Sturm-Liouville微分算子积的自伴随扩展的定义域

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI:10.1155/S0161171203008020

S. Ibrahim

{"title":"Sturm-Liouville微分算子积的自伴随扩展的定义域","authors":"S. Ibrahim","doi":"10.1155/S0161171203008020","DOIUrl":null,"url":null,"abstract":"The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"695-709"},"PeriodicalIF":1.0000,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203008020","citationCount":"1","resultStr":"{\"title\":\"On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators\",\"authors\":\"S. Ibrahim\",\"doi\":\"10.1155/S0161171203008020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).\",\"PeriodicalId\":39893,\"journal\":{\"name\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":\"2003 1\",\"pages\":\"695-709\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2003-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/S0161171203008020\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/S0161171203008020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/S0161171203008020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在区间I = (a, b)，−∞≤a, b≤∞上考虑二阶对称Sturm-Liouville微分表达式τ 1， τ 2，…，τ n具有实数系数。证明了奇异自伴随边界条件的刻划涉及Sturm-Liouville微分表达式与乘积算子的极大域元素的乘积的半线性形式，并且是正则情况的精确平行。这一特征是Everitt和Zettl(1977)、Hinton、Krall和Shaw(1987)、Ibrahim(1999)、Krall和Zettl(1988)、Lee(1975/1976)和Naimark(1968)所得到的特征的延伸。

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

On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators

The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).

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

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.