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Arestov, Vitalii Vladimirovich
Statistics Math-Net.Ru
Total publications: 53
Scientific articles: 46
Presentations: 3

Number of views:
This page:6526
Abstract pages:19916
Full texts:8151
References:1709
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: https://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.

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

Publications in Math-Net.Ru Citations
2024
1. R. R. Akopyan, V. V. Arestov, V. G. Timofeev, “Stechkin's Problem on the Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line”, Mat. Zametki, 115:6 (2024),  807–824  mathnet  mathscinet; Math. Notes, 115:6 (2024), 853–867  scopus
2023
2. V. V. Arestov, M. V. Deikalova, “A Generalized Translation Operator Generated by the Sinc Function on an Interval”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023),  27–48  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S32–S52  scopus
3. Vitalii V. Arestov, “Approximation of differentiation operators by bounded linear operators in lebesgue spaces on the axis and related problems in the spaces of $(p,q)$-multipliers and their predual spaces”, Ural Math. J., 9:2 (2023),  4–27  mathnet  elib
2022
4. V. V. Arestov, M. V. Deikalova, “On One Generalized Translation and the Corresponding Inequality of Different Metrics”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  40–53  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S30–S42  isi  scopus 4
5. Vitalii V. Arestov, Marina V. Deikalova, “On one inequality of different metrics for trigonometric polynomials”, Ural Math. J., 8:2 (2022),  27–45  mathnet  mathscinet  elib 2
2020
6. 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 1
7. 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 4
8. 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; Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S6–S13  isi  scopus
2019
9. 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 4
2018
10. 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; Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S9–S30  isi 10
2017
11. Vitalii V. Arestov, “A characterization of extremal elements in some linear problems”, Ural Math. J., 3:2 (2017),  22–32  mathnet  mathscinet  elib 4
2015
12. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015),  20–29  mathnet  zmath  elib 7
2014
13. 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 13
2013
14. V. V. Arestov, M. A. Filatova, “Approximation of differentiation operator in the space $L_2$ on semiaxis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 5,  3–12  mathnet; Russian Math. (Iz. VUZ), 57:5 (2013), 1–8 1
15. 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 20
2012
16. 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 2
2011
17. 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 3
2010
18. 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 11
2001
19. 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 11
2000
20. 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 3
1998
21. 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 3
1997
22. 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 4
23. 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 16
1996
24. 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 100
1995
25. V. V. Arestov, V. N. Gabushin, “Best approximation of unbounded operators by bounded operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 11,  42–68  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:11 (1995), 38–63 23
26. V. V. Arestov, V. Yu. Popov, “Jackson inequalities on a sphere in $L_2$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 8,  13–20  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 11–18 17
1994
27. 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 10
1992
28. 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 2
29. 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 6
30. 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 8
1990
31. 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 22
32. 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 5
1989
33. V. V. Arestov, “Optimal recovery of operators and related problems”, Trudy Mat. Inst. Steklov., 189 (1989),  3–20  mathnet  mathscinet 34
1986
34. 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 2
1983
35. 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 5
1981
36. 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 60
1980
37. 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 23
38. 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 7
1979
39. 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 11
1977
40. 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 16
1975
41. 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 9
42. 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 7
43. 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 5
1971
44. 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 4
1969
45. 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 11
1967
46. 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 12
2022
47. V. V. Arestov, V. I. Berdyshev, A. G. Babenko, M. V. Deikalova, “On S. B. Stechkin's International Workshop-Conference on Function Theory in Memory of Corresponding Member of RAS Y. N. Subbotin and Professor S. A. Telyakovskii”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  277–285  mathnet  elib
48. R. R. Akopyan, N. Yu. Antonov, V. V. Arestov, A. G. Babenko, N. V. Baidakova, V. I. Berdyshev, V. V. Vasin, S. I. Novikov, N. L. Patsko, A. G. Chentsov, N. I. Chernykh, V. T. Shevaldin, “Yurii Nikolaevich Subbotin (A Tribute to His Memory)”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  9–16  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S1–S6  isi
2021
49. V. V. Arestov, V. I. Berdyshev, A. G. Babenko, Yu. S. Volkov, M. V. Deikalova, “International S.B. Stechkin's Workshop-Conference on Function Theory dedicated to the 85th anniversary of Yu.N. Subbotin and N.I. Chernykh”, Sib. Èlektron. Mat. Izv., 18:2 (2021),  93–108  mathnet 1
2017
50. 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
51. 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
52. 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 3
1996
53. 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 2

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   

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