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IMA Journal of Applied Mathematics Advance Access originally published online on October 18, 2007
IMA Journal of Applied Mathematics 2007 72(6):817-831; doi:10.1093/imamat/hxm013
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Hongyu Liu{dagger} and Jun Zou{ddagger}

Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, People's Republic of China

{dagger} Email: hyliu{at}math.cuhk.hk

{ddagger} Email: zou{at}math.cuhk.edu.hk

Received on July 4, 2006; Revision received February 12, 2007. Accepted on April 11, 2007

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.

Keywords: inverse obstacle scattering; uniqueness; discs and balls.


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