  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.
