JournalszaaVol. 19, No. 3pp. 677–693

On the Method of Approximation by Families of Linear Polynomial Operators

  • Z. Burinska

    Friedrich-Schiller-Universität Jena, Germany
  • Konstantin V. Runovski

    Lomonosov State University, Sevastopol, Ukraine
  • Hans-Jürgen Schmeisser

    Friedrich-Schiller-University, Jena, Germany
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Abstract

It is shown that best approximation by trigonometric polynomials is achieved in average by families of linear polynomial operators in the LpL_p-metric for all p,0<p<p, 0 < p < \infty. This is compared with approximation by Fourier means and interpolation means which is restricted to 1p1 ≤ p ≤ \infty and p=p = \infty, respectively.

Cite this article

Z. Burinska, Konstantin V. Runovski, Hans-Jürgen Schmeisser, On the Method of Approximation by Families of Linear Polynomial Operators. Z. Anal. Anwend. 19 (2000), no. 3, pp. 677–693

DOI 10.4171/ZAA/974