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SPLITTING OF THE POLES OF A HELMHOLTZ RESONATOR

It is shown that in a neighborhood of a two-fold eigenvalue of the Neumann problem there are two poles of the Green's function of the Helmholtz resonator. Asymptotic expressions for them with respect to a small parameter ε (the linear size of the hole) are constructed, and the principal terms of the asymptotics are written out for the corresponding scattering and radiation problems.