Normal Extensions of Differential Operators for Degenerate First-order

IF 0.8 Q2 MATHEMATICS
M. Sertbaş, F. Yılmaz
{"title":"Normal Extensions of Differential Operators for Degenerate First-order","authors":"M. Sertbaş, F. Yılmaz","doi":"10.1134/s1995080224600882","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space <span>\\(L_{2}(H,(a,b)),\\,a,b\\in\\mathbb{R}\\)</span> to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600882","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space \(L_{2}(H,(a,b)),\,a,b\in\mathbb{R}\) to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.

畸变一阶微分算子的正态扩展
摘要 本文研究了在希尔伯特空间 \(L_{2}(H,(a,b)),\,a,b\in\mathbb{R}\)中由退化一阶微分算子表达式定义的极小算子形式上正则的必要条件和充分条件。同时,最小算子的所有正则扩展都给出了它们的域。此外,通过演化算子族给出了这些常扩展的谱集。
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 求助全文
来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信