According to equation (2.14) of the paper "The Uniform Convergence of Thin Plate Spline Interpolation in Two Dimensions" a radial basis function $\phi(\parallel x \parallel)$ has the property
$ \nabla^4 \phi( \parallel x \parallel ) = 8 \pi \delta(x) $
I'd like help proving this statement.
PS: I'm sorry but I'm not sure what are the appropriate tags for this question.