势理论中经典核函数汉克尔矩阵的计算

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Korean Mathematical Society Pub Date : 2020-07-01 DOI:10.4134/JKMS.J190487

Young-Bok Chung

{"title":"势理论中经典核函数汉克尔矩阵的计算","authors":"Young-Bok Chung","doi":"10.4134/JKMS.J190487","DOIUrl":null,"url":null,"abstract":"In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"973-986"},"PeriodicalIF":0.7000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computation of Hankel matrices in terms of classical kernel functions in potential theory\",\"authors\":\"Young-Bok Chung\",\"doi\":\"10.4134/JKMS.J190487\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.\",\"PeriodicalId\":49993,\"journal\":{\"name\":\"Journal of the Korean Mathematical Society\",\"volume\":\"57 1\",\"pages\":\"973-986\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J190487\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J190487","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文计算了一般有界域的Hardy空间上Hankel算子关于Hardy空间及其正交补的特殊正交基的Hankel矩阵表示。此外，我们还得到了单位圆盘情形下Hankel矩阵关于这些基的紧致形式。可以看出，由该计算生成的Hankel矩阵是单位圆盘从单个单连通域到具有大量基的多重连通域的情况的推广。

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

Computation of Hankel matrices in terms of classical kernel functions in potential theory

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

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

Journal of the Korean Mathematical Society 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).