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Arestov Vitalii Vladimirovich

Publications in Math-Net.Ru

  1. Best approximation of a fractional-order differentiation operator in the uniform norm on the axis on the class of functions with integrable Fourier transform of the highest derivative

    Trudy Inst. Mat. i Mekh. UrO RAN, 31:3 (2025),  47–63
  2. Approximation of one class of smooth functions by another class of smoother functions on the axis

    Ural Math. J., 11:2 (2025),  21–42
  3. 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
  4. A variant of Stechkin's problem on the best approximation of a fractional order differentiation operator on the axis

    Trudy Inst. Mat. i Mekh. UrO RAN, 30:4 (2024),  37–54
  5. A Generalized Translation Operator Generated by the Sinc Function on an Interval

    Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023),  27–48
  6. 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
  7. On One Generalized Translation and the Corresponding Inequality of Different Metrics

    Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  40–53
  8. On one inequality of different metrics for trigonometric polynomials

    Ural Math. J., 8:2 (2022),  27–45
  9. 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
  10. 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
  11. 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
  12. On the conjugacy of the space of multipliers

    Trudy Inst. Mat. i Mekh. UrO RAN, 25:4 (2019),  5–14
  13. 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
  14. A characterization of extremal elements in some linear problems

    Ural Math. J., 3:2 (2017),  22–32
  15. On the best approximation of the differentiation operator

    Ural Math. J., 1:1 (2015),  20–29
  16. Bernstein–Szegö inequality for fractional derivatives of trigonometric polynomials

    Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014),  17–31
  17. Approximation of differentiation operator in the space $L_2$ on semiaxis

    Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 5,  3–12
  18. Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere

    Trudy Inst. Mat. i Mekh. UrO RAN, 19:2 (2013),  34–47
  19. 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
  20. Exposition of the lectures by S. B. Stechkin on approximation theory

    Eurasian Math. J., 2:4 (2011),  5–155
  21. Sharp inequalities for trigonometric polynomials with respect to integral functionals

    Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  38–53
  22. Turán's problem for positive definite functions with supports in a hexagon

    Trudy Inst. Mat. i Mekh. UrO RAN, 7:1 (2001),  21–29
  23. 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
  24. 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
  25. An extremal problem for algebraic polynomials with zero mean value on an interval

    Mat. Zametki, 62:3 (1997),  332–342
  26. On Delsarte Scheme of Estimating the Contact Numbers

    Trudy Mat. Inst. Steklova, 219 (1997),  44–73
  27. Approximation of unbounded operators by bounded operators and related extremal problems

    Uspekhi Mat. Nauk, 51:6(312) (1996),  89–124
  28. Best approximation of unbounded operators by bounded operators

    Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 11,  42–68
  29. Jackson inequalities on a sphere in $L_2$

    Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 8,  13–20
  30. The Szegő inequality for derivatives of a conjugate trigonometric polynomial in $L_0$

    Mat. Zametki, 56:6 (1994),  10–26
  31. On some Szegő inequality for algebraic polynomials

    Trudy Inst. Mat. i Mekh. UrO RAN, 2 (1992),  27–33
  32. On extremal properties of the nonnegative trigonometric polynomials

    Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992),  50–70
  33. Best approximation ol unbounded operators invariant with respect to a shift by the linear bounded operators

    Trudy Mat. Inst. Steklov., 198 (1992),  3–20
  34. Integral inequalities for algebraic polynomials on the unit circle

    Mat. Zametki, 48:4 (1990),  7–18
  35. Certain extremal problem for nonnegative trigonometric polynomials

    Mat. Zametki, 47:1 (1990),  15–28
  36. Optimal recovery of operators and related problems

    Trudy Mat. Inst. Steklov., 189 (1989),  3–20
  37. Best approximation of unbounded by bounded operators, and allied problems

    Mat. Zametki, 40:2 (1986),  269–285
  38. Approximation of invariant operators

    Mat. Zametki, 34:1 (1983),  9–29
  39. On integral inequalities for trigonometric polynomials and their derivatives

    Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981),  3–22
  40. Inequality of different metrics for trigonometric polynomials

    Mat. Zametki, 27:4 (1980),  539–547
  41. Approximation of operators of convolution type by linear bounded operators

    Trudy Mat. Inst. Steklov., 145 (1980),  3–19
  42. On inequalities of S. N. Bernstein for algebraic and trigonometric polynomials

    Dokl. Akad. Nauk SSSR, 246:6 (1979),  1289–1292
  43. Uniform regularization of the problem of calculating the values of an operator

    Mat. Zametki, 22:2 (1977),  231–244
  44. Approximation of operators that are invariant under a shift

    Trudy Mat. Inst. Steklov., 138 (1975),  43–70
  45. Approximation of linear operators, and related extremal problems

    Trudy Mat. Inst. Steklov., 138 (1975),  29–42
  46. Some extremal problems for differentiable functions of one variable

    Trudy Mat. Inst. Steklov., 138 (1975),  3–28
  47. Approximation of classes of differentiable functions

    Mat. Zametki, 9:2 (1971),  105–112
  48. On the best uniform approximation of differentiation operators

    Mat. Zametki, 5:3 (1969),  273–284
  49. Best approximation of differentiation operators

    Mat. Zametki, 1:2 (1967),  149–154

  50. 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
  51. Yurii Nikolaevich Subbotin (A Tribute to His Memory)

    Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  9–16
  52. 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
  53. The 42nd International S.B. Stechkin's Workshop-Conference on function theory

    Ural Math. J., 3:2 (2017),  3–5
  54. International conference “Algorithmic analysis of unstable problems (AAUP-2011)”

    Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012),  329–333
  55. Yurii Nikolaevich Subbotin (on his 70th birthday)

    Uspekhi Mat. Nauk, 62:2(374) (2007),  187–190
  56. S. B. Stechkin and approximation theory

    Trudy Inst. Mat. i Mekh. UrO RAN, 4 (1996),  3–16

© Steklov Math. Inst. of RAS, 2026