valeriu 1 Steinbauer, Robert 1 Stonyakin, Fedor Sergeevich 1 Strelkova, N. P. 1 Strukov, Viktor Evgen’evich 1 Strukova, Irina Igor’evna 1 Sun, Longfa 1 Török, Andrei 1 Totik, Vilmos 1 Veeramani, P. 1 Zhang, Wen
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#### Cited in 33 Serials

 15 Mathematical Notes 12 Moscow University Mathematics Bulletin 5 Journal of Approximation Theory 5 Russian Mathematics 4 Discrete Mathematics and Applications 4 Journal of Mathematical Sciences (New York) 4 Proceedings of the Steklov Institute of Mathematics 3 Sbornik: Mathematics 3 Izvestiya: Mathematics 3 Computational Methods and Function Theory 2 Journal d’Analyse Mathématique 2 Journal of Computational and Applied Mathematics 2 Quaestiones Mathematicae 2 Topology and its Applications 2 Lobachevskii Journal of Mathematics 2 Eurasian Mathematical Journal 2 Diskretnyĭ Analiz i Issledovanie Operatsiĭ 1 Analysis Mathematica 1 Journal of Mathematical Analysis and Applications 1 Russian Mathematical Surveys 1 Numerical Functional Analysis and Optimization 1 Proceedings of the American Mathematical Society 1 Moscow University Computational Mathematics and Cybernetics 1 European Journal of Combinatorics 1 Acta Mathematica Hungarica 1 Aequationes Mathematicae 1 Turkish Journal of Mathematics 1 Abstract and Applied Analysis 1 Mediterranean Journal of Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Problemy Analiza. Issues of Analysis 1 Journal of Function Spaces 1 Prikladnaya Diskretnaya Matematika
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#### Cited in 21 Fields

 40 Approximations and expansions (41-XX) 25 Functional analysis (46-XX) 20 Functions of a complex variable (30-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Information and communication theory, circuits (94-XX) 7 Combinatorics (05-XX) 7 General topology (54-XX) 4 Geometry (51-XX) 4 Convex and discrete geometry (52-XX) 3 Real functions (26-XX) 3 Special functions (33-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Systems theory; control (93-XX)