On the resonances of the Laplacian on waveguides
Copyright policy )On the resonances of the Laplacian on waveguides
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.
- Florida International University United States
76Q05, 35P25; 81U99; 76Q05; 58J50, Asymptotic distributions of eigenvalues in context of PDEs, General theory of partial differential operators, Applied Mathematics, FOS: Physical sciences, 81U99, 58J50, Mathematical Physics (math-ph), Antennas, waveguides in optics and electromagnetic theory, Mathematics - Analysis of PDEs, Resonances, FOS: Mathematics, Waveguide, Laplacian, Analysis, Mathematical Physics, 35P25, Analysis of PDEs (math.AP)
76Q05, 35P25; 81U99; 76Q05; 58J50, Asymptotic distributions of eigenvalues in context of PDEs, General theory of partial differential operators, Applied Mathematics, FOS: Physical sciences, 81U99, 58J50, Mathematical Physics (math-ph), Antennas, waveguides in optics and electromagnetic theory, Mathematics - Analysis of PDEs, Resonances, FOS: Mathematics, Waveguide, Laplacian, Analysis, Mathematical Physics, 35P25, Analysis of PDEs (math.AP)
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