Resonance spectrum for one-dimensional layered media

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Resonance spectrum for one-dimensional layered media

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Publication Article, peer reviewed scientific
Title Resonance spectrum for one-dimensional layered media
Author(s) Iantchenko, Alexei
Date 2006
English abstract
We consider the “weighted” operator Pk= - ∂x a(x)∂ x on the real line with a step-like coefficient which appears when propagation of waves through a finite slab of a periodic medium is studied. The medium is transparent at certain resonant frequencies which are related to the complex resonance spectrum of Pk. If the coefficient is periodic on a finite interval (locally periodic) with k identical cells, then the resonance spectrum of Pk has band structure. In the article, we study a transition to semi-infinite medium by taking the limit ∞ . The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem (k=∞) with k - 1 or k resonances in each band. We prove that as ∞ , the resonance spectrum converges to the real axis.
DOI (link to publisher's fulltext)
Host/Issue Applicable Analysis;11
Volume 85
ISSN 0003-6811
Pages 1383-1410
Language eng (iso)
Subject(s) Layered
Truncated periodic
Scattering resonances
Research Subject Categories::MATHEMATICS
Research Subject Categories::NATURAL SCIENCES
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