Essential spectrum of a periodic waveguide with non-periodic perturbation

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http://hdl.handle.net/10138/314498

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Nazarov , S A & Taskinen , J 2018 , ' Essential spectrum of a periodic waveguide with non-periodic perturbation ' , Journal of Mathematical Analysis and Applications , vol. 463 , no. 2 , pp. 922-933 . https://doi.org/10.1016/j.jmaa.2018.03.057

Title: Essential spectrum of a periodic waveguide with non-periodic perturbation
Author: Nazarov, Sergei A.; Taskinen, Jari
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2018-07-15
Language: eng
Number of pages: 12
Belongs to series: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
URI: http://hdl.handle.net/10138/314498
Abstract: 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.
Subject: Dirichlet–Laplace problem
Periodic
Non-periodic perturbation
Essential spectrum
Waveguide
Sobolev space
Dirichlet-Laplace problem
MEDIA
GAPS
111 Mathematics
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