This article is cited in 10 papers

On families of linear polynomial operators generated by Riesz kernels

K.  Runovski^a, H.-J. Schmeisser<sup>b

a</sup> Sevastopol Branch of Moscow State University, Sevastopol, Ukraine
^b Mathematisches Institut, Friedrich-Schiller University, Jena, Germany

Abstract: Families of linear polynomial operators generated by the Riesz kernels are studied. Sharp ranges of convergence are found in many cases. It is shown that the approximation error is equivalent to the polynomial $K$-functional related to the apropricate power of the Laplace operator, if the family converges.

Keywords and phrases: Riesz kernels, families of operators, ranges of convergence, polynomial $K$-functionals related to (fractal) powers of the Laplace operator.

MSC: 42A10, 42A15

Received: 10.11.2010

Language: English

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