Gaussian RBF-kernels via Fock spaces: quaternionic and several complex variables settings

In this paper we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternonic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.