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Prokhorov, Dmitri Valentinovich

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Total publications: 37
Scientific articles: 30

Number of views:
This page:2110
Abstract pages:7188
Full texts:2566
References:510
Professor
Doctor of physico-mathematical sciences (1990)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 11.09.1946
E-mail:
Website: http://www.sgu.ru/faculties/mathematics/chairs/matan/prokhorov.php
Keywords: univalent functions; variational methods; Loewner equation; Hele–Shaw equation.

Subject:

There constructed a new method of solving extremal problems on the class of univalent functions based on the parametric Loewner representation and optimization principles. This allowed us to solve some known and new problems. The Jakubowski conjecture was proved stating that the Pick functions are extremal in the problem of estimating even coefficients in the class of univalent functions $f$, $|f(z)|<M$ for sufficiently large $M$. We proved the conjecture that the maximum of the product $|a_2a_n|$ in the class of univalent functions close to identity is<br> attained for the Pick functions. We solved the Hengartner–Shober–Goodman–Saff–Brannan problem on the radius of a disk such that every function convex in a direction maps this disk onto a domain convex in another given direction.

Biography

Graduated from Department of Mathematics and Mechanics of Saratov State University in 1968. Ph.D. thesis was defended in 1974. D.Sci. thesis was defended in 1990. A list of my works contains more than 80 titles.

A corresponding member of the Russian Academy of Natural Sciences.

   
Main publications:
  • Michalska M., Prokhorov D. V., Szynal J. The composition of hyperbolic triangle mappings // Complex Variable. 2000, 43, 179–186.
  • Jakubwski Z., Prokhorov D. V., Szynal J. Proof of a coefficient product conjecture for bounded univalent functions // Complex Variable, 2000, 43, 241–258.

http://www.mathnet.ru/eng/person17778
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/201559
http://orcid.org/0000-0002-0490-941X

Publications in Math-Net.Ru
2019
1. D. V. Prokhorov, “Value regions in classes of conformal mappings”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 19:3 (2019),  258–279  mathnet  isi  elib
2. V. G. Gordienko, D. V. Prokhorov, “The Bombieri Problem for Bounded Univalent Functions”, Mat. Zametki, 105:3 (2019),  364–374  mathnet  elib; Math. Notes, 105:3 (2019), 342–350  isi  scopus
2017
3. D. V. Prokhorov, “Extension of starlike functions to a finitely punctured plane”, Probl. Anal. Issues Anal., 6(24):1 (2017),  58–67  mathnet  isi  elib
2015
4. D. V. Prokhorov, D. V. Ukrainskii, “Asymptotic ratio of harmonic measures of slit sides”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:2 (2015),  160–167  mathnet  isi  elib
2014
5. M. V. Pavlov, D. V. Prokhorov, A. Yu. Vasiliev, A. M. Zaharov, “Löwner evolution and finite-dimensional reductions of integrable systems”, TMF, 181:1 (2014),  155–172  mathnet  mathscinet  elib; Theoret. and Math. Phys., 181:1 (2014), 1263–1278  isi  elib  scopus
2013
6. D. V. Prokhorov, K. A. Samsonova, “Integrals of the Loewner equation with exponential driving function”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:4(2) (2013),  98–108  mathnet  elib
2010
7. D. V. Prokhorov, A. M. Zaharov, “Integrability of a partial case of the Lëwner equation”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 10:2 (2010),  19–23  mathnet
2008
8. D. V. Prokhorov, V. G. Gordienko, “Definition of a boundary in the local Charzyński-Tammi conjecture”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, 9,  59–68  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 52:9 (2008), 51–59
2006
9. D. V. Prokhorov, S. V. Romanova, “Local extremal problems for bounded analytic functions without zeros”, Izv. RAN. Ser. Mat., 70:4 (2006),  209–224  mathnet  mathscinet  zmath  elib; Izv. Math., 70:4 (2007), 841–856  isi  elib  scopus
10. D. V. Prokhorov, A. A. Nikulin, “Asymptotic estimates for the coefficients of bounded univalent functions”, Sibirsk. Mat. Zh., 47:5 (2006),  1128–1138  mathnet  mathscinet  zmath  elib; Siberian Math. J., 47:5 (2006), 924–933  isi  elib  scopus
1998
11. Yu. E. Hohlov, D. V. Prokhorov, A. Yu. Vasil'ev, “On geometrical properties of free boundaries in the Hele–Shaw flows moving boundary problem”, Lobachevskii J. Math., 1 (1998),  3–12  mathnet  mathscinet  zmath
1997
12. D. V. Prokhorov, “The sum of coefficients of bounded univalent functions”, Mat. Zametki, 61:5 (1997),  728–733  mathnet  mathscinet  zmath; Math. Notes, 61:5 (1997), 609–613  isi
1993
13. D. V. Prokhorov, A. M. Zaharov, “The set of values of a function and its derivative in the class of univalent mappings of a half-plane”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, 2,  33–37  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:2 (1993), 31–35
1991
14. D. V. Prokhorov, “Set of values of the initial coefficients of bounded univalent typically real-valued functions”, Sibirsk. Mat. Zh., 32:5 (1991),  132–141  mathnet  mathscinet  zmath; Siberian Math. J., 32:5 (1991), 840–848  isi
1990
15. D. V. Prokhorov, “Sets of values of systems of functionals in classes of univalent functions”, Mat. Sb., 181:12 (1990),  1659–1677  mathnet  mathscinet  zmath; Math. USSR-Sb., 71:2 (1992), 499–516  isi
1988
16. D. V. Prokhorov, “Level curves of functions convex in the direction of an axis”, Mat. Zametki, 44:4 (1988),  523–527  mathnet  mathscinet  zmath; Math. Notes, 44:4 (1988), 767–769  isi
1986
17. D. V. Prokhorov, “Ranges of values of systems of functionals and integration of univalent functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1986, 10,  33–39  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 30:10 (1986), 44–53
18. D. V. Prokhorov, “The maximum principle in the solution of an extremal problem on the class of univalent functions”, Sibirsk. Mat. Zh., 27:1 (1986),  186–190  mathnet  mathscinet  zmath
1985
19. D. V. Prokhorov, “Relation of measures of boundary sets under a mapping of a disk onto a plane with cuts”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, 4,  53–55  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 29:4 (1985), 66–69
1984
20. D. V. Prokhorov, “Optimal control method in an extremal problem on the class of univalent functions”, Dokl. Akad. Nauk SSSR, 275:4 (1984),  798–801  mathnet  mathscinet  zmath
1983
21. D. V. Prokhorov, “Combined criteria for univalence of functions analytic in the disk”, Izv. Vyssh. Uchebn. Zaved. Mat., 1983, 8,  76–77  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 27:8 (1983), 94–97
1980
22. D. V. Prokhorov, “Integral transformations in some classes of univalent functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, 12,  45–49  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 24:12 (1980), 53–58
1979
23. D. V. Prokhorov, “Linearly invariant extensions of families of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, 9,  41–47  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 23:9 (1979), 40–47
1978
24. D. V. Prokhorov, “Integrals from univalent functions”, Mat. Zametki, 24:5 (1978),  671–678  mathnet  mathscinet  zmath; Math. Notes, 24:5 (1978), 858–862
1976
25. D. V. Prokhorov, B. N. Rakhmanov, “Integral representation of a class of univalent functions”, Mat. Zametki, 19:1 (1976),  41–48  mathnet  mathscinet  zmath; Math. Notes, 19:1 (1976), 24–28
1975
26. D. V. Prokhorov, “The geometric characterization of functions from Bazilevič subclasses”, Izv. Vyssh. Uchebn. Zaved. Mat., 1975, 2,  130–132  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 19:2 (1975), 106–107
27. D. V. Prokhorov, “A generalization of the Christoffel–Schwartz formula”, Mat. Zametki, 17:5 (1975),  749–756  mathnet  mathscinet  zmath; Math. Notes, 17:5 (1975), 445–449
1974
28. D. V. Prokhorov, “On functions of Bazilevitch's class”, Zap. Nauchn. Sem. LOMI, 44 (1974),  127–130  mathnet  mathscinet  zmath
1972
29. D. V. Prokhorov, “A generalization of a class of close-to-convex functions”, Mat. Zametki, 11:5 (1972),  509–516  mathnet  mathscinet  zmath; Math. Notes, 11:5 (1972), 311–315
1971
30. D. V. Prokhorov, “A geometric property of functions starlike of order $\alpha$”, Mat. Zametki, 10:3 (1971),  287–293  mathnet  mathscinet  zmath; Math. Notes, 10:3 (1971), 597–600

2018
31. L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “Farit Gabidinovich Avkhadiev (on his 70th birthday)”, Uspekhi Mat. Nauk, 73:1(439) (2018),  187–190  mathnet  mathscinet  elib; Russian Math. Surveys, 73:1 (2018), 181–185  isi
2017
32. D. V. Prokhorov, S. I. Dudov, A. M. Zakharov, V. B. Poplavskii, V. V. Rozen, S. P. Sidorov, “In memory of Alexandr Yu. Vasiliev”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 17:1 (2017),  117–121  mathnet
2010
33. D. V. Prokhorov, A. M. Zaharov, S. I. Dudov, “Avgust Petrovich Khromov (on his 75th birthday)”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 10:3 (2010),  92–93  mathnet
2007
34. D. V. Prokhorov, A. M. Zaharov, S. I. Dudov, “Avgust Petrovich Khromov”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 7:2 (2007),  82–84  mathnet
35. S. I. Dudov, A. M. Zaharov, D. V. Prokhorov, A. P. Khromov, “Petr Lavrentievich Ulianov”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 7:1 (2007),  89–93  mathnet  elib
1995
36. L. D. Kudryavtsev, S. M. Nikol'skii, D. V. Prokhorov, S. B. Stechkin, S. A. Telyakovskii, P. L. Ul'yanov, A. P. Khromov, V. A. Yurko, “Nikolai Petrovich Kuptsov (obituary)”, Uspekhi Mat. Nauk, 50:4(304) (1995),  71–72  mathnet  mathscinet; Russian Math. Surveys, 50:4 (1995), 727–729  isi
1988
37. A. M. Bogomolov, M. K. Potapov, A. A. Privalov, D. V. Prokhorov, “Четвертая Саратовская зимняя школа по теории функций и приближений”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, 6,  84–88  mathnet

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