Functions positively associated with integral transforms
Functional Analysis
2025-06-30 v2 Metric Geometry
Abstract
We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the -cosine transform and the spherical Radon transform. We show that positively associated functions control the comparison problem for linear operators generalizing the Busemann-Petty problem for convex bodies.
Cite
@article{arxiv.2503.23310,
title = {Functions positively associated with integral transforms},
author = {Alexander Koldobsky},
journal= {arXiv preprint arXiv:2503.23310},
year = {2025}
}
Comments
This is an expanded version of the paper