{"title":"Riesz容量：单调性、连续性、直径和体积","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":"{\"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}","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}
Riesz capacity: monotonicity, continuity, diameter and volume
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.
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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.
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