论文标题
反散射理论中的经过的电磁透射特征值
Modified electromagnetic transmission eigenvalues in inverse scattering theory
论文作者
论文摘要
最近对反问题感兴趣的问题是研究了散射理论及其作为材料无损测试目标特征的特征值问题。为了进行这种追求，我们引入了与麦克斯韦方程相关的新特征值问题，该问题是从测量的散射数据与非标准辅助散射问题的比较产生的。这种选择辅助问题允许在麦克斯韦方程中应用规律性结果，以表明相关的内部传输问题具有弗雷德霍尔姆属性，该属性用于确定特征值是离散的。我们研究了这一新的特征值的特性，并表明特征值可以通过测量的散射数据确定，并以简单的证明这一事实结论。
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. Towards 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 non-standard 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 fact.
