Kernel based approximation in Sobolev spaces with radial basis functions (Q1039692)

Minimal norm interpolants using radial basis functions are studied in the context of Sobolev spaces. This work includes uniqueness results and error estimates in reproducing kernel Hilbert spaces. Also, smoothing by convolution and radial basis functions of compact support are considered. An approach employing these is then used to obtain Sobolev space approximations of optimal approximation order.