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Resonance spectrum for one-dimensional layered media
Author: Iantchenko, Alexei
Source: Applicable Analysis, Volume 85, Number 11, November 2006 , pp. 1383-1410(28)
Publisher: Taylor and Francis Ltd
Abstract:
<p>We consider the "weighted" operator <i>P<sub>k</sub>=â-‰â^'â-‰â^,<sub>x</sub> a(x)â^, <sub>x</sub></i> 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 <i>P<sub>k</sub>.</i> If the coefficient is periodic on a finite interval (locally periodic) with <i>k</i> identical cells, then the resonance spectrum of <i>P<sub>k</sub></i> has band structure. In the article, we study a transition to semi-infinite medium by taking the limit <i>kâ†'â-‰â^žâ-‰.</i> The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem (<i>k=â^ž</i>) with <i>k</i>â-‰â^'â-‰1 or <i>k</i> resonances in each band. We prove that as <i>kâ†'â-‰â^žâ-‰</i>, the resonance spectrum converges to the real axis.</p>Keywords: One-dimensional; Layered; Truncated periodic; Scattering resonances
Document Type: Research article
DOI: http://dx.doi.org/10.1080/00036810600967830
Affiliations: 1: Malmö University, School of Technology and Society, SE-205 06 Malmö, Sweden
Publication date: 2006-11-01
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