Functions positively associated with integral transforms
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915361955250176 |
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| author | Koldobsky, Alexander |
| author_facet | Koldobsky, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functions positively associated with integral transforms Koldobsky, Alexander Functional Analysis Metric Geometry 44A15, 52A20 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. |
| title | Functions positively associated with integral transforms |
| topic | Functional Analysis Metric Geometry 44A15, 52A20 |
| url | https://arxiv.org/abs/2503.23310 |