Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets

[2508.06875] Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:2508.06875 (math) [Submitted on 9 Aug 2025 ( v1 ), last revised 11 Apr 2026 (this version, v11)] Title: Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets Authors: Sanguo Zhu View a PDF of the paper titled Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets, by Sanguo Zhu View PDF HTML (experimental) Abstract: Let $E$ be a Lalley-Gatzouras carpet determined by a set of contractive affine mappings $\{f_{ij}\}_{(i,j)\in G}$. We study the asymptotics of quantization error for the self-affine measures $\mu$ on $E$. We prove that the upper and lower quantization coefficient for $\mu$ are both bounded away from zero and infinity in the exact quantization dimension. This significantly generalizes the previous work concerning the quantization for self-affine measures on Bedford-McMullen carpets. The new ingredients lie in the method to bound the quantization error for $\mu$ from below and that to construct auxiliary measures by applying Prohorov's theorem. Subjects: Classical Analysis and ODEs (math.CA) ; Metric Geometry (math.MG) MSC classes: 28A80, 28A75 Cite as: arXiv:2508.06875 [math.CA] (or arXiv:2508.06875v11 [math.CA] for this version) https://doi.org/10.48550/arXiv.2508.06875 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Math. Anal. Appl. 565 (2027) 130956 Related DOI : https://doi.org/10.1016/j.jmaa.2026.130956 Focus to learn more DOI(s) linking to related resources Submission history From: Sanguo Zhu [ view email ] [v1] Sat, 9 Aug 2025 08:12:15 UTC (21 KB) [v2] Sun, 17 Aug 2025 11:28:03 UTC (23 KB) [v3] Tue, 19 Aug 2025 09:58:59 UTC (23 KB) [v4] Thu, 21 Aug 2025 08:20:50 UTC (23 KB) [v5] Mon, 25 Aug 2025 16:25:55 UTC (23 KB) [v6] Tue, 2 Sep 2025 08:09:56 UTC (23 KB) [v7] Sun, 14 Sep 2025 08:54:06 UTC (23 KB) [v8] Mon, 22 Sep 2025 13:14:39 UTC (23 KB) [v9] Wed, 24 Dec 2025 13:00:14 UTC (23 KB) [v10] Fri, 20 Mar 2026 11:21:43 UTC (22 KB) [v11] Sat, 11 Apr 2026 14:16:28 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets, by Sanguo Zhu View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2025-08 Change to browse by: math math.MG 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

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