# Native spaces for the classical radial basis functions and their properties

14 October 1999
15:00
Prof Will Light
Abstract
It has been known for some while now that every radial basis function in common usage for multi-dimensional interpolation has associated with it a uniquely defined Hilbert space, in which the radial basis function is the `minimal norm interpolant'. This space is usually constructed by utilising the positive definite nature of the radial function, but such constructions turn out to be difficult to handle. We will present a direct way of constructing the spaces, and show how to prove extension theorems in such spaces. These extension theorems are at the heart of improved error estimates in the $L_p$-norm.
• Computational Mathematics and Applications Seminar