Browsing by Subject "Essential spectrum"

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  • Bakharev, F. L.; Taskinen, J. (2017)
    We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order h > 0. The essential spectrum of the problem is known to have band-gap structure. We derive asymptotic formulas for the position of the spectral bands and gaps, as h -> 0.
  • Nazarov, Sergei A.; Taskinen, Jari (2018)
    Abstract We consider the spectral Dirichlet–Laplacian problem on a domain which is formed from a periodic waveguide Π perturbed by non-compact, non-periodic changes of geometry. We show that the domain perturbation causes an addition to the essential spectrum, which consists of isolated points belonging to the discrete spectrum of a model problem. This model problem is posed on a domain, which is just a compact perturbation of Π. We discuss the position of the new spectral components in relation to the essential spectrum of the problem in Π.
  • Schroderus, Riikka (2017)
    We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spares of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces of the upper half-plane. (C) 2016 Elsevier Inc. All rights reserved.