Аннотация:
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.
Ключевые слова и фразы:Riesz kernels, families of operators, ranges of convergence, polynomial $K$-functionals related to (fractal) powers of the Laplace operator.