Resonance spectrum for one-dimensional truncated periodic media

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Resonance spectrum for one-dimensional truncated periodic media

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Publication Conference Poster
Title Resonance spectrum for one-dimensional truncated periodic media
Author(s) Iantchenko, Alexei
Date 2006
English abstract
We consider the "weighted" operator $P_k=-\partial_x a(x)\partial_x$ on the line with a step-like coefficient which appears when propagation of waves thorough 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 $P_k.$ If the coefficient is periodic on a finite interval (locally periodic) with $k$ identical cells then the resonance spectrum of $P_k$ has band structure. In the present paper we study a transition to semi-infinite medium by taking the limit $k\to \infty.$ The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem ($k=\infty$) with $k-1$ or $k$ resonances in each band. We prove that as $k\to \infty$ the resonance spectrum converges to the real axis.
Language eng (iso)
Subject(s) resonances
periodic
Sciences
Research Subject Categories::MATHEMATICS
Note Spectral Theory and Mathematical Physics conference,A Conference in Honor of Barry Simon's 60th Birthday, Caltech, Pasadena, USA, March 27-31, 2006
Handle http://hdl.handle.net/2043/11621 (link to this page)
Link http://math.caltech.edu/mp2006conf.html (external link to related web page)

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