The studing of classical, modified and weak Banach–Mazur distance, volume ratios and others asymptotic characteristics of convex bodies in many-dimensional spaces. Proof of existance of space uniformly distant from all spaces with unconditional bases. Estimate distance between the sums of normed spaces, distances from space with unconditional bases, investigation of stability extreme distant spaces at adding summand of proportional dimensionality.
Biography
Graduated from Faculty of Mathematics and Mechanics of Saint Petersburg State University (SPbGU) in 1997 (department mathematical analysis). Ph.D. thesis was defended in 2001. A list of my works contains 7 titles.
Main publications:
Khrabrov A. I. Otsenki rasstoyanii mezhdu summami prostranstv $\ell^p_n$ // Vestn. S.-Peterburg. un-ta, Ser. 1. 2000. Vyp. 3 (# 17). S. 57–63.
Khrabrov A. I. Ekstremalnye ob'emnye otnosheniya dlya summ normirovannykh prostranstv // Problemy matematicheskogo analiza. Vyp. 21. Novosibirsk, Nauchnaya kniga. 2000. S. 264–275.
Khrabrov A. I. Obobschennye ob'emnye otnosheniya i rasstoyanie Banakha–Mazura // Matem. zametki. 2001. T. 70. # 6. S. 918–926.
Khrabrov A. I. Rasstoyaniya mezhdu prostranstvami s bezuslovnymi bazisami // Problemy matematicheskogo analiza. Vyp. 23. Novosibirsk, Nauchnaya kniga. 2001. S. 206–220.
A. I. Khrabrov, “Inequalities for mixed means”, Algebra i Analiz, 35:6 (2023), 169–191
2022
2.
A. I. Khrabrov, “Injective proofs of log concavity for some combinatorial sequences”, Zap. Nauchn. Sem. POMI, 518 (2022), 173–191
2020
3.
A. I. Khrabrov, “Volume ratio for the Cartesian product of convex bodies”, Algebra i Analiz, 32:5 (2020), 114–129; St. Petersburg Math. J., 32:5 (2021), 905–916
2018
4.
E. C. Krasko, I. N. Labutin, D. N. Moskvin, A. V. Omelchenko, A. I. Khrabrov, “On some enumerative problems of lambda calculus”, Zap. Nauchn. Sem. POMI, 475 (2018), 99–121
2015
5.
K. P. Kokhas', A. I. Khrabrov, “Точки на прямых, шнурки и доминошки”, Mat. Pros., Ser. 3, 19 (2015), 139–163
A. I. Khrabrov, “Comparison of Some Distances Between Sums of $\ell^{p}_n$ Spaces”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 91–94; Funct. Anal. Appl., 38:1 (2004), 75–77
2003
7.
A. I. Khrabrov, “Estimates of the distances between sums of the spaces $\ell^p_n$, II”, Zap. Nauchn. Sem. POMI, 303 (2003), 203–217; J. Math. Sci. (N. Y.), 129:4 (2005), 4040–4048
2001
8.
A. I. Khrabrov, “Generalized Volume Ratios and the Banach–Mazur Distance”, Mat. Zametki, 70:6 (2001), 918–926; Math. Notes, 70:6 (2001), 838–846
N. Agakhanov, M. Antipov, A. Antropov, S. Berlov, I. Bogdanov, D. Brodskii, A. Golovanov, M. Didin, K. Knop, P. Kozhevnikov, P. Kozlov, D. Krachun, S. Kudrya, A. Kuznetsov, Yu. Kuz'menko, E. Molchanov, F. Petrov, O. Podlipsky, K. Sukhov, D. Tereshin, I. Frolov, A. Khrabrov, D. Khramtsov, G. Chelnokov, O. Yuzhakov, “Заключительный этап XLVIII Всероссийской олимпиады школьников по математике”, Kvant, 2022, no. 7, 45–47
2003
10.
A. I. Khrabrov, “Вокруг монгольского неравенства”, Mat. Pros., Ser. 3, 7 (2003), 149–162
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