positive definite kernels and reproducing kernel hilbert spaces

In this paper, we give aspects of positive definite functions with their respective reproducing kernel hilbert spaces and applications. the following dissertation helps to understand reproducing kernel hilbert spaces and their boundary spaces. we provide a characterization of kernel functions and reproducing kernel, derive their properties, and discuss methods for designing them. given a kernel and a training set, we can form the matrix known as the kernel, or gram matrix: the matrix containing the evaluation of the kernel function on all pairs of data points.