TY - JOUR
T1 - Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
AU - LIU, HONGYU
AU - ZOU, JUN
PY - 2007/12
Y1 - 2007/12
N2 - 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. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
AB - 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. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
KW - discs and balls
KW - inverse obstacle scattering
KW - uniqueness
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-36549048998&origin=recordpage
U2 - 10.1093/imamat/hxm013
DO - 10.1093/imamat/hxm013
M3 - RGC 21 - Publication in refereed journal
SN - 0272-4960
VL - 72
SP - 817
EP - 831
JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
IS - 6
ER -