Polyharmonic to you maybe

I don't want to be nitpicking, but to me polyharmonic really means that after the application of the Laplacian a certain number of times, the function is zero. In here it just means that after a certain number of iteration of the laplacian, one is left with a bunch of diracs at every nodes of the spline. That's not nearly enough of a zero to me, but who am I to say this.....not a mathematician apparently.