半格上Jacobi算子的反共振问题

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI:10.1134/S1061920823030056

E. Korotyaev, E. Leonova

{"title":"半格上Jacobi算子的反共振问题","authors":"E. Korotyaev, E. Leonova","doi":"10.1134/S1061920823030056","DOIUrl":null,"url":null,"abstract":"<p> We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real and complex resonances. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"320 - 344"},"PeriodicalIF":1.7000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverse Resonance Problem for Jacobi Operators on a Half-Lattice\",\"authors\":\"E. Korotyaev, E. Leonova\",\"doi\":\"10.1134/S1061920823030056\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real and complex resonances. </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 3\",\"pages\":\"320 - 344\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823030056\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823030056","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

我们解决了具有有限支持扰动的半晶格上Jacobi算子的逆问题，特别是在共振方面。我们的证明是基于特定有限雅可比矩阵的特征值反问题的结果和多项式理论。我们确定了共振的禁域以及实共振和复共振的最大可能复数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Inverse Resonance Problem for Jacobi Operators on a Half-Lattice

查看原文本刊更多论文

Inverse Resonance Problem for Jacobi Operators on a Half-Lattice

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real and complex resonances.

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

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.