Professor of the Department of Theory of Functions and Functional Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. Professor of the RAS.

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Websites:

Keywords: Chebyshev sets and subspaces, density of semigroups in Banach spaces, simple partial fractions.

Education:

→ 1989-1994 – Faculty of Mechanics and Mathematics, Lomonosov Moscow State University;

→ 1994-1998 – graduate school of the Department of Theory of Functions and Functional Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, advisor Prof. E.P. Dolzhenko;

→ 1998 – PhD Thesis "Approximative properties of the subspaces in some Banach spaces" (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University);

→ 2012 – Dr. Sci. Thesis "Some approximative properties of the sets in Banach spaces" (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University).

Research Interests:

Approximation theory and the geometry of Banach spaces. He published more than 30 peer reviewed articles and also several methodical works.

Teaching:

In addition, he has been working as a teacher at Moscow school No. 54 since 1993. He has trained 5 doctoral students.

Publications (recent):

2024

→ P. A. Borodin, E. A. Savinova, "Any Chebyshev curve without self-intersections is monotone", Math. Notes, 116:2 (2024), 387–389, DOI.

→ P. A. Borodin, A. M. Ershov, "S. R. Nasyrov's Problem of Approximation by Simple Partial Fractions on an Interval", Math. Notes, 115:4 (2024), 520–527, DOI.

2023

→ P. A. Borodin, "Weak Convergence of a Greedy Algorithm and the WN-Property", Math. Notes, 113:4 (2023), 475–479, DOI.

→ P. A. Borodin, L. Sh. Burusheva, "Estimate of convergence rate for remote projections on three subspaces", Funktsional. Anal. i Prilozhen., 57:2 (2023), 100–105, DOI.

→ P. A. Borodin, K. S. Shklyaev, "Density of quantized approximations", Uspekhi Mat. Nauk, 78:5(473) (2023), 3–64, DOI.

2022

→ P. A. Borodin, E. Kopecká, "Weak Limits of Consecutive Projections and of Greedy Steps", Approximation Theory, Functional Analysis, and Applications. Collected papers. On the occasion of the 70th birthday of Academician B. S. Kashin. Trudy MIAN, 319 (2022), 56–63, DOI.

→ P. A. Borodin, "Approximation by Simple Partial Fractions: Universal Sets of Poles", Math. Notes, 111:1 (2022), 3–6, DOI.

2021

→ P. A. Borodin, S. V. Konyagin, "Projection Greedy Algorithm", Math. Notes, 110:1 (2021), 16–25, DOI.

→ P. A. Borodin, K. S. Shklyaev, "Approximation by simple partial fractions in unbounded domains", Sb. Math., 212:4 (2021), 449–474, DOI.

→ P. A. Borodin, "Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary", Math. Notes, 109:3 (2021), 379–385, DOI.

2020

→ P. A. Borodin, "Greedy approximation by arbitrary set", Izv. Math., 84:2 (2020), 246–261, DOI.

2018

→ 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, DOI.

→ P. A. Borodin, "Approximation by Sums of the Form \(\sum_k\lambda_kh(\lambda_kz)\) in the Disk", Math. Notes, 104:1 (2018), 3–9, DOI.

→ B. B. Bednov, P. A. Borodin, K. V. Chesnokova, "Existence of Lipschitz selections of the Steiner map", Sb. Math., 209:2 (2018), 145–162, DOI.

→ P. A. Borodin, "Density of sums of shifts of a single vector in sequence spaces", Proc. Steklov Inst. Math., 303 (2018), 31–35, DOI.

2017

→ P. A. Borodin, "Approximation by sums of shifts of a single function on the circle", Izv. Math., 81:6 (2017), 1080–1094, DOI.

→ P. A. Borodin, Yu. Yu. Druzhinin, K. V. Chesnokova, "Finite-Dimensional Subspaces of \(L_p\) with Lipschitz Metric Projection", Math. Notes, 102:4 (2017), 465–474, DOI.