{"title":"四阶微分算子的McLaughlin反问题","authors":"N.P. Bondarenko","doi":"10.1134/S1061920824040022","DOIUrl":null,"url":null,"abstract":"<p> In this paper, we revisit McLaughlin’s inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of norming constants. We prove the uniqueness for solution of this problem for the first time. Moreover, we obtain an interpretation of McLaughlin’s problem in the framework of the general inverse problem theory by Yurko for differential operators of arbitrary orders. An advantage of our approach is that it requires neither the smoothness of the coefficients nor the self-adjointness of the operator. In addition, we establish the connection between McLaughlin’s problem and Barcilon’s three-spectra inverse problem. </p><p> <b> DOI</b> 10.1134/S1061920824040022 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"587 - 605"},"PeriodicalIF":1.5000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"McLaughlin’s Inverse Problem for the Fourth-Order Differential Operator\",\"authors\":\"N.P. Bondarenko\",\"doi\":\"10.1134/S1061920824040022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> In this paper, we revisit McLaughlin’s inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of norming constants. We prove the uniqueness for solution of this problem for the first time. Moreover, we obtain an interpretation of McLaughlin’s problem in the framework of the general inverse problem theory by Yurko for differential operators of arbitrary orders. An advantage of our approach is that it requires neither the smoothness of the coefficients nor the self-adjointness of the operator. In addition, we establish the connection between McLaughlin’s problem and Barcilon’s three-spectra inverse problem. </p><p> <b> DOI</b> 10.1134/S1061920824040022 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"31 4\",\"pages\":\"587 - 605\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2025-02-09\",\"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/S1061920824040022\",\"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/S1061920824040022","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}
McLaughlin’s Inverse Problem for the Fourth-Order Differential Operator
In this paper, we revisit McLaughlin’s inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of norming constants. We prove the uniqueness for solution of this problem for the first time. Moreover, we obtain an interpretation of McLaughlin’s problem in the framework of the general inverse problem theory by Yurko for differential operators of arbitrary orders. An advantage of our approach is that it requires neither the smoothness of the coefficients nor the self-adjointness of the operator. In addition, we establish the connection between McLaughlin’s problem and Barcilon’s three-spectra inverse problem.
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.
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