Error bounds for multiquadrics without added constants

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x)=∑λjϕ(‖x−xj‖) exist uniquely for the multiquadric radial function ϕ(r)=r2+c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we obtain error bounds that no longer require this additional constant expression.