Persons: Borodin, Petr Anatolevich

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Borodin, Petr Anatolevich

Statistics Math-Net.Ru
Total publications:	38
Scientific articles:	37
Presentations:	17

Number of views:
This page:	5214
Abstract pages:	12830
Full texts:	3036
References:	1200

Professor of Russian Academy of Sciences

Associate professor

Doctor of physico-mathematical sciences (2012)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

E-mail:

Main publications:

P.A.Borodin, “O vypuklosti N-chebyshevskikh mnozhestv”, Izvestiya RAN. Ser. matem., 75:5 (2011), 19-46
P.A.Borodin, “Plotnost polugruppy v banakhovom prostranstve”, Izvestiya RAN. Ser. matem., 78:6 (2014), 21-48

http://www.mathnet.ru/eng/person8531

List of publications on Google Scholar

List of publications on ZentralBlatt

https://mathscinet.ams.org/mathscinet/MRAuthorID/357978

Publications in Math-Net.Ru

	2020
1.	P. A. Borodin, “Greedy approximation by arbitrary set”, Izv. RAN. Ser. Mat., 84:2 (2020), 43–59 ; Izv. Math., 84:2 (2020), 246–261
	2018
2.	P. A. Borodin, S. V. Konyagin, “Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line”, Anal. Math., 44:2 (2018), 163–183
3.	P. A. Borodin, “Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk”, Mat. Zametki, 104:1 (2018), 3–10 ; Math. Notes, 104:1 (2018), 3–9
4.	B. B. Bednov, P. A. Borodin, K. V. Chesnokova, “Existence of Lipschitz selections of the Steiner map”, Mat. Sb., 209:2 (2018), 3–21 ; Sb. Math., 209:2 (2018), 145–162
5.	P. A. Borodin, “Density of sums of shifts of a single vector in sequence spaces”, Tr. Mat. Inst. Steklova, 303 (2018), 39–44 ; Proc. Steklov Inst. Math., 303 (2018), 31–35
	2017
6.	P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. RAN. Ser. Mat., 81:6 (2017), 23–37 ; Izv. Math., 81:6 (2017), 1080–1094
7.	P. A. Borodin, Yu. Yu. Druzhinin, K. V. Chesnokova, “Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection”, Mat. Zametki, 102:4 (2017), 514–525 ; Math. Notes, 102:4 (2017), 465–474
	2016
8.	P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles. II”, Mat. Sb., 207:3 (2016), 19–30 ; Sb. Math., 207:3 (2016), 331–341
	2015
9.	P. A. Borodin, O. N. Kosukhin, “Quantitative Expressions for the Connectedness of Sets in ${\mathbb R}^n$”, Mat. Zametki, 98:5 (2015), 643–650 ; Math. Notes, 98:5 (2015), 707–713
	2014
10.	P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. RAN. Ser. Mat., 78:6 (2014), 21–48 ; Izv. Math., 78:6 (2014), 1079–1104
11.	B. B. Bednov, P. A. Borodin, “Banach spaces that realize minimal fillings”, Mat. Sb., 205:4 (2014), 3–20 ; Sb. Math., 205:4 (2014), 459–475
	2013
12.	P. A. Borodin, “Examples of Sets with Given Approximation Properties in $WCG$-Space”, Mat. Zametki, 94:5 (2013), 643–647 ; Math. Notes, 94:5 (2013), 605–608
	2012
13.	P. A. Borodin, “$2$-Chebyshev Subspaces in the Spaces $L_1$ and $C$”, Mat. Zametki, 91:6 (2012), 819–831 ; Math. Notes, 91:6 (2012), 770–781
14.	P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles”, Mat. Sb., 203:11 (2012), 23–40 ; Sb. Math., 203:11 (2012), 1553–1570
	2011
15.	P. A. Borodin, “On the convexity of $N$-Chebyshev sets”, Izv. RAN. Ser. Mat., 75:5 (2011), 19–46 ; Izv. Math., 75:5 (2011), 889–914
16.	P. A. Borodin, “The mirror property of metric $2$-projection”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, 2, 32–36 ; Moscow University Mathematics Bulletin, 66:2 (2011), 82–85
	2010
17.	Yu. V. Borodina, P. A. Borodin, “Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements”, Diskr. Mat., 22:3 (2010), 127–133 ; Discrete Math. Appl., 20:4 (2010), 441–449
18.	P. A. Borodin, “An Example of Nonexistence of a Steiner Point in a Banach Space”, Mat. Zametki, 87:4 (2010), 514–518 ; Math. Notes, 87:4 (2010), 485–488
	2009
19.	P. A. Borodin, I. A. Pyatyshev, “An Example of Non-Approximatively-Compact Existence Set with Finite-Valued Metric Projection”, Mat. Zametki, 86:2 (2009), 170–174 ; Math. Notes, 86:2 (2009), 159–162
20.	P. A. Borodin, “The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace”, Mat. Zametki, 85:2 (2009), 180–188 ; Math. Notes, 85:1 (2009), 168–175
21.	P. A. Borodin, “Approximation by simple partial fractions on the semi-axis”, Mat. Sb., 200:8 (2009), 25–44 ; Sb. Math., 200:8 (2009), 1127–1148
	2008
22.	P. A. Borodin, “Convexity of $2$-Chebyshev sets in Hilbert space”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, 3, 16–19
	2007
23.	P. A. Borodin, “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”, Mat. Zametki, 82:6 (2007), 803–810 ; Math. Notes, 82:6 (2007), 725–732
	2006
24.	P. A. Borodin, “On the existence of an element with given deviations from an expanding system of subspaces”, Mat. Zametki, 80:5 (2006), 657–667 ; Math. Notes, 80:5 (2006), 621–630
25.	P. A. Borodin, “On a condition for a polynomial that is sufficient for its norm to be minimal on a given compactum”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2006, 4, 14–18
	2005
26.	P. A. Borodin, O. N. Kosukhin, “On approximation by the simplest fractions on the real axis”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, 1, 3–8
	2003
27.	P. A. Borodin, “A new proof of Blaschke's ellipsoid theorem”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2003, 3, 17–22
	2002
28.	P. A. Borodin, “Approximation properties of subspaces in spaces of type $\mathbf{c}$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 5, 54–58
	2001
29.	P. A. Borodin, “The Banach–Mazur Theorem for Spaces with Asymmetric Norm”, Mat. Zametki, 69:3 (2001), 329–337 ; Math. Notes, 69:3 (2001), 298–305
	1999
30.	P. A. Borodin, V. M. Tikhomirov, “Критерии гильбертовости банахова пространства, связанные с теорией приближений”, Mat. Pros., Ser. 3, 3 (1999), 189–207
31.	P. A. Borodin, “On convex approximatively compact sets and Efimov–Stechkin spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, 4, 19–21
	1998
32.	P. A. Borodin, “Linearity of metric projections on Chebyshev subspaces in $L_1$ and $C$”, Mat. Zametki, 63:6 (1998), 812–820 ; Math. Notes, 63:6 (1998), 717–723
	1997
33.	P. A. Borodin, “Quasiorthogonal sets and conditions for a Banach space to be a Hilbert space”, Mat. Sb., 188:8 (1997), 63–74 ; Sb. Math., 188:8 (1997), 1171–1182
34.	P. A. Borodin, “On polynomials that deviate most from zero on a domain boundary”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, 1, 18–22
	1995
35.	P. A. Borodin, “Completeness of systems of successive primitives in the space $C(\Delta)$ and incomplete systems”, Mat. Zametki, 57:1 (1995), 118–121 ; Math. Notes, 57:1 (1995), 82–84
	1994
36.	P. A. Borodin, “An example of a bounded approximately compact set that is not compact”, Uspekhi Mat. Nauk, 49:4(298) (1994), 157–158 ; Russian Math. Surveys, 49:4 (1994), 153–154
37.	S. O. Kamo, P. A. Borodin, “Chebyshev polynomials for Julia sets”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1994, 5, 65–67

	2014
38.	A. I. Aptekarev, P. A. Borodin, B. S. Kashin, Yu. V. Nesterenko, P. V. Paramonov, A. V. Pokrovskii, A. G. Sergeev, A. T. Fomenko, “Evgenii Prokof'evich Dolzhenko (on his 80th birthday)”, Uspekhi Mat. Nauk, 69:6(420) (2014), 192–196 ; Russian Math. Surveys, 69:6 (2014), 1143–1148

Presentations in Math-Net.Ru

1.	Последовательности m-членных уклонений в гильбертовом пространстве P. A. Borodin Seminar on Theory of Functions of Real Variables October 23, 2020 18:30
2.	О последовательностях m-членных приближений P. A. Borodin Seminar on Theory of Functions of Real Variables March 6, 2020 18:30
3.	Сходимость последовательных проекций на подпространства в гильбертовом пространстве P. A. Borodin Operator models in mathematical physics October 25, 2019 16:45
4.	Циклические проекции, дальние проекции и жадные приближения P. A. Borodin Seminar on Theory of Functions of Real Variables October 11, 2019 18:30
5.	Жадные приближения произвольным множеством P. A. Borodin Seminar on Theory of Functions of Real Variables November 16, 2018 18:30
6.	Approximation by logarithmic derivatives of polynomials P. A. Borodin International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin October 8, 2018 15:00
7.	Сходимость к нулю экспоненциальных сумм с целыми неотрицательными коэффициентами и приближение суммами сдвигов одной функции на прямой P. A. Borodin, S. V. Konyagin Seminar on Approximation Theory February 15, 2018 10:30
8.	Сходимость к нулю почти всюду тригонометрических многочленов с натуральными коэффициентами и приближение суммами сдвигов одной функции на прямой P. A. Borodin, S. V. Konyagin Seminar on Theory of Functions of Real Variables December 15, 2017 18:30
9.	Dense semigroups in complex functional spaces P. A. Borodin Complex analysis and mathematical physics October 30, 2017 15:00
10.	Кратчайшие сети в банаховых пространствах P. A. Borodin Seminar on Theory of Functions of Real Variables April 21, 2017 18:30
11.	Липшицевость отображения Штейнера в банаховых пространствах P. A. Borodin Seminar on Theory of Functions of Real Variables October 28, 2016 18:30
12.	Приближение суммами сдвигов одной функции P. A. Borodin Seminar on Theory of Functions of Real Variables October 9, 2015 18:30
13.	Approximation by simple partial fractions with a restriction on the poles P. A. Borodin Seminar on Theory of Functions of Real Variables April 3, 2015 18:30
14.	Плотность полугруппы в банаховом пространстве и приближение наипростейшими дробями P. A. Borodin Meetings of the Moscow Mathematical Society March 17, 2015
15.	Approximations by simple partial fractions with constraints on the poles P. A. Borodin Seminar on Complex Analysis (Gonchar Seminar) February 9, 2015 18:00
16.	Minimal networks in Banach spaces P. A. Borodin Differential geometry and applications October 13, 2014 16:45
17.	Approximation by semigroups in Banach spaces P. A. Borodin International conference "Nonlinear Approximations and Applications" dedicated to the 60th birthday of Professor V. N. Temlyakov November 1, 2013 15:50

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