分数阶算子Schrödinger-type的最小速度界

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2025-05-24 DOI:10.1007/s11005-025-01943-y

Atsuhide Ishida

{"title":"分数阶算子Schrödinger-type的最小速度界","authors":"Atsuhide Ishida","doi":"10.1007/s11005-025-01943-y","DOIUrl":null,"url":null,"abstract":"<div><p>It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the Schrödinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01943-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Minimal velocity bound for Schrödinger-type operator with fractional powers\",\"authors\":\"Atsuhide Ishida\",\"doi\":\"10.1007/s11005-025-01943-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the Schrödinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities.</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"115 3\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11005-025-01943-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-025-01943-y\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-025-01943-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

在散射理论中，已知最小速度界在证明波算符的渐近完备性方面起决定性作用。在本研究中，我们证明了分数次方Schrödinger-type算子的最小速度界和其他重要估计。我们假设成对势函数属于广义类，包括长程衰减和库仑型局部奇点。

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

Minimal velocity bound for Schrödinger-type operator with fractional powers

It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the Schrödinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities.

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

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.