{"title":"均匀多项式曲面集上 Fekete 点的收敛速度","authors":"Hyunsoo Ahn, Ngoc Cuong Nguyen","doi":"arxiv-2408.03053","DOIUrl":null,"url":null,"abstract":"We obtain the convergence speed for Fekete points on uniformly polynomially\ncuspidal compact sets introduced by Pawlucki and Ple\\'sniak. This is done by\nshowing that these sets are $(\\mathscr{C}^{\\alpha},\n\\mathscr{C}^{\\alpha'})$-regular in the sense of Dinh, Ma and Nguyen.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"55 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence Speed for Fekete Points on Uniformly Polynomially Cuspidal Sets\",\"authors\":\"Hyunsoo Ahn, Ngoc Cuong Nguyen\",\"doi\":\"arxiv-2408.03053\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain the convergence speed for Fekete points on uniformly polynomially\\ncuspidal compact sets introduced by Pawlucki and Ple\\\\'sniak. This is done by\\nshowing that these sets are $(\\\\mathscr{C}^{\\\\alpha},\\n\\\\mathscr{C}^{\\\\alpha'})$-regular in the sense of Dinh, Ma and Nguyen.\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":\"55 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03053\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03053","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们得到了 Pawlucki 和 Ple\'sniak 引入的均匀多项式cuspidal 紧凑集上的 Fekete 点的收敛速度。这是通过证明这些集合在丁（Dinh）、马（Ma）和阮（Nguyen）的意义上是$(\mathscr{C}^{\alpha},\mathscr{C}^{\alpha'})$正则集合来实现的。
Convergence Speed for Fekete Points on Uniformly Polynomially Cuspidal Sets
We obtain the convergence speed for Fekete points on uniformly polynomially
cuspidal compact sets introduced by Pawlucki and Ple\'sniak. This is done by
showing that these sets are $(\mathscr{C}^{\alpha},
\mathscr{C}^{\alpha'})$-regular in the sense of Dinh, Ma and Nguyen.
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