{"title":"On the distribution of Born transmission eigenvalues in the complex plane","authors":"Narek Hovsepyan","doi":"10.3233/asy-231868","DOIUrl":null,"url":null,"abstract":"We analyze an approximate interior transmission eigenvalue problem in R d for d = 2 or d = 3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove their discreteness. Moreover, it is shown that there exists a horizontal strip in the complex plane around the real axis, that does not contain any transmission eigenvalues.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"69 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/asy-231868","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze an approximate interior transmission eigenvalue problem in R d for d = 2 or d = 3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove their discreteness. Moreover, it is shown that there exists a horizontal strip in the complex plane around the real axis, that does not contain any transmission eigenvalues.
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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