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Borodin Petr Anatolevich

Publications in Math-Net.Ru

  1. Any Chebyshev curve without self-intersections is monotone

    Mat. Zametki, 116:2 (2024),  321–323
  2. S. R. Nasyrov's Problem of Approximation by Simple Partial Fractions on an Interval

    Mat. Zametki, 115:4 (2024),  568–577
  3. A convergence rate estimate for remotest projections on three subspaces

    Funktsional. Anal. i Prilozhen., 57:2 (2023),  100–105
  4. Weak Convergence of a Greedy Algorithm and the WN-Property

    Mat. Zametki, 113:4 (2023),  483–488
  5. Density of quantized approximations

    Uspekhi Mat. Nauk, 78:5(473) (2023),  3–64
  6. Approximation by Simple Partial Fractions: Universal Sets of Poles

    Mat. Zametki, 111:1 (2022),  3–7
  7. Weak Limits of Consecutive Projections and of Greedy Steps

    Trudy Mat. Inst. Steklova, 319 (2022),  64–72
  8. Projection Greedy Algorithm

    Mat. Zametki, 110:1 (2021),  17–28
  9. Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary

    Mat. Zametki, 109:3 (2021),  352–360
  10. Approximation by simple partial fractions in unbounded domains

    Mat. Sb., 212:4 (2021),  3–28
  11. Greedy approximation by arbitrary set

    Izv. RAN. Ser. Mat., 84:2 (2020),  43–59
  12. 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
  13. Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk

    Mat. Zametki, 104:1 (2018),  3–10
  14. Existence of Lipschitz selections of the Steiner map

    Mat. Sb., 209:2 (2018),  3–21
  15. Density of sums of shifts of a single vector in sequence spaces

    Trudy Mat. Inst. Steklova, 303 (2018),  39–44
  16. Approximation by sums of shifts of a single function on the circle

    Izv. RAN. Ser. Mat., 81:6 (2017),  23–37
  17. Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection

    Mat. Zametki, 102:4 (2017),  514–525
  18. Approximation by simple partial fractions with constraints on the poles. II

    Mat. Sb., 207:3 (2016),  19–30
  19. Quantitative Expressions for the Connectedness of Sets in ${\mathbb R}^n$

    Mat. Zametki, 98:5 (2015),  643–650
  20. Density of a semigroup in a Banach space

    Izv. RAN. Ser. Mat., 78:6 (2014),  21–48
  21. Banach spaces that realize minimal fillings

    Mat. Sb., 205:4 (2014),  3–20
  22. Examples of Sets with Given Approximation Properties in $WCG$-Space

    Mat. Zametki, 94:5 (2013),  643–647
  23. $2$-Chebyshev Subspaces in the Spaces $L_1$ and $C$

    Mat. Zametki, 91:6 (2012),  819–831
  24. Approximation by simple partial fractions with constraints on the poles

    Mat. Sb., 203:11 (2012),  23–40
  25. On the convexity of $N$-Chebyshev sets

    Izv. RAN. Ser. Mat., 75:5 (2011),  19–46
  26. The mirror property of metric $2$-projection

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 2,  32–36
  27. 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
  28. An Example of Nonexistence of a Steiner Point in a Banach Space

    Mat. Zametki, 87:4 (2010),  514–518
  29. An Example of Non-Approximatively-Compact Existence Set with Finite-Valued Metric Projection

    Mat. Zametki, 86:2 (2009),  170–174
  30. The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace

    Mat. Zametki, 85:2 (2009),  180–188
  31. Approximation by simple partial fractions on the semi-axis

    Mat. Sb., 200:8 (2009),  25–44
  32. Convexity of $2$-Chebyshev sets in Hilbert space

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, no. 3,  16–19
  33. 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
  34. On the existence of an element with given deviations from an expanding system of subspaces

    Mat. Zametki, 80:5 (2006),  657–667
  35. 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, no. 4,  14–18
  36. On approximation by the simplest fractions on the real axis

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, no. 1,  3–8
  37. A new proof of Blaschke's ellipsoid theorem

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2003, no. 3,  17–22
  38. Approximation properties of subspaces in spaces of type $\mathbf{c}$

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 5,  54–58
  39. The Banach–Mazur Theorem for Spaces with Asymmetric Norm

    Mat. Zametki, 69:3 (2001),  329–337
  40. Критерии гильбертовости банахова пространства, связанные с теорией приближений

    Mat. Pros., Ser. 3, 3 (1999),  189–207
  41. On convex approximatively compact sets and Efimov–Stechkin spaces

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 4,  19–21
  42. Linearity of metric projections on Chebyshev subspaces in $L_1$ and $C$

    Mat. Zametki, 63:6 (1998),  812–820
  43. Quasiorthogonal sets and conditions for a Banach space to be a Hilbert space

    Mat. Sb., 188:8 (1997),  63–74
  44. On polynomials that deviate most from zero on a domain boundary

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, no. 1,  18–22
  45. Completeness of systems of successive primitives in the space $C(\Delta)$ and incomplete systems

    Mat. Zametki, 57:1 (1995),  118–121
  46. An example of a bounded approximately compact set that is not compact

    Uspekhi Mat. Nauk, 49:4(298) (1994),  157–158
  47. Chebyshev polynomials for Julia sets

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1994, no. 5,  65–67

  48. Vladimir Igorevich Bogachev (on his 60th birthday)

    Uspekhi Mat. Nauk, 76:6(462) (2021),  201–208
  49. Mikhail Konstantinovich Potapov (on his 90th birthday)

    Uspekhi Mat. Nauk, 76:2(458) (2021),  185–186
  50. Evgenii Prokof'evich Dolzhenko (on his 80th birthday)

    Uspekhi Mat. Nauk, 69:6(420) (2014),  192–196
  51. Московский государственный университет им. М.В. Ломоносова

    Kvant, 2007, no. 1,  44–52
  52. Московский государственный университет им. М.В. Ломоносова

    Kvant, 2005, no. 1,  40–49

© Steklov Math. Inst. of RAS, 2025