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Approximation by translates of a single function of functions in space induced by the convolution with a given function

Author

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  • Dũng, Dinh
  • Micchelli, Charles A.
  • Huy, Vu Nhat

Abstract

We study approximation by arbitrary linear combinations of n translates of a single function of periodic functions. We construct some linear methods of this approximation for functions in a class induced by the convolution with a given function, and prove upper bounds of the Lp-approximation convergence rate by these methods, when n → ∞, for 1 < p < ∞. We also prove a lower bound of the quantity of best approximation of this class by arbitrary linear combinations of n translates of arbitrary function, for the particular case p=2.

Suggested Citation

  • Dũng, Dinh & Micchelli, Charles A. & Huy, Vu Nhat, 2019. "Approximation by translates of a single function of functions in space induced by the convolution with a given function," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 777-787.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:777-787
    DOI: 10.1016/j.amc.2019.06.034
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