TY - JOUR
AU - Gadyl'shin, R.
AB - UDC 517.9 R. R. Gadyl'shin The classical Helmholtz acoustic resonator is an ideally hard sphere with a small hole [1, 2]. Rayleigh [1] has shown (by nonrigorous methods) that for some frequencies the field scattered by the resonator differs essentially from the field scattered by a sphere without holes. These resonance phenomena are due to the poles of the analytic continuation of the corresponding Green function [3-5] whose imaginary parts vanish as the hole disappears [6, 7]. Recently, rigorous results concerning the existence of such poles have been obtained for the analog of the classical resonator comprising the interior f/in and the exterior f~ex of a spherical annulus connected by a narrow channel [8-15]. This paper deals with the Neumann problem, which was also considered in [9, 12]. Let ~in be the set of eigenfrequencies (square roots of eigenvalues) of the Neumann problem for the operator -zX in f/i~, let ~x be the set of poles of the analytic continuation of the Green function corresponding to the Neumann problem for the Helmholtz operator in f/e~, and let Nch = {=t=~rm/h}~=~, where h is the channel length. Let K be a domain in the complex plane. Beale [9] showed that 
TI - On the poles of an acoustic resonator
JF - Functional Analysis and Its Applications
DO - 10.1007/BF01078839
DA - 2005-01-16
UR - https://www.deepdyve.com/lp/springer-journals/on-the-poles-of-an-acoustic-resonator-WlkF9A24O3
SP - 229
EP - 239
VL - 27
IS - 4
DP - DeepDyve
ER -