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  • 1.
    Shestopalov, Yuri
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Smirnov, Yury
    Penza State Univ, Dept Math & Supercomp, Penza 440017, Russia..
    Eigenwaves in waveguides with dielectric inclusions: completeness2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, 1824-1845 p.Article in journal (Refereed)
    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.

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