多项式∞的有界连通分量

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-09-30 DOI:10.1007/s13324-024-00969-0

Adam Kraus, Brian Simanek

{"title":"多项式∞的有界连通分量","authors":"Adam Kraus, Brian Simanek","doi":"10.1007/s13324-024-00969-0","DOIUrl":null,"url":null,"abstract":"<div><p>We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of <span>\\(\\bar{z}\\)</span> to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.\n</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 5","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounded connected components of polynomial lemniscates\",\"authors\":\"Adam Kraus, Brian Simanek\",\"doi\":\"10.1007/s13324-024-00969-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of <span>\\\\(\\\\bar{z}\\\\)</span> to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.\\n</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"14 5\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-09-30\",\"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/s13324-024-00969-0\",\"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/s13324-024-00969-0","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

摘要

我们考虑复平面上的多项式∞族，并确定它们是否约束了一个约旦域。这样，我们就能找到一些区域的例子，从而计算出这些区域的 \(\bar{z}\) 对有界区域的伯格曼空间的投影。这些知识可以应用于扭转刚性的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Bounded connected components of polynomial lemniscates

We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of \(\bar{z}\) to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

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.