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Zhuk Vladimir Vasilievich

Publications in Math-Net.Ru

  1. On a strong form of asymptotic formulas of Voronovskaya–Bernstein type with pointwise estimate of the remainder term

    Zap. Nauchn. Sem. POMI, 449 (2016),  32–59
  2. On two-sided estimates for some functionals in terms of the best approximations

    Zap. Nauchn. Sem. POMI, 449 (2016),  15–31
  3. Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients

    Zap. Nauchn. Sem. POMI, 445 (2016),  5–32
  4. Constants in Jackson-type inequations for the best approximation of periodic differentiable functions

    Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2015, no. 1,  33–41
  5. On strong approximation of functions by positive operators

    Zap. Nauchn. Sem. POMI, 440 (2015),  68–80
  6. On some modifications of Jackson's generalized theorem for the best approximations of periodic functions

    Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2014, no. 1,  40–50
  7. Some inequalities for trigonometric polynomials and Fourier coefficients

    Zap. Nauchn. Sem. POMI, 429 (2014),  64–81
  8. On approximation of periodic functions by modified Steklov averages in $L_2$

    Zap. Nauchn. Sem. POMI, 429 (2014),  20–33
  9. Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in the spaces of functions defined on the segment

    Algebra i Analiz, 25:3 (2013),  86–120
  10. On the constants in inequalities of the generalized Jackson theorem type

    Zap. Nauchn. Sem. POMI, 418 (2013),  28–59
  11. Estimates of functionals by the second moduli of continuity of even derivatives

    Zap. Nauchn. Sem. POMI, 416 (2013),  70–90
  12. Estimates for functional with a known finite set of moments in terms of moduli of continuity and behaviour of constants in the Jackson-type inequalities

    Algebra i Analiz, 24:5 (2012),  1–43
  13. Estimates of best approximations of periodic function by linear combinations values of the function itself and its primitives

    Zap. Nauchn. Sem. POMI, 404 (2012),  157–174
  14. Inequalities of type generalized Jackson theorem for best approximations

    Zap. Nauchn. Sem. POMI, 404 (2012),  135–156
  15. Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences

    Zap. Nauchn. Sem. POMI, 392 (2011),  32–66
  16. The Detalization of the Irrational Behavior Proof Condition

    Contributions to Game Theory and Management, 3 (2010),  431–440
  17. The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity

    Zap. Nauchn. Sem. POMI, 383 (2010),  33–52
  18. Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means

    Zap. Nauchn. Sem. POMI, 383 (2010),  5–32
  19. On approximating periodic functions by the Fourier sums

    Zap. Nauchn. Sem. POMI, 371 (2009),  78–108
  20. On approximating periodic functions by Riesz sums

    Zap. Nauchn. Sem. POMI, 371 (2009),  18–36
  21. Approximation of periodic functions in the uniform metric by Jackson type polynomials

    Zap. Nauchn. Sem. POMI, 357 (2008),  115–142
  22. Approximation of periodic functions by Jackson type interpolation sums

    Zap. Nauchn. Sem. POMI, 357 (2008),  90–114
  23. Approximating periodic functions in Hölder type metrics by the Fourier sums and the Riesz means

    Zap. Nauchn. Sem. POMI, 350 (2007),  70–88
  24. On approximating periodic functions using linear approximation methods

    Zap. Nauchn. Sem. POMI, 337 (2006),  134–164
  25. On approximating periodic functions by singular integrals with positive kernels

    Zap. Nauchn. Sem. POMI, 337 (2006),  51–72
  26. Some orthogonalities in approximation theory

    Zap. Nauchn. Sem. POMI, 314 (2004),  83–123
  27. Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines

    Zap. Nauchn. Sem. POMI, 290 (2002),  5–26
  28. Semi-norms and continuity modules of functions defined on a segment

    Zap. Nauchn. Sem. POMI, 276 (2001),  155–203
  29. Parseval-type inequalities and some of their applications

    Dokl. Akad. Nauk, 341:6 (1995),  737–739
  30. On the convergence of the Fourier trigonometric series at a point

    Dokl. Akad. Nauk, 326:5 (1992),  770–775
  31. Approximation of functions on standard simplexes

    Dokl. Akad. Nauk, 324:4 (1992),  734–737
  32. Certain exact bounds for seminorms given on spaces of periodic functions

    Mat. Zametki, 21:6 (1977),  789–798
  33. Some exact inequalities between the best approximations and moduli of continuity of high orders

    Mat. Zametki, 21:2 (1977),  281–288
  34. Some sharp inequalities for uniform best approximations of periodic functions

    Dokl. Akad. Nauk SSSR, 214:6 (1974),  1245–1246
  35. Properties of functions, and growth of the derivatives of the approximating polynomials

    Dokl. Akad. Nauk SSSR, 212:1 (1973),  19–22
  36. Certain inequalities between best approximations of periodic functions

    Izv. Vyssh. Uchebn. Zaved. Mat., 1973, no. 9,  18–26
  37. Certain sharp inequalities between best approximations

    Izv. Vyssh. Uchebn. Zaved. Mat., 1973, no. 1,  51–56
  38. The accuracy of the representation of a continuous $2\pi$-periodic function by means of linear approximation methods

    Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 8,  46–59
  39. Some sharp inequalities between uniform best approximations of periodic functions

    Dokl. Akad. Nauk SSSR, 201:2 (1971),  263–265
  40. Some exact inequalities between best approximations and moduli of continuity

    Dokl. Akad. Nauk SSSR, 196:4 (1971),  748–750
  41. Certain exact inequalities between best approximations and moduli of continuity

    Sibirsk. Mat. Zh., 12:6 (1971),  1283–1291
  42. The rate of approximation of a continuous $2\pi$-periodic function by partial sums of its Fourier series

    Dokl. Akad. Nauk SSSR, 190:5 (1970),  1015–1018
  43. Some relations between moduli of continuity and functionals defined on sets of periodic functions

    Izv. Vyssh. Uchebn. Zaved. Mat., 1970, no. 5,  24–33
  44. The order of approximation of a continuous $2\pi$-periodic function by linear methods

    Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 10,  40–50
  45. Saturation theory converse problem

    Mat. Zametki, 6:5 (1969),  583–590
  46. The approximation of periodic functions by linear approximation methods

    Dokl. Akad. Nauk SSSR, 179:5 (1968),  1038–1041
  47. On the order of approximation of a continuous $2\pi$-periodic function by Fejer and Poisson means of its Fourier series

    Mat. Zametki, 4:1 (1968),  21–32
  48. The question of approximating periodic functions by linear summation methods for Fourier series

    Sibirsk. Mat. Zh., 9:3 (1968),  713–716
  49. Approximation of periodic functions by linear methods of summation of Fourier series

    Dokl. Akad. Nauk SSSR, 173:1 (1967),  30–33
  50. Approximation of periodic functions bounded by a subadditive operator

    Dokl. Akad. Nauk SSSR, 169:3 (1966),  515–518
  51. Some modifications of the concept of modulus of smoothness and their applications

    Dokl. Akad. Nauk SSSR, 162:1 (1965),  19–22
  52. A modification of the concept of modulus of smoothness and its application to the estimation of Fourier coefficients

    Dokl. Akad. Nauk SSSR, 160:4 (1965),  758–761
  53. On the absolute convergence of Fourier series

    Dokl. Akad. Nauk SSSR, 160:3 (1965),  519–522

  54. Garal'd Isidorovich Natanson (obituary)

    Uspekhi Mat. Nauk, 59:4(358) (2004),  181–185
  55. Viktor Solomonovich Videnskii (on his 80th birthday)

    Uspekhi Mat. Nauk, 57:5(347) (2002),  182–186
  56. Nikolai Andreevich Lebedev and the Leningrad school of function theory in the 1950–1970s

    Zap. Nauchn. Sem. POMI, 276 (2001),  5–19

© Steklov Math. Inst. of RAS, 2025