ABSTRACT
Abstract. It is already well-understood that approximation by ra dial functions is a useful practical tool, especially when the data is high dimensional, or scattered. The theoretical understanding of the approxi mating power of these functions has improved dramatically over the last 10 years, particularly with the use of Fourier transform methods for data which is regularly distributed throughout IRn. Good progress has now been made towards understanding a variety of aspects of approximating on compact domains, and using scattered data sites. We shall discuss a selection of these advances with particular references to our own interests in this area.
