Eigenwaves in waveguides with dielectric inclusions: completeness |
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Authors: | Yury Shestopalov Yury Smirnov |
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Institution: | 1. Karlstad University, Karlstad, SE 65188, Sweden.youri.shestopalov@kau.se;3. Department of Mathematics and Supercomputing, Penza State University, ul. Krasnaya 40, Penza 440017, Russia. |
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Abstract: | 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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Keywords: | eigenwave waveguide pencil spectrum completeness basis |
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