二阶块算子矩阵的谱浓度和共振及相关的λ有理Sturm-Liouville问题

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI:10.1098/rspa.2003.1272

B. M. Brown, M. Langer, M. Marletta

{"title":"二阶块算子矩阵的谱浓度和共振及相关的λ有理Sturm-Liouville问题","authors":"B. M. Brown, M. Langer, M. Marletta","doi":"10.1098/rspa.2003.1272","DOIUrl":null,"url":null,"abstract":"This paper studies the resonances and points of spectral concentration of the block operator matrix ( − d2 d x 2 +q tw tw ) in the space L2(0,1)⊕L2(0,1). In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Spectral concentrations and resonances of a second–order block operator matrix and an associated λ–rational Sturm-Liouville problem\",\"authors\":\"B. M. Brown, M. Langer, M. Marletta\",\"doi\":\"10.1098/rspa.2003.1272\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the resonances and points of spectral concentration of the block operator matrix ( − d2 d x 2 +q tw tw ) in the space L2(0,1)⊕L2(0,1). In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.\",\"PeriodicalId\":20722,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.2003.1272\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.2003.1272","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

本文研究了L2(0,1)⊕L2(0,1)空间中块算子矩阵(- d2 d x 2 +q tw tw)的谱集中共振点和谱集中点。特别地，我们研究了共振/特征值λ(t)的动力学，表明嵌入的特征值可以演变成共振，并且被本质谱吸收的特征值产生共振点。在共振和谱集中点之间也建立了联系。最后给出了一些数值算例，表明上述每种理论可能性都是可以实现的。

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

Spectral concentrations and resonances of a second–order block operator matrix and an associated λ–rational Sturm-Liouville problem

This paper studies the resonances and points of spectral concentration of the block operator matrix ( − d2 d x 2 +q tw tw ) in the space L2(0,1)⊕L2(0,1). In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.

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

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

自引率

0.00%

发文量

期刊介绍： Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.