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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 9
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Articles

Eigenwaves in waveguides with dielectric inclusions: completeness

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Pages 1824-1845 | Received 20 Aug 2013, Accepted 26 Sep 2013, Published online: 27 Nov 2013

References

  • Smirnov YuG, Shestopalov YuV. Eigenwaves in waveguides with dielectric inclusions. Part I: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980.
  • Radzievskii GV. Multiple completeness of root vectors of a Keldyš pencil perturbed by an operator-valued function analytic in a disc. Math. USSR-Sbornik. 1973;20:323–347.
  • Kolmogorov AN, Fomin SV. Elements of the theory of functions and functional analysis. New York: Dover; 1999.
  • Markus AS, Matsaev VI. Spectral theory of holomorphic operator-functions in Hilbert space. Funct. Anal. Appl. 1975;9:73–84.
  • Keldysh MV. On the completeness of the eigenfunctions of some classes of non-selfadjoint linear operators. Russ. Math. Surv. 1971;26:15–44.
  • Ilinski AS, Smirnov YuG. Variational method in the eigenvalue problem for partially filled waveguide with nonregular boundary. In: Computational methods on the inverse problems in mathematical physics. Moscow: Moscow State University; 1988. p. 127–137.
  • Smirnov YuG. On the completeness of the system of eigenwaves and joined waves of partially filled waveguide with nonregular boundary. Dokl. AN SSSR. 1987;297:829–832.
  • Weinstien LA. Electromagnetic waves. Moscow: Radio i Svyaz’; 1988.
  • Smirnov YuG. Mathematical methods for electrodynamic problems. Penza: Penza State University; 2009.
  • Smirnov YuG. Application of the operator pencil method in the eigenvalue problem for partially filled waveguide. Dokl. AN SSSR. 1990;312:597–599.
  • Smirnov YuG. The method of operator pencils in the boundary transmission problems for elliptic system of equations. Diff. Equ. 1991;27:112–118.
  • Sanchez-Palencia E. Non-homogeneous media and vibration theory. Berlin: Springer; 1980.
  • Bykhovsky EB, Smirnov NV. On orthogonal decomposition of vector space of square integrable functions on a certain domain and operators of vector analysis. Trudy MIAN SSSR. 1960;59:5–36.
  • Sadovnichii VA. Theory of operators. Moscow: Moscow University Press; 1989.
  • Gokhberg I, Krein M. Introduction in the theory of linear nonselfadjoint operators in Hilbert space. Providence (RI): American Mathematical Society; 1969.

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