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Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness

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Abstract

We study properties of generalized K-functionals and generalized moduli of smoothness in Lp(ℝ) spaces with 1 ≤ p < ∞ as well as in the space C(ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized K-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods, K-functionals related to fractional derivatives and fractional moduli of smoothness.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow Institute of Electronics and Mathematics, Moscow, Russian Federation

    S. Artamonov

  2. Lomonosov Moscow State University, Moscow, Russian Federation

    K. Runovski

  3. Friedrich Schiller University, Jena, Germany

    H.-J. Schmeisser

Authors
  1. S. Artamonov
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  2. K. Runovski
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  3. H.-J. Schmeisser
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Correspondence to H.-J. Schmeisser.

Additional information

The first named author was partially supported by the grant of the President of Russian Federation for young candidates of sciences, project no. MK-176.2017.1.

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Artamonov, S., Runovski, K. & Schmeisser, HJ. Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness. Anal Math 45, 1–24 (2019). https://doi.org/10.1007/s10476-018-0302-1

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  • DOI: https://doi.org/10.1007/s10476-018-0302-1

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