Complete nonselfadjointness for Schrödinger operators on the semi-axis

IF 0.7 4区 数学 Q2 MATHEMATICS St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1802
C. Fischbacher, S. Naboko, I. Wood
{"title":"Complete nonselfadjointness for Schrödinger operators on the semi-axis","authors":"C. Fischbacher, S. Naboko, I. Wood","doi":"10.1090/spmj/1802","DOIUrl":null,"url":null,"abstract":"<p>This note is devoted to the study of complete nonselfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. It is shown that all maximally dissipative extensions that preserve the differential expression are completely nonselfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. A characterization of these extensions and the corresponding subspaces is given, accompanied by a specific example.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"135 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1802","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

Abstract

This note is devoted to the study of complete nonselfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. It is shown that all maximally dissipative extensions that preserve the differential expression are completely nonselfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. A characterization of these extensions and the corresponding subspaces is given, accompanied by a specific example.

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
半轴上薛定谔算子的完全非自相接性
本论文主要研究具有耗散约束势和耗散边界条件的半线上薛定谔算子的所有最大耗散扩展的完全非自相接性。研究表明,所有保留微分表达式的最大耗散扩展都是完全非自相接的。然而,最大耗散扩展有可能具有一维还原子空间,在该空间上的算子是自交的。本文给出了这些扩展和相应子空间的特征,并附有一个具体的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
审稿时长
>12 weeks
期刊介绍: This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
期刊最新文献
Shape, velocity, and exact controllability for the wave equation on a graph with cycle On Kitaev’s determinant formula Resolvent stochastic processes Complete nonselfadjointness for Schrödinger operators on the semi-axis Behavior of large eigenvalues for the two-photon asymmetric quantum Rabi model
×
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