Quasi-interpolation in the Fourier algebra
In this paper, the most interesting topic of quasi-interpolation by the so-called Schoenberg operator is studied. This is an important operator especially in univariate and multivariate spline theory, as well as in, for example, the theory of radial basis functions. Here, the convergence of these operators in certain algebras is studied. That is, the convergence in generalisations of \(L^p\)-norms of the approximations generated by these operators to the functions approximated is established. An example for these results is the convergence proof in the Fourier algebra.
scientific article; zbMATH DE number 5125996
scientific article