On families of linear polynomial operators generated by Riesz kernels

Konstantin Runovski; Hans-Jurgen Schmeisser

On families of linear polynomial operators generated by Riesz kernels

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Authors

Konstantin Runovski
Hans-Jurgen Schmeisser

Keywords:

Riesz kernels, families of operators, ranges of convergence, polynomial K-functionals related to (fractal) powers of the Laplace operator

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 appropriate power of the Laplace operator, if the family converges.

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Published

2024-05-21

How to Cite

Runovski, K., & Schmeisser, H.-J. (2024). On families of linear polynomial operators generated by Riesz kernels. Eurasian Mathematical Journal, 1(4). Retrieved from https://emj.enu.kz/index.php/main/article/view/64