{"title":"An inverse problem for Dirac systems on p-star-shaped graphs","authors":"Yu Ping Wang , Yan-Hsiou Cheng","doi":"10.1016/j.acha.2025.101760","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study direct and inverse problems for Dirac systems with complex-valued potentials on <em>p</em>-star-shaped graphs. More precisely, we firstly obtain sharp 2-term asymptotics of the corresponding eigenvalues. We then formulate and address a Horváth-type theorem, specifically, if the potentials on <span><math><mi>p</mi><mo>−</mo><mn>1</mn></math></span> edges of the <em>p</em>-star-shaped graph are predetermined, we demonstrate that the remaining potential on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>]</mo></math></span> can be uniquely determined by part of its eigenvalues and the given remaining potential on <span><math><mo>[</mo><mi>a</mi><mo>,</mo><mi>π</mi><mo>]</mo></math></span>, <span><math><mn>0</mn><mo><</mo><mi>a</mi><mo>≤</mo><mi>π</mi></math></span>, under certain conditions.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"77 ","pages":"Article 101760"},"PeriodicalIF":2.6000,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520325000144","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study direct and inverse problems for Dirac systems with complex-valued potentials on p-star-shaped graphs. More precisely, we firstly obtain sharp 2-term asymptotics of the corresponding eigenvalues. We then formulate and address a Horváth-type theorem, specifically, if the potentials on edges of the p-star-shaped graph are predetermined, we demonstrate that the remaining potential on can be uniquely determined by part of its eigenvalues and the given remaining potential on , , under certain conditions.
期刊介绍:
Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.