Positive definiteness‎, ‎reproducing kernel Hilbert spaces and beyond

Abstract

Positive definiteness‎, ‎reproducing kernel Hilbert spaces‎, ‎integral operators and Mercer's‎ ‎theorem in its various formats are common topics in many branches of‎ ‎mathematics. In this paper we review and upgrade upon some recent‎ ‎results that always involve at least two of them and indicate a few‎ ‎directions in which additional research could be carried out‎.