Abstract
A Helmholtz resonator is a shell Ωshell separating a compact cavity Ωint from a noncompact outer domain Ωout. A small opening Ω δ in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on Ω = ℝ3\Ωshell.
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