on the positive definite rbfs by using integral transforms

In this paper, we construct new positive definite radial basis functions (rbfs) by using integral transforms with non-negative densities and completely monotone integral kernels. in order to show the efficiency of the proposed basis, we interpolate the runge function and a function with jump discontinuities with a new positive definite rbf obtained from the laplacetransform of the pulse function. numerical experiments reveal that the proposed rbf not only gives very accurate results but also it does not suffer of the runge and gibbs phenomena.