Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering

摘要

Some novel interlacing properties of the zeros for the Bessel and spherical Bessel functions are first presented and then applied to prove an interesting uniqueness result in inverse acoustic obstacle scattering. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R3 or a sound-soft/sound-hard disc in R2 is uniquely determined by a single far-field datum measured at some fixed spot corresponding to a single incident plane wave.