The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (239 KB) | Metadata | Table of Contents | ZAA summary
Volume 19, Issue 3, 2000, pp. 677–693
DOI: 10.4171/ZAA/974

Published online: 2000-09-30

On the Method of Approximation by Families of Linear Polynomial Operators

Z. Burinska[1], Konstantin V. Runovski[2] and Hans-Jürgen Schmeisser[3]

(1) Friedrich-Schiller-Universität Jena, Germany
(2) Lomonosov State University, Sevastopol, Ukraine
(3) Friedrich-Schiller-University, Jena, Germany

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

Keywords: Families of linear polynomial operators, best approximation by trigonometric polynomials, Fourier and interpolation means

Burinska Z., Runovski Konstantin, Schmeisser Hans-Jürgen: On the Method of Approximation by Families of Linear Polynomial Operators. Z. Anal. Anwend. 19 (2000), 677-693. doi: 10.4171/ZAA/974