Kharkiv school of M. I. Kadets and mathematics of Tula
https://doi.org/10.22405/2226-8383-2021-22-4-324-331
Abstract
The authors of the article set themselves the tasks: to tell about the unexpected and long cooperation and interaction of teachers and scientists of the Tolstoy Tula State Pedagogical University and the Mikhail Iosifovich Kadets Kharkiv School, as well as about
some scientific works of the Kharkiv mathematicians of the Mikhail Iosifovich Kadets School and mathematicians of the city of Tula in the twenty-year period 1986-2006. he role of V. I. Rybakov is particularly noted. Under his leadership, a Tula student conducted scientific work, who later, after studying at the Mikhail Iosifovich Kadets Kharkiv School, became a candidate of physical and mathematical sciences. Vladislav Ivanovich Rybakov obtained deep, meaningful scientific results. For example, you can read about "the classical theory of Rybakov"in books and articles published in the international mathematical press. Mikhail Iosifovich Kadets was interested in Vladislav Ivanovich’s scientific activity. The Kharkiv school of Kadets at that time became
world famous. Not only scientific work, Mikhail Iosifovich paid a lot of attention and effort to pedagogical work. Nineteen of his students, including Rybakov’s student, defended their
PhD theses, seven of them became doctors of science. M. I. Kadets generously shared his mathematical ideas with his students. The article presents some results obtained by Kharkiv
mathematicians of the Kadets school and Tula mathematicians close to them in scientific interests in the period 1986-2006.
About the Authors
Evgeny Viktorovich Manokhin
Financial University under the Government of the Russian Federation (Tula Branch)
Russian Federation
Russian Federation
candidate of physical and mathematical sciences, associate
professor
Nadezhda Olegovna Kozlova
Financial University under the Government of the Russian Federation (Tula Branch)
Russian Federation
Russian Federation
candidate of technical sciences
Valery Engelsovich Komov
Financial University under the Government of the Russian Federation (Tula Branch)
Russian Federation
Russian Federation
candidate of economic sciences, associate professor
References
1. Vector and Operator Valued Measures and Applications. Editors Don H. Tucker (Department of Mathematics, University of Utah, Salt Lake City, Utah),Hugh B. Maynard (Department of
2. Mathematics, University of Utah, Salt Lake City, Utah), 1973, Pages 474
3. Notas de Matem´atica (58): Vector Measures and Control Systems, Series: North-Holland Mathematics Studies, Year: 1975, Volume 20, Page 169
4. Handbook of Measure Theory, Volume I, 2002, Pages 249.
5. Yu. I. Lyubich, V. A. Marchenko, S. P. Novikov, M. I. Ostrovskii, L. A. Pastur, A. N. Plichko, M. M. Popov, E. M. Semenov, S. L. Troyanskii, V. P. Fonf, E. Ya. Khruslov., 2011, “Mikhail
6. Iosifovich Kadets (obituary)” Russian Math. Surveys, 66:4, pp.809–811
7. M. I. Kadets, 1967, “Proof of the topological equivalence of all separable infinite-dimensional Banach spaces”, Funct. Anal. Appl., 1:1, pp.61–70 .
8. E. V. Manokhin, A. E. Ustyan, G. V. Kuznetsov, 2019, "Scholar and teacher. To the 80th anniversary Vladislav Ivanovich Rybakov (13.12.1939–27.09.2016) Chebyshevskii sbornik, vol.
9. ,no. 4, pp. 450–457.
10. M. I. Ostrovskii, 1987, “Properties of Banach spaces stable and unstable with respect to the gap”, Siberian Math. J., 28:1, pp.140–142
11. M. I. Ostrovskii, 1987, “Banach–Saks and Mazur properties in Banach spaces”, Math. Notes, 42:6, 931–933 .
12. M. I. Ostrovskii, 1990, V. P. Fonf, “Operators with dense images and extensions of minimal systems”, Soviet Math. (Iz. VUZ), 34:6, 53–56
13. Manokhin E.V., 1992, “About geometrical and linearly-topological properties of some Banach spaces.” The author’s PHD-abstract. Kharkov State University, Kharkov.
14. V. M. Kadets, M. I. Kadets, V. P. Fonf, 1988, “Resolving and strongly resolving regularizers”, Siberian Math. J., 29:3, 380–384
15. V. M. Kadets, 1988, “The domain of weak limits of Riemann integral sums of an abstract function”, Soviet Math. (Iz. VUZ), 32:9, 56–66
16. V. A. Akimovich, 1987, “On a class of Banach functional spaces”, Soviet Mathematics (Izvestiya VUZ. Matematika), 31:7, 1–6
17. B. V. Godun, S. L. Troyanski, 1991, “Norm-attaining operators, and the geometry of the unit sphere of a Banach space”, Dokl. Math., 42:2, 532–534
18. M. I. Kadets, 1996, “Absolute, Perfect, and Unconditional Convergence of Double Series”, Funct. Anal. Appl., 30:2, 140–142
19. M. I. Kadets, K. E. Kaibkhanov, 1997, “Continuation of a linear operator to an involution operator”, Math. Notes, 61:5, 561–565
20. V. I. Rybakov, 1993, “On resultant-preserving functionals”, Math. Notes, 54:1, pp.710–712
21. V. I. Rybakov, 1996, “On convergence on the boundary of the unit ball in dual space”, Math. Notes, 59:5, pp.543–546 .
22. V. I. Rybakov, 1996, “Pettis integrability of Stone transforms”, Math. Notes, 60:2, pp.175–185
23. 17. V. I. Rybakov, 2003, “Yet Another Class of Namioka Spaces”, Math. Notes, 73:2, pp.244–248.
24. V. M. Kadets, A. N. Plichko, M. M. Popov, 1988, “Complete minimal systems of a certain type in Banach spaces”, Soviet Math. (Iz. VUZ), 32:5, 39–48
25. A. N. Plichko, 1988, “Nonnorming subspaces and integral operators with a nonregularizable inverse”, Siberian Math. J., 29:4, 687–689
26. I. K. Matsak, A. N. Plichko, 1991, “On the support of a measure in a Banach space and finite representability”, Theory Probab. Appl., 36:2, 381–385
27. Dobrovolsky N. M., Manokhin E. V. Banach spaces of periodic functions / / Izv. TulSU. Ser. Mechanics. Mathematics. Informatics. T. 4. Issue 3. Tula, 1998. pp. 56-67.
28. L. P. Bocharova, N. M. Dobrovolsky, I. Yu. Rebrova “ Fifty years of the number-theoretic method in approximate analysis: problems and achievements”, Chebyshevsky sb., 8:4 (2007),
29. -49
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For citations:
Manokhin E.V., Kozlova N.O., Komov V.E. Kharkiv school of M. I. Kadets and mathematics of Tula. Chebyshevskii Sbornik. 2021;22(4):324-331. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-4-324-331
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