On maximal intersection position for logarithmically concave functions and measures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908379219230720 |
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| author | Hoehner, Steven Roysdon, Michael |
| author_facet | Hoehner, Steven Roysdon, Michael |
| contents | A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) and Artstein-Avidan and Putterman (2022). Our main result is a John-type theorem for the maximal intersection position of a pair of log-concave functions, including the corresponding decomposition of the identity. The main result holds under very weak assumptions on the functions; in particular, the functions considered may both have unbounded supports. As an application of our results, we introduce a John-type position for even $\log$-concave measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On maximal intersection position for logarithmically concave functions and measures Hoehner, Steven Roysdon, Michael Functional Analysis 46N10, 52A39, 52A40, 60E05 (Primary) 28A75 (Secondary) A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) and Artstein-Avidan and Putterman (2022). Our main result is a John-type theorem for the maximal intersection position of a pair of log-concave functions, including the corresponding decomposition of the identity. The main result holds under very weak assumptions on the functions; in particular, the functions considered may both have unbounded supports. As an application of our results, we introduce a John-type position for even $\log$-concave measures. |
| title | On maximal intersection position for logarithmically concave functions and measures |
| topic | Functional Analysis 46N10, 52A39, 52A40, 60E05 (Primary) 28A75 (Secondary) |
| url | https://arxiv.org/abs/2401.01033 |