{"title":"Sierpiński垫片上谐波结构的非简并性","authors":"Konstantinos Tsougkas","doi":"10.4171/JFG/73","DOIUrl":null,"url":null,"abstract":"We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<50. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2016-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/73","citationCount":"3","resultStr":"{\"title\":\"Non-degeneracy of the harmonic structure on Sierpiński gaskets\",\"authors\":\"Konstantinos Tsougkas\",\"doi\":\"10.4171/JFG/73\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<50. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2016-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/JFG/73\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/JFG/73\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fractal Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JFG/73","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Non-degeneracy of the harmonic structure on Sierpiński gaskets
We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<50. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
