Journal of Mathematical Sciences

, Volume 210, Issue 5, pp 590–621 | Cite as

Perturbation of Threshold of Essential Spectrum for Waveguides with Windows. II: Asymptotics

  • D. I. Borisov

We consider a quantum waveguide described by a pair of three-dimensional plane-parallel layers with common boundary containing a window joining the layers. As the window expands, the threshold of the essential spectrum generates bound states, anti-bound states, or resonances. We propose an original efficient algorithm for constructing complete asymptotic expansions for the associated spectral parameters and nontrivial solutions. Using a nontrivial technique, we justify the constructed asymptotic expansions and analyze their structure. Bibliography: 36 titles. Illustrations: 1 figure.


Asymptotic Expansion Holomorphic Function Small Neighborhood Nontrivial Solution Resonance State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of MathematicsUSC RASUfaRussia
  2. 2.Bashkir State Pedagogical UniversityUfaRussia
  3. 3.University of Hradec KrálovéHradec KrálovéCzech Republic

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