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Eurasian Mathematical Journal, 2010, Volume 1, Number 4, Pages 124–139 (Mi emj39)  
This article is cited in 10 scientific papers (total in 10 papers)

On families of linear polynomial operators generated by Riesz kernels

K.  Runovskia, H.-J. Schmeisserb

a Sevastopol Branch of Moscow State University, Sevastopol, Ukraine
b Mathematisches Institut, Friedrich-Schiller University, Jena, Germany
Full-text PDF (452 kB) Citations (10)
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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.
Received: 10.11.2010
Bibliographic databases:
Document Type: Article
MSC: 42A10, 42A15
Language: English
Citation: K.  Runovski, H.-J. Schmeisser, “On families of linear polynomial operators generated by Riesz kernels”, Eurasian Math. J., 1:4 (2010), 124–139
Citation in format AMSBIB
\Bibitem{RunSch10}
\by K.~~Runovski, H.-J.~Schmeisser
\paper On families of linear polynomial operators generated by Riesz kernels
\jour Eurasian Math. J.
\yr 2010
\vol 1
\issue 4
\pages 124--139
\mathnet{http://mi.mathnet.ru/emj39}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2905205}
\zmath{https://zbmath.org/?q=an:1232.42006}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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