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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.02803 |
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| _version_ | 1866913975000629248 |
|---|---|
| author | Jaech, Aaron Joseph, Alan |
| author_facet | Jaech, Aaron Joseph, Alan |
| contents | We construct a nonnegative step function comprising 2,399 equally spaced intervals such that \[
\frac{\|f * f\|_{L^{2}(\mathbb{R})}^{2}}{\|f * f\|_{L^{\infty}(\mathbb{R})}\,\|f * f\|_{L^{1}(\mathbb{R})}}
\;\ge\;
.926529. \] Using a 4x upsampling procedure on this 559-interval optimizer, we further increase the bound to $.94136$, closing roughly 40\% of the gap between the previous best bound (.901562 on 575 intervals) and the trivial upper limit of 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further Improvements to the Lower Bound for an Autoconvolution Inequality Jaech, Aaron Joseph, Alan Classical Analysis and ODEs We construct a nonnegative step function comprising 2,399 equally spaced intervals such that \[ \frac{\|f * f\|_{L^{2}(\mathbb{R})}^{2}}{\|f * f\|_{L^{\infty}(\mathbb{R})}\,\|f * f\|_{L^{1}(\mathbb{R})}} \;\ge\; .926529. \] Using a 4x upsampling procedure on this 559-interval optimizer, we further increase the bound to $.94136$, closing roughly 40\% of the gap between the previous best bound (.901562 on 575 intervals) and the trivial upper limit of 1. |
| title | Further Improvements to the Lower Bound for an Autoconvolution Inequality |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.02803 |