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Acta Mathematica Sinica, English Series

, Volume 34, Issue 10, pp 1563–1577 | Cite as

Generalized Logan’s Problem for Entire Functions of Exponential Type and Optimal Argument in Jackson’s Inequality in L2(ℝ3)

  • Valerii Ivanov
  • Alexey Ivanov
Article
  • 19 Downloads

Abstract

We study Jackson’s inequality between the best approximation of a function fL2(ℝ3) by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson’s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson’s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue–Morse modulus of continuity of order r ∈ ℕ. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.

Keywords

Best approximation generalized modulus of continuity Jackson’s inequality optimal argument Logan’s problem quadrature formula 

MR(2010) Subject Classification

30D20 41A17 41A44 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceTula State UniversityTulaRussia

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