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Eurasian Math. J., 2010, Volume 1, Number 4, Pages 124–139 (Mi emj39)  

This article is cited in 5 scientific papers (total in 5 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

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.

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Bibliographic databases:
MSC: 42A10, 42A15
Received: 10.11.2010
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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://www.ams.org/mathscinet-getitem?mr=2905205}
\zmath{https://zbmath.org/?q=an:1232.42006}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Runovski, H.-J. Schmeisser, “Methods of trigonometric approximation and generalized smoothness. I”, Eurasian Math. J., 2:3 (2011), 98–124  mathnet  mathscinet  zmath
    2. Runovski K.V., Schmeisser H.-J., “Moduli of Smoothness Related To Fractional Riesz-Derivatives”, Z. Anal. ihre. Anwend., 34:1 (2015), 109–125  crossref  mathscinet  zmath  isi  elib
    3. Kolomoitsev Yu., Prestin J., “Sharp Estimates of Approximation of Periodic Functions in Holder Spaces”, J. Approx. Theory, 200 (2015), 68–91  crossref  mathscinet  zmath  isi  scopus
    4. K. V. Runovskii, “Approximation by Fourier Means and Generalized Moduli of Smoothness”, Math. Notes, 99:4 (2016), 564–575  mathnet  crossref  crossref  mathscinet  isi  elib
    5. K. V. Runovski, “Trigonometric polynomial approximation, $K$-functionals and generalized moduli of smoothness”, Sb. Math., 208:2 (2017), 237–254  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Eurasian Mathematical Journal
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