Positivity and Green's operators

TL;DR

This paper explores the extent to which positive Green's operators deviate from being positivity preserving and identifies a broad class of operators with related positivity properties.

Contribution

It characterizes the gap between positivity and positivity preservation in Green's operators and introduces a class with related positivity features.

Findings

Positive Green's operators are not always positivity preserving

A broad class of Green's operators with positivity-related properties is identified

The paper clarifies the relationship between positivity and positivity preservation

Abstract

It is well known that positive Green's operators are not necessarily positivity preserving. In this paper we investigate the matter of just how far from being positivity preserving a positive Green's operator can be. We will also identify a broad class of Green's operators that are not necessarily positivity preserving but have properties related to positivity preservation that one expects from positivity preserving Green's operators.