{"title":"一个没有自相似能的p.c.f.自相似集","authors":"Roberto Peirone","doi":"10.4171/jfg/82","DOIUrl":null,"url":null,"abstract":"A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2017-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/jfg/82","citationCount":"3","resultStr":"{\"title\":\"A p.c.f. self-similar set with no self-similar energy\",\"authors\":\"Roberto Peirone\",\"doi\":\"10.4171/jfg/82\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2017-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/jfg/82\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jfg/82\",\"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/82","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A p.c.f. self-similar set with no self-similar energy
A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
