Extremizers of a Fourier uncertainty principle related to averaging
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912553105358848 |
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| author | Saucedo, Miquel Tikhonov, Sergey |
| author_facet | Saucedo, Miquel Tikhonov, Sergey |
| contents | We study the uncertainty principle
$$\lVert\widehatμ(ξ) |ξ|^β\rVert_\infty^α
\left(\int |x|^αd μ\right)^β \geq C(α,β,d){\lVertμ\rVert_{TV}^{α+β}}$$ for finite non-negative measures on $\mathbb{R}^d $. We prove that $C(α,β,d)>0$ for all $α,β>0$ and that extremizers exist. Moreover, we obtain an abstract characterization of the extremizers, which allows us to describe their asymptotic behavior and, for certain parameter values, to determine them explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremizers of a Fourier uncertainty principle related to averaging Saucedo, Miquel Tikhonov, Sergey Classical Analysis and ODEs 42B10(Primary) 42B35 (Secondary) We study the uncertainty principle $$\lVert\widehatμ(ξ) |ξ|^β\rVert_\infty^α \left(\int |x|^αd μ\right)^β \geq C(α,β,d){\lVertμ\rVert_{TV}^{α+β}}$$ for finite non-negative measures on $\mathbb{R}^d $. We prove that $C(α,β,d)>0$ for all $α,β>0$ and that extremizers exist. Moreover, we obtain an abstract characterization of the extremizers, which allows us to describe their asymptotic behavior and, for certain parameter values, to determine them explicitly. |
| title | Extremizers of a Fourier uncertainty principle related to averaging |
| topic | Classical Analysis and ODEs 42B10(Primary) 42B35 (Secondary) |
| url | https://arxiv.org/abs/2508.17938 |