Radial kernels via scale derivatives

We generate various new radial kernels by taking derivatives of known kernels with respect to scale. This is different from the well-known scale mixtures used before. In addition, we provide a simple recipe that explicitly constructs new kernels from the negative Laplacian of known kernels. Surprisingly, these two methods for generating new kernels can be proven to coincide for certain standard classes of radial kernels. The resulting radial kernels are positive definite, and a few illustrations are provided.