A note on functions preserving positive definiteness
Functional Analysis
2020-01-13 v2
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.
Cite
@article{arxiv.1912.04340,
title = {A note on functions preserving positive definiteness},
author = {Piotr Niemiec},
journal= {arXiv preprint arXiv:1912.04340},
year = {2020}
}
Comments
All results of that paper are already known - they were obtained in the 1950's e.g. by Rudin