ON ACOUSTIC HELMHOLTZ RESONATOR AND ON ITS ELECTROMAGNETIC ANALOG

A study of the acoustic Helmholtz resonator and of its electromagnetic analog (a cylinder with a narrow slit) is performed. For the associated Green functions, power series asymptotics with respect to a small parameter epsilon (''radius'' of the resonator hole or the width of the slit), and In epsilon of poles tau(epsilon) with small imaginary parts are obtained by using the method of matching asymptotic expansions. The principal terms of solution asymptotics for corresponding boundary value problems are given.