Series kernels and their approximation properties
Barbara Zwicknagl · 2009
Many popular kernel functions can be expanded in series of simple basis functions. Examples of such basis functions include monomials leading to power series kernels [2], or wavelet-type functions leading to multiscale kernels [1]. The approximation properties of trial spaces built by translates of such series kernels are discussed. The focus of the talk is on the interplay between the multiscale structure of the kernel and the choice of data points. Applications of the results range from multivariate polynomial approximation to the eective numerical