Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Saucedo, Miquel, Tikhonov, Sergey
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077974985
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