Investigation of the spectrum of the problem of normal waves in a closed regular inhomogeneous dielectric waveguide of arbitrary cross section
type: Item
instance of: scholarly article
title: Investigation of the spectrum of the problem of normal waves in a closed regular inhomogeneous dielectric waveguide of arbitrary cross section
zbMATH Open document ID: 1397.78043
DOI: 10.1134/S1064562418010271
published in: Doklady Mathematics
publication date: 2018-06-20T00:00:00Z
review text: 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.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 78A50
Mathematics Subject Classification ID: 78A40
Mathematics Subject Classification ID: 35P10
Mathematics Subject Classification ID: 78M30
zbMATH DE Number: 6892232
zbMATH Keywords: normal wave
zbMATH Keywords: dielectric wave-guide
zbMATH Keywords: electromagnetic field
author: Yu G. Smirnov
author: E. Yu. Smol'kin
MaRDI profile type: Publication
cites work: The statement and solubility of boundary-value problems for Maxwell's equations in a cylinder
cites work: Boundary Integral Operators on Lipschitz Domains: Elementary Results
cites work: Q5526485
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cites work: Completeness of root vectors of a Keldysh pencil perturbed by an analytic operator-valued function \(s(\lambda)\) with \(S(\infty)=0\)
full work available at URL: s1064562418010271
OpenAlex ID: W2790904472
Wikidata QID: Q130120308
description: scientific article; zbMATH DE number 6892232