On the resonances of the Laplacian on waveguides

2001/09/21 by Julian Edward, Edward, Julian
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #35P25 #58J50 #76Q05 #81U99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35P25 #msc:58J50 #msc:76Q05 #msc:81U99

paper · pdf · doi:10.48550/arxiv.math-ph/0109022

arxiv created 2001/09/21 · openalex publication_date 2001/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The resonances for the Dirichlet and Neumann Laplacian are studied on compactly perturbed waveguides. An upper bound on the number of resonances near the physical plane is proven. In the absence of resonances, an upper bound is proven for the localised resolvent. This is then used to prove that the existence of a quasimode whose asymptotics is bounded away from the thresholds implies the existence of resonances converging to the real axis.

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