Eigenoscillations of cylindrical cavity slotted resonators with rectangular cross section (Q5955520)

The problem of natural oscillations of cylindrical slotted resonator formed by cylindrical regions of rectangular cross sections is considered. This problem is reduced to the determinations of the characteristic numbers of the integral operator-function. The existence of discrete real spectrum of natural oscillations is proved. The characteristic numbers considered as functions of a small parameter are resolved into asymptotic series.