Improved stability estimates and a characterization of the native space for matrix-valued RBFs

In this paper we derive several new results involving matrix-valued radial basis functions (RBFs). We begin by introducing a class of matrix-valued RBFs which can be used to construct interpolants that are curl-free. Next, we offer a characterization of the native space for divergence-free and curl-free kernels based on the Fourier transform. Finally, we investigate the stability of the interpolation matrix for both the divergence-free and curl-free cases, and when the kernel has finite smoothness we obtain sharp estimates.