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Uniqueness on the Class of Odd-Dimensional Starlike Obstacles with Cross Section Data
We determine the uniqueness on starlike obstacles by using the cross section
data. We see cross section data as spectral measure in polar coordinate at far
field. Cross section scattering data suffice to give the local behavior of the
wave trace. These local trace formulas contain the geometric information on the
obstacle. Local wave trace behavior is connected to the cross section
scattering data by Lax-Phillips' formula. Once the scattering data are
identical from two different obstacles, the short time behavior of the
localized wave trace is expected to give identical heat/wave invariants
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