{"title":"The high-order estimate of the entire function associated with inverse Sturm–Liouville problems","authors":"Zhaoying Wei, Guangsheng Wei, Yan Wang","doi":"10.1515/jiip-2023-0082","DOIUrl":null,"url":null,"abstract":"The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math. Phys. 50 2009, 3, Article ID 033505] remains true for more general case.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"21 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inverse and Ill-Posed Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jiip-2023-0082","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math. Phys. 50 2009, 3, Article ID 033505] remains true for more general case.
研究了具有平滑势的反 Sturm-Liouville 问题。建立了与两个 Sturm-Liouville 问题相关的全函数的高阶估计。将这一估算表达式应用于反 Sturm-Liouville 问题，我们证明了 [L. Amour, J. Faupin and T.Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math.50 2009, 3, Article ID 033505] 中的结论对于更一般的情况仍然适用。
期刊介绍：
This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.
Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest.
The following topics are covered:
Inverse problems
existence and uniqueness theorems
stability estimates
optimization and identification problems
numerical methods
Ill-posed problems
regularization theory
operator equations
integral geometry
Applications
inverse problems in geophysics, electrodynamics and acoustics
inverse problems in ecology
inverse and ill-posed problems in medicine
mathematical problems of tomography
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