Distance Functions for Reproducing Kernel Hilbert Spaces

摘要: Suppose H is a space of functions on X. If Hilbert with reproducing kernel then that structure can be used to build distance We describe some those and their interpretations interrelations. also present computational properties examples. 1. Introduction Summary there an associated set, X;and the elements are realized as X:The define will several these discuss interpretations, interrelations properties. find it particularly interesting ideas interface so many other areas mathematics. Some our computations comments new but details presented here known, although perhaps not well known they might be. One goals in this note bring together place them unified larger picture. The choices specific topics however reflects recent interests authors relevant get little or no mention. model cases for what we hyperbolic pseudohyperbolic unit disk D. recall material next section. In section after introduce definitions, notation, basic spaces kernels. Section 4 function �, show provide it. pair first considered context by Kobayshi which, same �;are closely related. 6 relation between have been introduced distances coming from having Riemannian metric case three quantities disk,