Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means

  • O. L. Vinogradov
  • V. V. Zhuk

Some estimates for functionals indicated in the title are established. As implications, Jackson type inequalities with constants smaller than the previously known ones are obtained. The results hold in various spaces of both periodic and nonperiodic functions. Bibliography: 9 titles.


General Estimate Type Inequality Moment Sequence Integrate Difference Jackson Type 
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  1. 1.
    V. V. Zhuk, “On V. A. Steklov funetions,” in: Differential Equations in Partial Derivatives {General Theory and Applications} [in Russian], St.Petersburg (1992), pp. 74–85.Google Scholar
  2. 2.
    V. V. Zhuk and V. F. Kuzyutin, Function Approximation and Numerical Integration [in Russian], St.Petersburg (1995).Google Scholar
  3. 3.
    S. Foucart, Y. Kryakin, and A. Shadrin, “On the exact constant in the Jackson-Stechkin inequality for the uniform metric,” Constr. Approx.. 29, 157–179 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    O. L. Vinogradov and V. V. Zhuk, “An estimate for functionals in terms of powers of deviations of summator-integral operat0rs,” in: Approximation Theory (International Conference held in St.Petersburg on May 6–8, 2010), Abstracts (2010), pp. 9–10.Google Scholar
  5. 5.
    B. M. Levitan, Almost Periodic Functions [in Russian], Moscow (1953).Google Scholar
  6. 6.
    G. R. L. Graham, D. E. Knutli, and O. Patashnik, Concrete Mathematics [Russian translation], Moscow (1998).Google Scholar
  7. 7.
    O. L. Vinogradov, “Sharp Jackson type inequalities for approximations of classes of convolutions by entier functions of finite degrees,” Algebra Analiz, 17, No. 4, 56–111 (2005).Google Scholar
  8. 8.
    V. V. Zhuk, Structural Properties of Functions and Approximation Accuracy [in Russian], Leningrad (1984).Google Scholar
  9. 9.
    O. L. Vinogradov and V. V. Zhuk, “The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus,” Zap. Nauchn. Semin. POMI, 383, 33–52 (2010).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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