SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6412-6441, January 2020.
A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Toward this pursuit we introduce a new eigenvalue problem related to Maxwell's equations that is generated from a comparison of measured scattering data to that of a nonstandard auxiliary scattering problem. This choice of auxiliary problem permits the application of regularity results for Maxwell's equations in order to show that a related interior transmission problem possesses the Fredholm property, which is used to establish that the eigenvalues are discrete. We investigate the properties of this new class of eigenvalues and show that the eigenvalues may be determined from measured scattering data, concluding with a simple demonstration of this result.

中文翻译：

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逆散射理论中的修正电磁传输特征值

SIAM数学分析杂志，第52卷，第6期，第6412-6441页，2020年1月。
反问题最近引起关注的一个问题是对由散射理论产生的特征值问题及其在材料的无损检测中作为目标特征的潜在应用的研究。为此，我们引入了一个新的与麦克斯韦方程有关的特征值问题，该问题是通过将测得的散射数据与非标准辅助散射问题进行比较得出的。辅助问题的这种选择允许对麦克斯韦方程组应用规则性结果，以表明相关的内部传递问题具有Fredholm属性，该属性用于确定特征值是离散的。我们调查了这种新的特征值类别的性质，并表明该特征值可以从测得的散射数据确定，