A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the electromagnetic Stekloff eigenvalue problem that depends upon a smoothing parameter, for which we establish two main results that were previously unavailable for this type of eigenvalue problem. First, we use the theory of trace class operators to prove that infinitely many eigenvalues exist for a sufficiently high degree of smoothing, even for an absorbing medium. Second, we leverage regularity results for Maxwell's equations in order to establish stability results for the eigenvalues with respect to the material coefficients, and we show that this generalized class of Stekloff eigenvalues converges to the standard class as the smoothing parameter approaches zero.

中文翻译：

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具有迹线类修改的Stekloff电磁特征值的存在性和稳定性

最近的一个感兴趣的领域是散射理论中出现的本征值问题的发展和研究，这些问题可能会为材料的无损检测提供潜在的目标特征。我们考虑了依赖于平滑参数的电磁Stekloff特征值问题的推广，为此，我们建立了两个主要结果，这些结果以前对于这种类型的特征值问题是不可用的。首先，我们使用跟踪类算子的理论来证明，即使对于吸收性介质，也存在无限多个特征值，以实现足够高的平滑度。其次，我们利用Maxwell方程的正则结果来建立关于材料系数的特征值的稳定性结果，