Investigation of the spectrum of the problem of normal waves in a closed regular inhomogeneous dielectric waveguide of arbitrary cross section
The paper under review is concerned with the mathematical analysis of the problem of normal waves in a closed regular wave-guide of arbitrary cross section. This study is performed by reducing the problem to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. In such a way, the problem of normal waves is reduced to the study of an operator function. The analysis developed in this paper is based on variational arguments. The spectral properties of the associated operators are also examined, and the completeness of the system of eigenvectors of the operator function is investigated.
scientific article; zbMATH DE number 6892232