Eigenwaves in waveguides with dielectric inclusions: completeness

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.

Keywords:

• eigenwave
• waveguide
• pencil
• spectrum
• completeness
• basis

AMS Subject Classifications:

• 45E99
• 31B20
• 83C50
• 74S10

Acknowledgements

This work is supported by the Visby Program of the Swedish Institute, Russian Foundation for Basic Research, projects 11-07-00330-a and 12-07-97010-p-a, and the Ministry of Education and Science of the Russian Federation, grant 14.B37.21.1950.