对称算子I的扩展:内特征函数情况

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2014-03-18 DOI:10.1515/conop-2015-0004
R.T.W. Martin
{"title":"对称算子I的扩展:内特征函数情况","authors":"R.T.W. Martin","doi":"10.1515/conop-2015-0004","DOIUrl":null,"url":null,"abstract":"Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"2 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2014-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2015-0004","citationCount":"6","resultStr":"{\"title\":\"Extensions of symmetric operators I: The inner characteristic function case\",\"authors\":\"R.T.W. Martin\",\"doi\":\"10.1515/conop-2015-0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.\",\"PeriodicalId\":53800,\"journal\":{\"name\":\"Concrete Operators\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2014-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/conop-2015-0004\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Concrete Operators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/conop-2015-0004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2015-0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 6

摘要

给定Hilbert空间上的一个对称线性变换,一个自然要考虑的问题是它的对称扩展集的刻画。这个问题等价于研究固定偏等距的偏等距扩展。通过构造该集合的商与大于或等于θB的所有压缩解析函数φ的集合之间的一个双射,给出了具有有限等指标的对称线性变换B的所有自伴随扩展集和内部Livšic特征函数θB的一个新的函数论刻划。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Extensions of symmetric operators I: The inner characteristic function case
Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
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
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
On the compactness and the essential norm of operators defined by infinite tridiagonal matrices m-Isometric tensor products Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains Generalized Crofoot transform and applications Generalized Hausdorff operator on Bergmann spaces
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1