The Scaled Polarity transform and related inequalities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909711871246336 |
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| author | Gilboa, Shoni Segal, Alexander Slomka, Boaz A. |
| author_facet | Gilboa, Shoni Segal, Alexander Slomka, Boaz A. |
| contents | In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform $\mathcal A$ can be rescaled so that the Mahler product it induces has upper and lower bounds of the same asymptotics. We discuss a similar result for the $\mathcal J$ transform.
As an application, we extend the König-Milman duality of entropy result to the class of geometric log-concave functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Scaled Polarity transform and related inequalities Gilboa, Shoni Segal, Alexander Slomka, Boaz A. Functional Analysis 52A41, 26A51, 46B10 In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform $\mathcal A$ can be rescaled so that the Mahler product it induces has upper and lower bounds of the same asymptotics. We discuss a similar result for the $\mathcal J$ transform. As an application, we extend the König-Milman duality of entropy result to the class of geometric log-concave functions. |
| title | The Scaled Polarity transform and related inequalities |
| topic | Functional Analysis 52A41, 26A51, 46B10 |
| url | https://arxiv.org/abs/2502.11524 |