A note on functions preserving positive definiteness
arXiv:1912.04340
Abstract
The aim of the paper is to give a full characterization of functions f from I into the real line R (where I is an interval in R that satisfies certain natural conditions) such that for any I-valued positive definite kernel K defined on an arbitrary set X the kernel formed by composing f with K is positive definite as well.
All results of that paper are already known - they were obtained in the 1950's e.g. by Rudin