Utskrift från Malmö högskola - mah.se

# Resonance spectrum for one-dimensional truncated periodic media

 Tweet

## Simple item record

 Publication Conference Poster Title Resonance spectrum for one-dimensional truncated periodic media Author(s) 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) resonancesperiodicSciencesResearch 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)