Forthcoming events in this series
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.