An explicit construction of a reproducing Gaussian kernel Hilbert space

In this paper, we propose a method to explicitly construct a reproducing kernel Hilbert space (RKHS) associated with a Gaussian kernel by means of polynomial spaces. In contrast to the conventional Mercer's theorem approach that implicitly defines kernels by an eigendecomposition, the functionals in this reproducing kernel Hilbert space are explicitly constructed and are not necessary orthonormal. We also point out an intriguing connection between this reproducing kernel Hilbert space and a generalized Fock space. We give an experimental result on approximation of the constructed kernel to a Gaussian kernel.