Reproducing kernels and choices of associated feature spaces, in the form of $L^2$-spaces

Abstract

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in the form $L^2\left(\mu \right)$; and we study the question of which measures $\mu$ are right for a particular kernel $K$. The answer to this depends on the particular application at hand. Such applications are the focus of the separate sections in the paper.

References in corpus (1)

• Moving Parseval frames for vector bundles