二维辐射解的虚部重构

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI:10.1134/S1061920825601077

A.V. Nair, R.G. Novikov

{"title":"二维辐射解的虚部重构","authors":"A.V. Nair, R.G. Novikov","doi":"10.1134/S1061920825601077","DOIUrl":null,"url":null,"abstract":" We consider a radiation solution \\(\\psi\\) for the Helmholtz equation in an exterior domain in \\(\\mathbb{R}^2\\). We show that \\(\\psi\\) in the exterior domain is uniquely determined by its imaginary part \\(\\operatorname{Im}(\\psi)\\) on an interval of a line \\(L\\) lying in the exterior domain. This result has a holographic prototype in the recent paper by Nair and Novikov (2025, J. Geom. Anal. 35, 4, 123). Some other curves for measurements, instead of the lines \\(L\\), are also considered. Applications to the Gelfand–Krein–Levitan inverse problem (from boundary values of the spectral measure in \\(\\mathbb{R}^2\\)) and to passive imaging are also indicated. DOI 10.1134/S1061920825601077 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"554 - 561"},"PeriodicalIF":1.5000,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Reconstruction from the Imaginary Part for Radiation Solutions in Two Dimensions\",\"authors\":\"A.V. Nair, R.G. Novikov\",\"doi\":\"10.1134/S1061920825601077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We consider a radiation solution \\\\(\\\\psi\\\\) for the Helmholtz equation in an exterior domain in \\\\(\\\\mathbb{R}^2\\\\). We show that \\\\(\\\\psi\\\\) in the exterior domain is uniquely determined by its imaginary part \\\\(\\\\operatorname{Im}(\\\\psi)\\\\) on an interval of a line \\\\(L\\\\) lying in the exterior domain. This result has a holographic prototype in the recent paper by Nair and Novikov (2025, J. Geom. Anal. 35, 4, 123). Some other curves for measurements, instead of the lines \\\\(L\\\\), are also considered. Applications to the Gelfand–Krein–Levitan inverse problem (from boundary values of the spectral measure in \\\\(\\\\mathbb{R}^2\\\\)) and to passive imaging are also indicated. DOI 10.1134/S1061920825601077 \",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"32 3\",\"pages\":\"554 - 561\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2025-09-29\",\"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/S1061920825601077\",\"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/S1061920825601077","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

我们考虑了\(\mathbb{R}^2\)外域亥姆霍兹方程的辐射解\(\psi\)。我们证明了外域的\(\psi\)是由其虚部\(\operatorname{Im}(\psi)\)在位于外域的直线\(L\)的区间上唯一确定的。这一结果在Nair和Novikov （2025， J. Geom）最近的论文中有一个全息原型。肛门。35,4,123)。还考虑了一些其他的测量曲线，而不是\(L\)线。应用于Gelfand-Krein-Levitan反问题（从光谱测量的边界值在\(\mathbb{R}^2\)）和被动成像也指出。Doi 10.1134/ s1061920825601077

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

On the Reconstruction from the Imaginary Part for Radiation Solutions in Two Dimensions

We consider a radiation solution \(\psi\) for the Helmholtz equation in an exterior domain in \(\mathbb{R}^2\). We show that \(\psi\) in the exterior domain is uniquely determined by its imaginary part \(\operatorname{Im}(\psi)\) on an interval of a line \(L\) lying in the exterior domain. This result has a holographic prototype in the recent paper by Nair and Novikov (2025, J. Geom. Anal. 35, 4, 123). Some other curves for measurements, instead of the lines \(L\), are also considered. Applications to the Gelfand–Krein–Levitan inverse problem (from boundary values of the spectral measure in \(\mathbb{R}^2\)) and to passive imaging are also indicated.

DOI 10.1134/S1061920825601077

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.