TY - JOUR

T1 - Essential spectrum of a periodic waveguide with non-periodic perturbation

AU - Nazarov, S. A.

AU - Taskinen, Jari

PY - 2018/7/15

Y1 - 2018/7/15

N2 - 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.

AB - 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.

KW - Dirichlet–Laplace problem

KW - Essential spectrum

KW - Non-periodic perturbation

KW - Periodic

KW - Sobolev space

KW - Waveguide

UR - http://www.scopus.com/inward/record.url?scp=85044500118&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.03.057

DO - 10.1016/j.jmaa.2018.03.057

M3 - Article

VL - 463

SP - 922

EP - 933

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -