The \(L^p\)-weighted Lagrange interpolation on Markov-Sonin zeros
The theme of this paper is the approximation in univariate weighted \(L^p\)-spaces. Here, the index \(p\) is restricted to \((1,\infty)\). The approximation takes place with polynomials by Lagrange interpolation. For the Lagrange interpolation process, certain knots, so-called Markov-Sonin knots, are chosen. The knots are the zeros of Markov-Sonin polynomials. With this choice, error estimates à la Jackson are established in the article. The weight-functions used in the error estimates are always exponentials times some powers.
scientific article; zbMATH DE number 5082277