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arXiv · 2503.23310

Functions positively associated with integral transforms

Alexander Koldobsky
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Abstract

We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the $q$-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.

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Alexander Koldobsky. 2025-03-30. Functions positively associated with integral transforms. https://arxiv.org/abs/2503.23310

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