{"title":"具有右端点局部平滑矩形势的狄拉克型系统的局部博格-马尔钦科唯一性定理","authors":"Tiezheng Li, Guangsheng Wei","doi":"10.1007/s43034-024-00333-0","DOIUrl":null,"url":null,"abstract":"<div><p>We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, <i>b</i>), where <span>\\(0<b\\le \\infty .\\)</span> We present a new proof of the local Borg–Marchenko uniqueness theorem. The high-energy asymptotics of the Weyl–Titchmarsh functions and the local Borg–Marchenko uniqueness theorem are derived for locally smooth potentials at the right endpoint.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The local Borg–Marchenko uniqueness theorem for Dirac-type systems with locally smooth at the right endpoint rectangular potentials\",\"authors\":\"Tiezheng Li, Guangsheng Wei\",\"doi\":\"10.1007/s43034-024-00333-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, <i>b</i>), where <span>\\\\(0<b\\\\le \\\\infty .\\\\)</span> We present a new proof of the local Borg–Marchenko uniqueness theorem. The high-energy asymptotics of the Weyl–Titchmarsh functions and the local Borg–Marchenko uniqueness theorem are derived for locally smooth potentials at the right endpoint.</p></div>\",\"PeriodicalId\":48858,\"journal\":{\"name\":\"Annals of Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43034-024-00333-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-024-00333-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑在区间 [0, b) 上具有矩形矩阵势的自联合狄拉克型系统，其中 \(0<b\le \infty .\) 我们提出了局部博格-马尔琴科唯一性定理的新证明。对于右端点的局部平滑势，我们导出了韦尔-蒂奇马什函数的高能渐近线和局部博格-马尔琴科唯一性定理。
The local Borg–Marchenko uniqueness theorem for Dirac-type systems with locally smooth at the right endpoint rectangular potentials
We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, b), where \(0<b\le \infty .\) We present a new proof of the local Borg–Marchenko uniqueness theorem. The high-energy asymptotics of the Weyl–Titchmarsh functions and the local Borg–Marchenko uniqueness theorem are derived for locally smooth potentials at the right endpoint.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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