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Eigenwaves in waveguides with dielectric inclusions: completeness
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0002-2691-2820
Penza State Univ, Dept Math & Supercomp, Penza 440017, Russia..ORCID iD: 0000-0001-9040-628X
2014 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, 1824-1845 p.Article in journal (Refereed) PublishedText
Abstract [en]

We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then, we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the mnimality' of this system and show that this system is generally not a Schauder basis. This work is a continuation of the paper Eigenwaves in waveguides with dielectric inclusions: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980 by Y. Smirnov and Y. Shestopalov. Therefore, we omit the problem statements and all necessary basic definitions given in the previous paper.

Place, publisher, year, edition, pages
Taylor & Francis, 2014. Vol. 93, no 9, 1824-1845 p.
Keyword [en]
eigenwave, waveguide, pencil, spectrum, completeness, basis
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-41585DOI: 10.1080/00036811.2013.850494ISI: 000339059500003OAI: oai:DiVA.org:kau-41585DiVA: diva2:923080
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2016-06-08Bibliographically approved

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