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Arestov, Vitalii Vladimirovich

Statistics Math-Net.Ru
Total publications: 45
Scientific articles: 41
Presentations: 3

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Professor
Doctor of physico-mathematical sciences (1985)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 16.07.1943
E-mail: ,
Website: http://www.imm.uran.ru
Keywords: approximation of functions; extremal properties of polynomials and entire functions; harmonic analysis; positive definite functions; approximation of operators; ill-posed problems.

Subject:

The problem of the best approximation of unbounded operators by bounded ones was studied. Some mutual relation was established between this problem and the problem of the least constants in inequalities between norms of derivatives of differentiable functions (Kolmogorov inequalities), the problem of the best approximation of one class of functions by another class of more smooth functions, the ill-posed problem of optimal recovery of unbounded operators on classes of elements given with an error. Solution of these problems was found in a number of concrete cases. It was created a method of investigation of problems for trigonometric polynomials in the spaces $L_p, 0\le p<1$; the best constant in Bernstein inequality for trigonometric polynomials in $L_p, 0\le p<1$ was found with the help of this method. Cojointly with A. G. Babenko it was solved Delsarte problem which is connected with the problem about contact number of four-dimensional Euclidian space.

Biography

Graduated from Faculty of Mathematics and Mechanics of Saratov State University in 1965. Ph.D. thesis was defended in 1970. D.Sci. thesis was defended in 1985. In 1991 I was awarded the title of Professor. A list of my works contains about 80 titles.

I am a member of editorial board of the international mathematical journal "East Journal on Approximations". In 1999 and 2001 I was awarded the title of the Soros Professor. During 1998, 1999, 2000–2003 I receive state scientific scholarship for outstanding scientists of Russia.

   
Main publications:
  • Arestov V. V. Ob integralnykh neravenstvakh dlya trigonometricheskikh polinomov i ikh proizvodnykh // Izv. AN SSSR. Ser. matem. 1981. T. 45, # 1. S. 3–22.
  • Arestov V. V. Integralnye neravenstva dlya algebraicheskikh mnogochlenov na edinichnoi okruzhnosti // Matem. zametki. 1990. T. 48, vyp. 4. S. 7–18.
  • Arestov V. V. Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi // Uspekhi matem. nauk. 1996. T. 51, vyp. 6. S. 89–124.
  • Arestov V. V., Babenko A. G. O skheme Delsarta otsenki kontaktnykh chisel // Trudy Matem. in-ta im. V. A. Steklova RAN. 1997. T. 219: Teoriya priblizhenii. Garmonicheskii analiz. S. 44–73.
  • Arestov V. V. Nailuchshee priblizhenie odnogo klassa funktsii mnogikh peremennykh drugim i rodstvennye ekstremalnye zadachi // Matem. zametki. 1998. T. 64, vyp. 3. S. 323–340.

http://www.mathnet.ru/eng/person17283
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List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/194566

Publications in Math-Net.Ru
2020
1. V. V. Arestov, V. I. Berdyshev, M. V. Deikalova, S. V. Konyagin, D. S. Telyakovskii, “On the International Workshop-Conference on Function Theory Dedicated to the Centenary of the Birth of S.B. Stechkin”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:4 (2020),  290–299  mathnet  mathscinet  elib
2. V. V. Arestov, R. R. Akopyan, “Stechkin's problem on the best approximation of an unbounded operator by bounded ones and related problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:4 (2020),  7–31  mathnet  elib
3. V. V. Arestov, A. A. Seleznev, “Best $L^2$-extension of algebraic polynomials from the unit Euclidean sphere to a concentric sphere”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020),  47–55  mathnet  elib
2019
4. V. V. Arestov, “On the conjugacy of the space of multipliers”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:4 (2019),  5–14  mathnet  elib
2018
5. V. V. Arestov, “Best uniform approximation of the differentiation operator by operators bounded in the space $L_2$”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:4 (2018),  34–56  mathnet  elib
2017
6. Vitalii V. Arestov, “A characterization of extremal elements in some linear problems”, Ural Math. J., 3:2 (2017),  22–32  mathnet  mathscinet  elib
2015
7. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015),  20–29  mathnet  zmath  elib
2014
8. V. V. Arestov, P. Yu. Glazyrina, “Bernstein–Szegö inequality for fractional derivatives of trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014),  17–31  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 13–28  isi  scopus
2013
9. V. V. Arestov, M. A. Filatova, “Approximation of differentiation operator in the space $L_2$ on semiaxis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, 5,  3–12  mathnet; Russian Math. (Iz. VUZ), 57:5 (2013), 1–8
10. V. V. Arestov, M. V. Deikalova, “Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:2 (2013),  34–47  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 9–23  isi  scopus
2012
11. V. V. Arestov, M. A. Filatova, “On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012),  35–50  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 24–40  isi  scopus
2011
12. V. V. Arestov, V. I. Berdyshev, N. I. Chernykh, T. V. Demina, N. N. Kholschevnikova, S. V. Konyagin, Yu. N. Subbotin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Yudin, “Exposition of the lectures by S. B. Stechkin on approximation theory”, Eurasian Math. J., 2:4 (2011),  5–155  mathnet  mathscinet  zmath
2010
13. V. V. Arestov, “Sharp inequalities for trigonometric polynomials with respect to integral functionals”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  38–53  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S21–S36  isi  scopus
2001
14. V. V. Arestov, E. E. Berdysheva, “Turán's problem for positive definite functions with supports in a hexagon”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:1 (2001),  21–29  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 1, S20–S29
2000
15. V. V. Arestov, A. G. Babenko, “Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in $\mathbb R^4$”, Mat. Zametki, 68:4 (2000),  483–503  mathnet  mathscinet  zmath; Math. Notes, 68:4 (2000), 419–435  isi
1998
16. V. V. Arestov, “The best approximation to a class of functions of several variables by another class and related extremum problems”, Mat. Zametki, 64:3 (1998),  323–340  mathnet  mathscinet  zmath  elib; Math. Notes, 64:3 (1998), 279–294  isi
1997
17. V. V. Arestov, V. Yu. Raevskaya, “An extremal problem for algebraic polynomials with zero mean value on an interval”, Mat. Zametki, 62:3 (1997),  332–342  mathnet  mathscinet  zmath  elib; Math. Notes, 62:3 (1997), 278–287  isi
18. V. V. Arestov, A. G. Babenko, “On Delsarte Scheme of Estimating the Contact Numbers”, Trudy Mat. Inst. Steklova, 219 (1997),  44–73  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 219 (1997), 36–65
1996
19. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Uspekhi Mat. Nauk, 51:6(312) (1996),  89–124  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:6 (1996), 1093–1126  isi  scopus
1995
20. V. V. Arestov, V. N. Gabushin, “Best approximation of unbounded operators by bounded operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, 11,  42–68  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:11 (1995), 38–63
21. V. V. Arestov, V. Yu. Popov, “Jackson inequalities on a sphere in $L_2$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, 8,  13–20  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 11–18
1994
22. V. V. Arestov, “The Szegő inequality for derivatives of a conjugate trigonometric polynomial in $L_0$”, Mat. Zametki, 56:6 (1994),  10–26  mathnet  mathscinet  zmath; Math. Notes, 56:6 (1994), 1216–1227  isi
1992
23. V. V. Arestov, “On some Szegő inequality for algebraic polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 2 (1992),  27–33  mathnet  mathscinet  zmath  elib
24. V. V. Arestov, “On extremal properties of the nonnegative trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992),  50–70  mathnet  mathscinet  zmath  elib
25. V. V. Arestov, “Best approximation ol unbounded operators invariant with respect to a shift by the linear bounded operators”, Trudy Mat. Inst. Steklov., 198 (1992),  3–20  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 198 (1994), 1–16
1990
26. V. V. Arestov, “Integral inequalities for algebraic polynomials on the unit circle”, Mat. Zametki, 48:4 (1990),  7–18  mathnet  mathscinet  zmath; Math. Notes, 48:4 (1990), 977–984  isi
27. V. V. Arestov, V. P. Kondrat'ev, “Certain extremal problem for nonnegative trigonometric polynomials”, Mat. Zametki, 47:1 (1990),  15–28  mathnet  mathscinet  zmath; Math. Notes, 47:1 (1990), 10–20  isi
1989
28. V. V. Arestov, “Optimal recovery of operators and related problems”, Trudy Mat. Inst. Steklov., 189 (1989),  3–20  mathnet  mathscinet
1986
29. V. V. Arestov, “Best approximation of unbounded by bounded operators, and allied problems”, Mat. Zametki, 40:2 (1986),  269–285  mathnet  mathscinet  zmath; Math. Notes, 40:2 (1986), 655–663  isi
1983
30. V. V. Arestov, “Approximation of invariant operators”, Mat. Zametki, 34:1 (1983),  9–29  mathnet  mathscinet  zmath; Math. Notes, 34:1 (1983), 489–499  isi
1981
31. V. V. Arestov, “On integral inequalities for trigonometric polynomials and their derivatives”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981),  3–22  mathnet  mathscinet  zmath; Math. USSR-Izv., 18:1 (1982), 1–17
1980
32. V. V. Arestov, “Inequality of different metrics for trigonometric polynomials”, Mat. Zametki, 27:4 (1980),  539–547  mathnet  mathscinet  zmath; Math. Notes, 27:4 (1980), 265–269  isi
33. V. V. Arestov, “Approximation of operators of convolution type by linear bounded operators”, Trudy Mat. Inst. Steklov., 145 (1980),  3–19  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 145 (1981), 1–18
1979
34. V. V. Arestov, “On inequalities of S. N. Bernstein for algebraic and trigonometric polynomials”, Dokl. Akad. Nauk SSSR, 246:6 (1979),  1289–1292  mathnet  mathscinet  zmath
1977
35. V. V. Arestov, “Uniform regularization of the problem of calculating the values of an operator”, Mat. Zametki, 22:2 (1977),  231–244  mathnet  mathscinet  zmath; Math. Notes, 22:2 (1977), 618–626
1975
36. V. V. Arestov, “Approximation of operators that are invariant under a shift”, Trudy Mat. Inst. Steklov., 138 (1975),  43–70  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 138 (1977), 45–74
37. V. V. Arestov, “Approximation of linear operators, and related extremal problems”, Trudy Mat. Inst. Steklov., 138 (1975),  29–42  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 138 (1977), 31–44
38. V. V. Arestov, “Some extremal problems for differentiable functions of one variable”, Trudy Mat. Inst. Steklov., 138 (1975),  3–28  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 138 (1977), 1–29
1971
39. V. V. Arestov, V. N. Gabushin, “Approximation of classes of differentiable functions”, Mat. Zametki, 9:2 (1971),  105–112  mathnet  mathscinet  zmath; Math. Notes, 9:2 (1971), 63–67
1969
40. V. V. Arestov, “On the best uniform approximation of differentiation operators”, Mat. Zametki, 5:3 (1969),  273–284  mathnet  mathscinet  zmath; Math. Notes, 5:3 (1969), 167–173
1967
41. V. V. Arestov, “Best approximation of differentiation operators”, Mat. Zametki, 1:2 (1967),  149–154  mathnet  mathscinet  zmath; Math. Notes, 1:2 (1967), 100–103

2017
42. Vitalii V. Arestov, Vitalii I. Berdyshev, “The 42nd International S.B. Stechkin's Workshop-Conference on function theory”, Ural Math. J., 3:2 (2017),  3–5  mathnet  elib
2012
43. A. L. Ageev, V. V. Arestov, V. V. Vasin, “International conference “Algorithmic analysis of unstable problems (AAUP-2011)””, Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012),  329–333  mathnet  elib
2007
44. V. V. Arestov, V. I. Berdyshev, O. V. Besov, N. N. Krasovskii, S. M. Nikol'skii, S. I. Novikov, Yu. S. Osipov, S. A. Telyakovskii, N. I. Chernykh, V. T. Shevaldin, “Yurii Nikolaevich Subbotin (on his 70th birthday)”, Uspekhi Mat. Nauk, 62:2(374) (2007),  187–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:2 (2007), 403–406  isi
1996
45. V. V. Arestov, V. I. Berdyshev, Yu. N. Subbotin, N. I. Chernykh, “S. B. Stechkin and approximation theory”, Trudy Inst. Mat. i Mekh. UrO RAN, 4 (1996),  3–16  mathnet  mathscinet  zmath  elib

Presentations in Math-Net.Ru
1. Approximation of invariant operators
V. V. Arestov
International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin
September 8, 2021 12:30   
2. Approximation of the differentiation operator by bounded linear operators in the space $L_2$ on the half-line
V. V. Arestov
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 12:05   
3. Approximation of differentiation operators by bounded operators and related problems
V. V. Arestov
International conference "Nonlinear Approximations and Applications" dedicated to the 60th birthday of Professor V. N. Temlyakov
November 1, 2013 09:30   

Organisations
 
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