Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
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DOI：
10.1093/imamat/hxm013
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发表时间：
2007-12
影响因子：
1.2
通讯作者：
Hongyu Liu;J. Zou
中科院分区：
文献类型：
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作者：
Hongyu Liu;J. Zou
首先提出了贝塞尔函数和球面贝塞尔函数的零点的一些新的交织性质，然后应用于证明逆声障碍物散射的一个有趣的唯一性结果。结果表明，在共振区，R3中的声软/声硬球或R2中的声软/声硬盘的形状，唯一地取决于在某一固定点上测量的单个远场数据，该远场数据对应于单个入射平面波。
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 R 3 or a sound-soft/sound-hard disc in R 2 is uniquely determined by a single far-field datum measured at some fixed spot corresponding to a single incident plane wave.