{"title":"Riesz capacity: monotonicity, continuity, diameter and volume","authors":"Carrie Clark, Richard S. Laugesen","doi":"10.1007/s13324-024-01000-2","DOIUrl":null,"url":null,"abstract":"<div><p>Properties of Riesz capacity are developed with respect to the kernel exponent <span>\\(p \\in (-\\infty ,n)\\)</span>, namely that capacity is strictly monotonic as a function of <i>p</i>, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to <i>p</i> and is right-continuous provided (when <span>\\(p \\ge 0\\)</span>) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-01000-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Properties of Riesz capacity are developed with respect to the kernel exponent \(p \in (-\infty ,n)\), namely that capacity is strictly monotonic as a function of p, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to p and is right-continuous provided (when \(p \ge 0\)) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
