On a new class of positive definite RBFs by using Fourier cosine transform

In this article, we use Fourier cosine transform in order to introduce a new family of infinitely smooth positive definite radial basis functions from completely monotone functions. These bases are represented in terms of positive Borel measures and their Fourier transforms are also given. The proposed theory is used for reconstructing the well-known Matérn RBF and presenting a new positive definite RBF. Numerical results show an accurate reconstruction of the Franke’s function and also mitigating the Runge phenomenon as a key error mechanism.