Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform

[2608.15126] Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:2608.15126 (math) [Submitted on 15 Aug 2026] Title: Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform Authors: Xingyu Zhao , Longben Wei , Zhiwen Duan View a PDF of the paper titled Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform, by Xingyu Zhao and 2 other authors View PDF HTML (experimental) Abstract: We establish quantitative uniqueness and a fractal uncertainty principle for the Fourier Bessel transform. In arbitrary dimension, we prove a quantitative uniqueness estimate on relatively dense sets for functions whose Fourier Bessel transforms decay according to a quasi-analytic weight. In dimension one, if $X\subset[0,1]$ and $Y\subset[a,a+h^{-1}]$ are$\delta$-regular on the relevant scales, then, for $a\geq a_0h^{-1}$, \[ \operatorname{supp}\mathcal H_\nu f\subset Y \quad\Longrightarrow\quad \|\mathbf 1_Xf\|_{L^2_\nu} \leq Ch^\beta\|f\|_{L^2_\nu}. \] The lack of translation invariance prevents a direct application of the classical Fourier argument. We overcome this by constructing damping functions adapted to translated regular sets and combining Beurling Malliavin multipliers with large-argument Bessel asymptotics and a Bourgain Dyatlov multiscale iteration. Comments: No Comments Subjects: Classical Analysis and ODEs (math.CA) MSC classes: 43A32, 28A80 Cite as: arXiv:2608.15126 [math.CA] (or arXiv:2608.15126v1 [math.CA] for this version) https://doi.org/10.48550/arXiv.2608.15126 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Longben Wei [ view email ] [v1] Sat, 15 Aug 2026 08:58:17 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform, by Xingyu Zhao and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform#611076
• Dynamic Spacetime Fluid Theory (FED 2.5): A Consistent Framework for Fractal Density Networks and Galactic Rotation Curves. Consolidated and Verified Version.#118962
• Some statistical properties of spiral galaxies#639581
• Direct estimation of arbitrary observables of an oscillator#128356
• Physical Observables as Signatures of Projection#694354